MOTIVATION: Spatial transcriptomics enables in-depth molecular characterization of samples on a morphology and RNA level while preserving spatial location. Integrating the resulting multi-modal data is an unsolved problem, and developing new solutions in precision medicine depends on improved methodologies. RESULTS: We introduce AESTETIK, a convolutional deep learning model that jointly integrates spatial, transcriptomics, and morphology information to learn accurate spot representations. AESTETIK yielded substantially improved cluster assignments on widely adopted technology platforms (e.g. 10x Genomics™, NanoString™) across multiple datasets. We achieved performance enhancement on structured tissues (e.g. brain) with a 21% increase in median ARI over previous state-of-the-art methods. Notably, AESTETIK also demonstrated superior performance on cancer tissues with heterogeneous cell populations, showing a 2-fold increase in breast cancer, 79% in melanoma, and 21% in liver cancer. We expect that these advances will enable a multi-modal understanding of key biological processes. AVAILABILITY AND IMPLEMENTATION: AESTETIK is implemented in Python 3 and is available as open source software at http://www.github.com/ratschlab/aestetik. The Snakemake pipeline for reproducing the results is available at http://www.github.com/ratschlab/st-rep.

MOTIVATION: RNA sequencing enables the characterization of a cell's transcript isoforms in healthy and disease conditions. In the context of cancer, local transcript variability may translate to splicing-derived tumor-associated peptides recognized by the immune system. A software tool that extracts such candidate peptides, is of great interest for personalized cancer therapy. RESULTS: We present the open-source software tool ImmunoPepper, which extracts a set of biologically plausible peptides from a splicing graph, derived from a set of RNA-seq datasets. This peptide set can be personalized with germline and somatic variation and takes novel RNA splice variants into account. ImmunoPepper supports several filtering options, including subtraction of normal tissue background, prediction of MHC-binding affinity, as well as MassSpec-based validation of identified peptides. We analyzed 32 ovarian cancer (TCGA-OV) and 31 breast invasive carcinoma (TCGA-BRCA) samples, with a strict cancer-specific filtering configuration, and obtained on average 834 and 569 cancer-specific predicted MHC-I binding 9-mers per sample, for each cohort, respectively. MassSpec validation with the target-decoy competition Subset-Neighbor-Search (SNS) showed an average validation rate of 4.5% per TCGA-OV sample and 5.3% per TCGA-BRCA sample. This corresponded to 25 MHC-I binders 9-mers per TCGA-OV sample, and 20 MHC-I binders 9-mers per TCGA-BRCA sample in average. Finally, we draw conclusions about the best framework for generation of splicing-derived neoepitopes and recommend to use joint data structures when processing homogeneously a cancer and a normal cohort and to focus on reproducibility of the candidates across generation pipelines. AVAILABILITY AND IMPLEMENTATION: ImmunoPepper is implemented in Python 3 and is available as open-source software at https://github.com/ratschlab/immunopepper. The online documentation can be found at https://immunopepper.readthedocs.io/en/latest/.

Applying reinforcement learning (RL) to real-world problems is often made challenging by the inability to interact with the environment and the difficulty of designing reward functions. Offline RL addresses the first challenge by considering access to an offline dataset of environment interactions labeled by the reward function. In contrast, Preference-based RL does not assume access to the reward function and learns it from preferences, but typically requires an online interaction with the environment. We bridge the gap between these frameworks by exploring efficient methods for acquiring preference feedback in a fully offline setup. We propose Sim-OPRL, an offline preference-based reinforcement learning algorithm, which leverages a learned environment model to elicit preference feedback on simulated rollouts. Drawing on insights from both the offline RL and the preference-based RL literature, our algorithm employs a pessimistic approach for out-of-distribution data, and an optimistic approach for acquiring informative preferences about the optimal policy. We provide theoretical guarantees regarding the sample complexity of our approach, dependent on how well the offline data covers the optimal policy. Finally, we demonstrate the empirical performance of Sim-OPRL in various environments.

Single-source domain generalization (SDG) aims to learn a model from a single source domain that can generalize well on unseen target domains. This is an important task in computer vision, particularly relevant to medical imaging where domain shifts are common. In this work, we consider a challenging yet practical setting: SDG for cross-modality medical image segmentation. We combine causality-inspired theoretical insights on learning domain-invariant representations with recent advancements in diffusion-based augmentation to improve generalization across diverse imaging modalities. Guided by the “intervention-augmentation equivariant” principle, we use controlled diffusion models (DMs) to simulate diverse imaging styles while preserving the content, leveraging rich generative priors in large-scale pretrained DMs to comprehensively perturb the multidimensional style variable. Extensive experiments on challenging cross-modality segmentation tasks demonstrate that our approach consistently outperforms state-of-the-art SDG methods across three distinct anatomies and imaging modalities. The source code is available at https://github.com/ratschlab/ICMSeg.

Normalization layers are one of the key building blocks for deep neural networks. Several theoretical studies have shown that batch normalization improves the signal propagation, by avoiding the representations from becoming collinear across the layers. However, results on mean-field theory of batch normalization also conclude that this benefit comes at the expense of exploding gradients in depth. Motivated by these two aspects of batch normalization, in this study we pose the following question: *Can a batch-normalized network keep the optimal signal propagation properties, but avoid exploding gradients?* We answer this question in the affirmative by giving a particular construction of an *MLP with linear activations* and batch-normalization that provably has *bounded gradients* at any depth. Based on Weingarten calculus, we develop a rigorous and non-asymptotic theory for this constructed MLP that gives a precise characterization of forward signal propagation, while proving that gradients remain bounded for linearly independent input samples, which holds in most practical settings. Inspired by our theory, we also design an activation shaping scheme that empirically achieves the same properties for non-linear activations.

A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding: unobserved variables may influence both the actions taken by the agent and the observed outcomes. Hidden confounding can compromise the validity of any causal conclusion drawn from data and presents a major obstacle to effective offline RL. In the present paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to hidden confounding bias, termed delphic uncertainty, which uses variation over world models compatible with the observations, and differentiate it from the well-known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as on electronic health records. Our results suggest that nonidentifiable hidden confounding bias can be mitigated to improve offline RL solutions in practice.

Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection of relevant features and interactions. Approaching NAMs from a Bayesian perspective, we augment them in three primary ways, namely by a) providing credible intervals for the individual additive sub-networks; b) estimating the marginal likelihood to perform an implicit selection of features via an empirical Bayes procedure; and c) facilitating the ranking of feature pairs as candidates for second-order interaction in fine-tuned models. In particular, we develop Laplace-approximated NAMs (LA-NAMs), which show improved empirical performance on tabular datasets and challenging real-world medical tasks.

MOTIVATION: Acute kidney injury (AKI) is a syndrome that affects a large fraction of all critically ill patients, and early diagnosis to receive adequate treatment is as imperative as it is challenging to make early. Consequently, machine learning approaches have been developed to predict AKI ahead of time. However, the prevalence of AKI is often underestimated in state-of-the-art approaches, as they rely on an AKI event annotation solely based on creatinine, ignoring urine output. We construct and evaluate early warning systems for AKI in a multi-disciplinary ICU setting, using the complete KDIGO definition of AKI. We propose several variants of gradient-boosted decision tree (GBDT)-based models, including a novel time-stacking based approach. A state-of-the-art LSTM-based model previously proposed for AKI prediction is used as a comparison, which was not specifically evaluated in ICU settings yet. RESULTS: We find that optimal performance is achieved by using GBDT with the time-based stacking technique (AUPRC = 65.7%, compared with the LSTM-based model's AUPRC = 62.6%), which is motivated by the high relevance of time since ICU admission for this task. Both models show mildly reduced performance in the limited training data setting, perform fairly across different subcohorts, and exhibit no issues in gender transfer. Following the official KDIGO definition substantially increases the number of annotated AKI events. In our study GBDTs outperform LSTM models for AKI prediction. Generally, we find that both model types are robust in a variety of challenging settings arising for ICU data. AVAILABILITY AND IMPLEMENTATION: The code to reproduce the findings of our manuscript can be found at: https://github.com/ratschlab/AKI-EWS.

MOTIVATION: The Oxford Nanopore Technologies (ONT) ReadUntil API enables selective sequencing, which aims to selectively favor interesting over uninteresting reads, e.g. to deplete or enrich certain genomic regions. The performance gain depends on the selective sequencing decision-making algorithm (SSDA) which decides whether to reject a read, stop receiving a read, or wait for more data. Since real runs are time-consuming and costly, simulating the ONT sequencer with support for the ReadUntil API is highly beneficial for comparing and optimizing new SSDAs. Existing software like MinKNOW and UNCALLED only return raw signal data, are memory-intensive, require huge and often unavailable multi-fast5 files (≥100GB) and are not clearly documented. RESULTS: We present the ONT device simulator SimReadUntil that takes a set of full reads as input, distributes them to channels and plays them back in real time including mux scans, channel gaps and blockages, and allows to reject reads as well as stop receiving data from them. Our modified ReadUntil API provides the basecalled reads rather than the raw signal, reducing computational load and focusing on the SSDA rather than on basecalling. Tuning the parameters of tools like ReadFish and ReadBouncer becomes easier because a GPU for basecalling is no longer required. We offer various methods to extract simulation parameters from a sequencing summary file and adapt ReadFish to replicate one of their enrichment experiments. SimReadUntil's gRPC interface allows standardized interaction with a wide range of programming languages. AVAILABILITY AND IMPLEMENTATION: Code and fully worked examples are available on GitHub (https://github.com/ratschlab/sim_read_until).

MOTIVATION: Exponential growth in sequencing databases has motivated scalable De Bruijn graph-based (DBG) indexing for searching these data, using annotations to label nodes with sample IDs. Low-depth sequencing samples correspond to fragmented subgraphs, complicating finding the long contiguous walks required for alignment queries. Aligners that target single-labelled subgraphs reduce alignment lengths due to fragmentation, leading to low recall for long reads. While some (e.g. label-free) aligners partially overcome fragmentation by combining information from multiple samples, biologically irrelevant combinations in such approaches can inflate the search space or reduce accuracy. RESULTS: We introduce a new scoring model, 'multi-label alignment' (MLA), for annotated DBGs. MLA leverages two new operations: To promote biologically relevant sample combinations, 'Label Change' incorporates more informative global sample similarity into local scores. To improve connectivity, 'Node Length Change' dynamically adjusts the DBG node length during traversal. Our fast, approximate, yet accurate MLA implementation has two key steps: a single-label seed-chain-extend aligner (SCA) and a multi-label chainer (MLC). SCA uses a traditional scoring model adapting recent chaining improvements to assembly graphs and provides a curated pool of alignments. MLC extracts seed anchors from SCAs alignments, produces multi-label chains using MLA scoring, then finally forms multi-label alignments. We show via substantial improvements in taxonomic classification accuracy that MLA produces biologically relevant alignments, decreasing average weighted UniFrac errors by 63.1%-66.8% and covering 45.5%-47.4% (median) more long-read query characters than state-of-the-art aligners. MLAs runtimes are competitive with label-combining alignment and substantially faster than single-label alignment. AVAILABILITY AND IMPLEMENTATION: The data, scripts, and instructions for generating our results are available at https://github.com/ratschlab/mla.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

Models that can predict the occurrence of events ahead of time with low false-alarm rates are critical to the acceptance of decision support systems in the medical community. This challenging task is typically treated as a simple binary classification, ignoring temporal dependencies between samples, whereas we propose to exploit this structure. We first introduce a common theoretical framework unifying dynamic survival analysis and early event prediction. Following an analysis of objectives from both fields, we propose Temporal Label Smoothing (TLS), a simpler, yet best-performing method that preserves prediction monotonicity over time. By focusing the objective on areas with a stronger predictive signal, TLS improves performance over all baselines on two large-scale benchmark tasks. Gains are particularly notable along clinically relevant measures, such as event recall at low false-alarm rates. TLS reduces the number of missed events by up to a factor of two over previously used approaches in early event prediction.

The number of published metagenome assemblies is rapidly growing due to advances in sequencing technologies. However, sequencing errors, variable coverage, repetitive genomic regions, and other factors can produce misassemblies, which are challenging to detect for taxonomically novel genomic data. Assembly errors can affect all downstream analyses of the assemblies. Accuracy for the state of the art in reference-free misassembly prediction does not exceed an AUPRC of 0.57, and it is not clear how well these models generalize to real-world data. Here, we present the Residual neural network for Misassembled Contig identification (ResMiCo), a deep learning approach for reference-free identification of misassembled contigs. To develop ResMiCo, we first generated a training dataset of unprecedented size and complexity that can be used for further benchmarking and developments in the field. Through rigorous validation, we show that ResMiCo is substantially more accurate than the state of the art, and the model is robust to novel taxonomic diversity and varying assembly methods. ResMiCo estimated 7% misassembled contigs per metagenome across multiple real-world datasets. We demonstrate how ResMiCo can be used to optimize metagenome assembly hyperparameters to improve accuracy, instead of optimizing solely for contiguity. The accuracy, robustness, and ease-of-use of ResMiCo make the tool suitable for general quality control of metagenome assemblies and assembly methodology optimization.

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or require carefully increasing the batch size over the course of the algorithm’s execution, which leads to computing full gradients. In contrast, the proposed method, equipped with a stochastic average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques. In applications we put special emphasis on problems with a large number of separable constraints. Such problems are prevalent among semidefinite programming (SDP) formulations arising in machine learning and theoretical computer science. We provide numerical experiments on matrix completion, unsupervised clustering, and sparsest-cut SDPs.

Data augmentation is commonly applied to improve performance of deep learning by enforcing the knowledge that certain transformations on the input preserve the output. Currently, the data augmentation parameters are chosen by human effort and costly cross-validation, which makes it cumbersome to apply to new datasets. We develop a convenient gradient-based method for selecting the data augmentation without validation data during training of a deep neural network. Our approach relies on phrasing data augmentation as an invariance in the prior distribution on the functions of a neural network, which allows us to learn it using Bayesian model selection. This has been shown to work in Gaussian processes, but not yet for deep neural networks. We propose a differentiable Kronecker-factored Laplace approximation to the marginal likelihood as our objective, which can be optimised without human supervision or validation data. We show that our method can successfully recover invariances present in the data, and that this improves generalisation and data efficiency on image datasets.

MOTIVATION: Several recently developed single-cell DNA sequencing technologies enable whole-genome sequencing of thousands of cells. However, the ultra-low coverage of the sequenced data (<0.05× per cell) mostly limits their usage to the identification of copy number alterations in multi-megabase segments. Many tumors are not copy number-driven, and thus single-nucleotide variant (SNV)-based subclone detection may contribute to a more comprehensive view on intra-tumor heterogeneity. Due to the low coverage of the data, the identification of SNVs is only possible when superimposing the sequenced genomes of hundreds of genetically similar cells. Thus, we have developed a new approach to efficiently cluster tumor cells based on a Bayesian filtering approach of relevant loci and exploiting read overlap and phasing. RESULTS: We developed Single Cell Data Tumor Clusterer (SECEDO, lat. 'to separate'), a new method to cluster tumor cells based solely on SNVs, inferred on ultra-low coverage single-cell DNA sequencing data. We applied SECEDO to a synthetic dataset simulating 7250 cells and eight tumor subclones from a single patient and were able to accurately reconstruct the clonal composition, detecting 92.11% of the somatic SNVs, with the smallest clusters representing only 6.9% of the total population. When applied to five real single-cell sequencing datasets from a breast cancer patient, each consisting of ≈2000 cells, SECEDO was able to recover the major clonal composition in each dataset at the original coverage of 0.03×, achieving an Adjusted Rand Index (ARI) score of ≈0.6. The current state-of-the-art SNV-based clustering method achieved an ARI score of ≈0, even after merging cells to create higher coverage data (factor 10 increase), and was only able to match SECEDOs performance when pooling data from all five datasets, in addition to artificially increasing the sequencing coverage by a factor of 7. Variant calling on the resulting clusters recovered more than twice as many SNVs as would have been detected if calling on all cells together. Further, the allelic ratio of the called SNVs on each subcluster was more than double relative to the allelic ratio of the SNVs called without clustering, thus demonstrating that calling variants on subclones, in addition to both increasing sensitivity of SNV detection and attaching SNVs to subclones, significantly increases the confidence of the called variants. AVAILABILITY AND IMPLEMENTATION: SECEDO is implemented in C++ and is publicly available at https://github.com/ratschlab/secedo. Instructions to download the data and the evaluation code to reproduce the findings in this paper are available at: https://github.com/ratschlab/secedo-evaluation. The code and data of the submitted version are archived at: https://doi.org/10.5281/zenodo.6516955. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is still inhibited by the intrinsic complexity of exact GP inference. We improve the scalability of these methods through principled sparse inference approaches. We propose a new scalable GP-VAE model that outperforms existing approaches in terms of runtime and memory footprint, is easy to implement, and allows for joint end-to-end optimization of all components.

Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present a scalable marginal-likelihood estimation method to select both hyperparameters and network architectures, based on the training data alone. Some hyperparameters can be estimated online during training, simplifying the procedure. Our marginal-likelihood estimate is based on Laplace’s method and Gauss-Newton approximations to the Hessian, and it outperforms cross-validation and manual tuning on standard regression and image classification datasets, especially in terms of calibration and out-of-distribution detection. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable (e.g., in nonstationary settings).

Intensive care units (ICU) are increasingly looking towards machine learning for methods to provide online monitoring of critically ill patients. In machine learning, online monitoring is often formulated as a supervised learning problem. Recently, contrastive learning approaches have demonstrated promising improvements over competitive supervised benchmarks. These methods rely on well-understood data augmentation techniques developed for image data which do not apply to online monitoring. In this work, we overcome this limitation by supplementing time-series data augmentation techniques with a novel contrastive learning objective which we call neighborhood contrastive learning (NCL). Our objective explicitly groups together contiguous time segments from each patient while maintaining state-specific information. Our experiments demonstrate a marked improvement over existing work applying contrastive methods to medical time-series.

Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature impacts time and memory consumption, address the problem with the notion of local curvature, and provide a novel approximate backtracking algorithm for estimating local curvature. We give new theoretical convergence rates for our algorithms and provide experimental validation on synthetic and real-world datasets.

MOTIVATION: Since the amount of published biological sequencing data is growing exponentially, efficient methods for storing and indexing this data are more needed than ever to truly benefit from this invaluable resource for biomedical research. Labeled de Bruijn graphs are a frequently-used approach for representing large sets of sequencing data. While significant progress has been made to succinctly represent the graph itself, efficient methods for storing labels on such graphs are still rapidly evolving. RESULTS: In this article, we present RowDiff, a new technique for compacting graph labels by leveraging expected similarities in annotations of vertices adjacent in the graph. RowDiff can be constructed in linear time relative to the number of vertices and labels in the graph, and in space proportional to the graph size. In addition, construction can be efficiently parallelized and distributed, making the technique applicable to graphs with trillions of nodes. RowDiff can be viewed as an intermediary sparsification step of the original annotation matrix and can thus naturally be combined with existing generic schemes for compressed binary matrices. Experiments on 10 000 RNA-seq datasets show that RowDiff combined with multi-BRWT results in a 30% reduction in annotation footprint over Mantis-MST, the previously known most compact annotation representation. Experiments on the sparser Fungi subset of the RefSeq collection show that applying RowDiff sparsification reduces the size of individual annotation columns stored as compressed bit vectors by an average factor of 42. When combining RowDiff with a multi-BRWT representation, the resulting annotation is 26 times smaller than Mantis-MST. AVAILABILITY AND IMPLEMENTATION: RowDiff is implemented in C++ within the MetaGraph framework. The source code and the data used in the experiments are publicly available at https://github.com/ratschlab/row_diff.

Tumors contain multiple subpopulations of genetically distinct cancer cells. Reconstructing their evolutionary history can improve our understanding of how cancers develop and respond to treatment. Subclonal reconstruction methods cluster mutations into groups that co-occur within the same subpopulations, estimate the frequency of cells belonging to each subpopulation, and infer the ancestral relationships among the subpopulations by constructing a clone tree. However, often multiple clone trees are consistent with the data and current methods do not efficiently capture this uncertainty; nor can these methods scale to clone trees with a large number of subclonal populations. Here, we formalize the notion of a partially-defined clone tree (partial clone tree for short) that defines a subset of the pairwise ancestral relationships in a clone tree, thereby implicitly representing the set of all clone trees that have these defined pairwise relationships. Also, we introduce a special partial clone tree, the Maximally-Constrained Ancestral Reconstruction (MAR), which summarizes all clone trees fitting the input data equally well. Finally, we extend commonly used clone tree validity conditions to apply to partial clone trees and describe SubMARine, a polynomial-time algorithm producing the subMAR, which approximates the MAR and guarantees that its defined relationships are a subset of those present in the MAR. We also extend SubMARine to work with subclonal copy number aberrations and define equivalence constraints for this purpose. Further, we extend SubMARine to permit noise in the estimates of the subclonal frequencies while retaining its validity conditions and guarantees. In contrast to other clone tree reconstruction methods, SubMARine runs in time and space that scale polynomially in the number of subclones. We show through extensive noise-free simulation, a large lung cancer dataset and a prostate cancer dataset that the subMAR equals the MAR in all cases where only a single clone tree exists and that it is a perfect match to the MAR in most of the other cases. Notably, SubMARine runs in less than 70 seconds on a single thread with less than one Gb of memory on all datasets presented in this paper, including ones with 50 nodes in a clone tree. On the real-world data, SubMARine almost perfectly recovers the previously reported trees and identifies minor errors made in the expert-driven reconstructions of those trees. The freely-available open-source code implementing SubMARine can be downloaded at https://github.com/morrislab/submarine.

The goal of the unsupervised learning of disentangled representations is to separate the independent explanatory factors of variation in the data without access to supervision. In this paper, we summarize the results of (Locatello et al. 2019b) and focus on their implications for practitioners. We discuss the theoretical result showing that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases and the practical challenges it entails. Finally, we comment on our experimental findings, highlighting the limitations of state-of-the-art approaches and directions for future research.

Multivariate time series with missing values are common in areas such as healthcare and finance, and have grown in number and complexity over the years. This raises the question whether deep learning methodologies can outperform classical data imputation methods in this domain. However, naive applications of deep learning fall short in giving reliable confidence estimates and lack interpretability.We propose a new deep sequential latent variable model for dimensionality reduction and data imputation. Our modeling assumption is simple and interpretable: the high dimensional time series has a lower-dimensional representation which evolves smoothly in time according to a Gaussian process. The non-linear dimensionality reduction in the presence of missing data is achieved using a VAE approach with a novel structured variational approximation. We demonstrate that our approach outperforms both classical and recent deep learning-based data imputation methods on high dimensional data from the domains of computer vision and healthcare.

Intelligent agents should be able to learn useful representations by observing changes in their environment. We model such observations as pairs of non-i.i.d. images sharing at least one of the underlying factors of variation. First, we theoretically show that only knowing how many factors have changed, but not which ones, is sufficient to learn disentangled representations. Second, we provide practical algorithms that learn disentangled representations from pairs of images without requiring annotation of groups, individual factors, or the number of factors that have changed. Third, we perform a large-scale empirical study and show that such pairs of observations are sufficient to reliably learn disentangled representations on several benchmark data sets. Finally, we evaluate our learned representations and find that they are simultaneously useful on a diverse suite of tasks, including generalization under covariate shifts, fairness, and abstract reasoning. Overall, our results demonstrate that weak supervision enables learning of useful disentangled representations in realistic scenarios.

The Jaccard similarity index is an important measure of the overlap of two sets, widely used in machine learning, computational genomics, information retrieval, and many other areas. We design and implement SimilarityAtScale, the first communication-efficient distributed algorithm for computing the Jaccard similarity among pairs of large datasets. Our algorithm provides an efficient encoding of this problem into a multiplication of sparse matrices. Both the encoding and sparse matrix product are performed in a way that minimizes data movement in terms of communication and synchronization costs. We apply our algorithm to obtain similarity among all pairs of a set of large samples of genomes. This task is a key part of modern metagenomics analysis and an evergrowing need due to the increasing availability of high-throughput DNA sequencing data. The resulting scheme is the first to enable accurate Jaccard distance derivations for massive datasets, using large-scale distributed-memory systems. We package our routines in a tool, called GenomeAtScale, that combines the proposed algorithm with tools for processing input sequences. Our evaluation on real data illustrates that one can use GenomeAtScale to effectively employ tens of thousands of processors to reach new frontiers in large-scale genomic and metagenomic analysis. While GenomeAtScale can be used to foster DNA research, the more general underlying SimilarityAtScale algorithm may be used for high-performance distributed similarity computations in other data analytics application domains.

We present an algorithm for the optimal alignment of sequences to genome graphs . It works by phrasing the edit distance minimization task as finding a shortest path on an implicit alignment graph. To find a shortest path, we instantiate the A \(^\star \) paradigm with a novel domain-specific heuristic function that accounts for the upcoming subsequence in the query to be aligned, resulting in a provably optimal alignment algorithm called AStarix . Experimental evaluation of AStarix shows that it is 1–2 orders of magnitude faster than state-of-the-art optimal algorithms on the task of aligning Illumina reads to reference genome graphs. Implementations and evaluations are available at https://github.com/eth-sri/astarix .

MOTIVATION: Understanding the underlying mutational processes of cancer patients has been a long-standing goal in the community and promises to provide new insights that could improve cancer diagnoses and treatments. Mutational signatures are summaries of the mutational processes, and improving the derivation of mutational signatures can yield new discoveries previously obscured by technical and biological confounders. Results from existing mutational signature extraction methods depend on the size of available patient cohort and solely focus on the analysis of mutation count data without considering the exploitation of metadata. RESULTS: Here we present a supervised method that utilizes cancer type as metadata to extract more distinctive signatures. More specifically, we use a negative binomial non-negative matrix factorization and add a support vector machine loss. We show that mutational signatures extracted by our proposed method have a lower reconstruction error and are designed to be more predictive of cancer type than those generated by unsupervised methods. This design reduces the need for elaborate post-processing strategies in order to recover most of the known signatures unlike the existing unsupervised signature extraction methods. Signatures extracted by a supervised model used in conjunction with cancer-type labels are also more robust, especially when using small and potentially cancer-type limited patient cohorts. Finally, we adapted our model such that molecular features can be utilized to derive an according mutational signature. We used APOBEC expression and MUTYH mutation status to demonstrate the possibilities that arise from this ability. We conclude that our method, which exploits available metadata, improves the quality of mutational signatures as well as helps derive more interpretable representations. AVAILABILITY AND IMPLEMENTATION: https://github.com/ratschlab/SNBNMF-mutsig-public. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Recent technological advances have led to an increase in the production and availability of single-cell data. The ability to integrate a set of multi-technology measurements would allow the identification of biologically or clinically meaningful observations through the unification of the perspectives afforded by each technology. In most cases, however, profiling technologies consume the used cells and thus pairwise correspondences between datasets are lost. Due to the sheer size single-cell datasets can acquire, scalable algorithms that are able to universally match single-cell measurements carried out in one cell to its corresponding sibling in another technology are needed. RESULTS: We propose Single-Cell data Integration via Matching (SCIM), a scalable approach to recover such correspondences in two or more technologies. SCIM assumes that cells share a common (low-dimensional) underlying structure and that the underlying cell distribution is approximately constant across technologies. It constructs a technology-invariant latent space using an autoencoder framework with an adversarial objective. Multi-modal datasets are integrated by pairing cells across technologies using a bipartite matching scheme that operates on the low-dimensional latent representations. We evaluate SCIM on a simulated cellular branching process and show that the cell-to-cell matches derived by SCIM reflect the same pseudotime on the simulated dataset. Moreover, we apply our method to two real-world scenarios, a melanoma tumor sample and a human bone marrow sample, where we pair cells from a scRNA dataset to their sibling cells in a CyTOF dataset achieving 90% and 78% cell-matching accuracy for each one of the samples, respectively. AVAILABILITY AND IMPLEMENTATION: https://github.com/ratschlab/scim. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train over $14000$ models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on eight data sets. We observe that while the different methods successfully enforce properties “encouraged” by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, different evaluation metrics do not always agree on what should be considered “disentangled” and exhibit systematic differences in the estimation. Finally, increased disentanglement does not seem to necessarily lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.

The key idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train more than $12000$ models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on seven different data sets. We observe that while the different methods successfully enforce properties “encouraged” by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, increased disentanglement does not seem to lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.

Motivation: Technological advancements in high-throughput DNA sequencing have led to an exponential growth of sequencing data being produced and stored as a byproduct of biomedical research. Despite its public availability, a majority of this data remains hard to query for the research community due to a lack of efficient data representation and indexing solutions. One of the available techniques to represent read data is a condensed form as an assembly graph. Such a representation contains all sequence information but does not store contextual information and metadata. Results: We present two new approaches for a compressed representation of a graph coloring: a lossless compression scheme based on a novel application of wavelet tries as well as a highly accurate lossy compression based on a set of Bloom filters. Both strategies retain a coloring even when adding to the underlying graph topology. We present construction and merge procedures for both methods and evaluate their performance on a wide range of different datasets. By dropping the requirement of a fully lossless compression and using the topological information of the underlying graph, we can reduce memory requirements by up to three orders of magnitude. Representing individual colors as independently stored modules, our approaches can be efficiently parallelized and provide strategies for dynamic use. These properties allow for an easy upscaling to the problem sizes common to the biomedical domain. Availability and implementation: We provide prototype implementations in C++, summaries of our experiments as well as links to all datasets publicly at https://github.com/ratschlab/graph_annotation. Supplementary information: Supplementary data are available at Bioinformatics online.

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. However, as is the case with many other variational inference algorithms, its theoretical properties have not been studied. In the present work, we study the convergence properties of this approach from a modern optimization viewpoint by establishing connections to the classic Frank-Wolfe algorithm. Our analyses yields novel theoretical insights regarding the sufficient conditions for convergence, explicit rates, and algorithmic simplifications. Since a lot of focus in previous works for variational inference has been on tractability, our work is especially important as a much needed attempt to bridge the gap between probabilistic models and their corresponding theoretical properties.

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear $O(1/t)$ rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate $O(1/t^2)$ for matching pursuit and steepest coordinate descent on convex objectives.

Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational approximation. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with an iteratively constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions.

A major challenge in the training of recurrent neural networks is the so-called vanishing or exploding gradient problem. The use of a norm-preserving transition operator can address this issue, but parametrization is challenging. In this work we focus on unitary operators and describe a parametrization using the Lie algebra u(n) associated with the Lie group U(n) of n × n unitary matrices. The exponential map provides a correspondence between these spaces, and allows us to define a unitary matrix using n2 real coefficients relative to a basis of the Lie algebra. The parametrization is closed under additive updates of these coefficients, and thus provides a simple space in which to do gradient descent. We demonstrate the effectiveness of this parametrization on the problem of learning arbitrary unitary operators, comparing to several baselines and outperforming a recently-proposed lower-dimensional parametrization. We additionally use our parametrization to generalize a recently-proposed unitary recurrent neural network to arbitrary unitary matrices, using it to solve standard long-memory tasks.

Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized as the conic hull of a generic atom set, leading to the first principled definitions of non-negative MP algorithms for which we give explicit convergence rates and demonstrate excellent empirical performance. In particular, we derive sublinear (O(1/t)) convergence on general smooth and convex objectives, and linear convergence (O(e^{-t})) on strongly convex objectives, in both cases for general sets of atoms. Furthermore, we establish a clear correspondence of our algorithms to known algorithms from the MP and FW literature. Our novel algorithms and analyses target general atom sets and general objective functions, and hence are directly applicable to a large variety of learning settings.

MOTIVATION: Deep sequencing based ribosome footprint profiling can provide novel insights into the regulatory mechanisms of protein translation. However, the observed ribosome profile is fundamentally confounded by transcriptional activity. In order to decipher principles of translation regulation, tools that can reliably detect changes in translation efficiency in case-control studies are needed. RESULTS: We present a statistical framework and an analysis tool, RiboDiff, to detect genes with changes in translation efficiency across experimental treatments. RiboDiff uses generalized linear models to estimate the over-dispersion of RNA-Seq and ribosome profiling measurements separately, and performs a statistical test for differential translation efficiency using both mRNA abundance and ribosome occupancy. AVAILABILITY AND IMPLEMENTATION: RiboDiff webpage http://bioweb.me/ribodiff Source code including scripts for preprocessing the FASTQ data are available at http://github.com/ratschlab/ribodiff CONTACTS: [email protected] or [email protected] information: Supplementary data are available at Bioinformatics online.

Neural language models are a powerful tool to embed words into semantic vector spaces. However, learning such models generally relies on the availability of abundant and diverse training examples. In highly specialised domains this requirement may not be met due to difficulties in obtaining a large corpus, or the limited range of expression in average use. Such domains may encode prior knowledge about entities in a knowledge base or ontology. We propose a generative model which integrates evidence from diverse data sources, enabling the sharing of semantic information. We achieve this by generalising the concept of co-occurrence from distributional semantics to include other relationships between entities or words, which we model as affine transformations on the embedding space. We demonstrate the effectiveness of this approach by outperforming recent models on a link prediction task and demonstrating its ability to profit from partially or fully unobserved data training labels. We further demonstrate the usefulness of learning from different data sources with overlapping vocabularies.

MOTIVATION: Mapping high-throughput sequencing data to a reference genome is an essential step for most analysis pipelines aiming at the computational analysis of genome and transcriptome sequencing data. Breaking ties between equally well mapping locations poses a severe problem not only during the alignment phase but also has significant impact on the results of downstream analyses. We present the multi-mapper resolution (MMR) tool that infers optimal mapping locations from the coverage density of other mapped reads. RESULTS: Filtering alignments with MMR can significantly improve the performance of downstream analyses like transcript quantitation and differential testing. We illustrate that the accuracy (Spearman correlation) of transcript quantification increases by 15% when using reads of length 51. In addition, MMR decreases the alignment file sizes by more than 50%, and this leads to a reduced running time of the quantification tool. Our efficient implementation of the MMR algorithm is easily applicable as a post-processing step to existing alignment files in BAM format. Its complexity scales linearly with the number of alignments and requires no further inputs. AVAILABILITY AND IMPLEMENTATION: Open source code and documentation are available for download at http://github.com/ratschlab/mmr Comprehensive testing results and further information can be found at http://bioweb.me/mmr. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Understanding the occurrence and regulation of alternative splicing (AS) is a key task towards explaining the regulatory processes that shape the complex transcriptomes of higher eukaryotes. With the advent of high-throughput sequencing of RNA (RNA-Seq), the diversity of AS transcripts could be measured at an unprecedented depth. Although the catalog of known AS events has grown ever since, novel transcripts are commonly observed when working with less well annotated organisms, in the context of disease, or within large populations. Whereas an identification of complete transcripts is technically challenging and computationally expensive, focusing on single splicing events as a proxy for transcriptome characteristics is fruitful and sufficient for a wide range of analyses. RESULTS: We present SplAdder, an alternative splicing toolbox, that takes RNA-Seq alignments and an annotation file as input to (i) augment the annotation based on RNA-Seq evidence, (ii) identify alternative splicing events present in the augmented annotation graph, (iii) quantify and confirm these events based on the RNA-Seq data and (iv) test for significant quantitative differences between samples. Thereby, our main focus lies on performance, accuracy and usability. AVAILABILITY: Source code and documentation are available for download at http://github.com/ratschlab/spladder Example data, introductory information and a small tutorial are accessible via http://bioweb.me/spladder CONTACTS: : [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Personal genomes carry inherent privacy risks and protecting privacy poses major social and technological challenges. We consider the case where a user searches for genetic information (e.g. an allele) on a server that stores a large genomic database and aims to receive allele-associated information. The user would like to keep the query and result private and the server the database. APPROACH: We propose a novel approach that combines efficient string data structures such as the Burrows-Wheeler transform with cryptographic techniques based on additive homomorphic encryption. We assume that the sequence data is searchable in efficient iterative query operations over a large indexed dictionary, for instance, from large genome collections and employing the (positional) Burrows-Wheeler transform. We use a technique called oblivious transfer that is based on additive homomorphic encryption to conceal the sequence query and the genomic region of interest in positional queries. RESULTS: We designed and implemented an efficient algorithm for searching sequences of SNPs in large genome databases. During search, the user can only identify the longest match while the server does not learn which sequence of SNPs the user queried. In an experiment based on 2184 aligned haploid genomes from the 1000 Genomes Project, our algorithm was able to perform typical queries within [Formula: see text] 4.6 s and [Formula: see text] 10.8 s for client and server side, respectively, on laptop computers. The presented algorithm is at least one order of magnitude faster than an exhaustive baseline algorithm. AVAILABILITY AND IMPLEMENTATION: https://github.com/iskana/PBWT-sec and https://github.com/ratschlab/PBWT-sec CONTACTS: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Protein translation is a fundamental biochemical process and the regulation of this process in response to a variety of changes has been demonstrated to play a key role in cellular functional activity. Recently, the translational control of oncogenes is implicated in many cancers [ 1 ]. We recently reported a translation initiation factor eIF4A RNA helicase-dependent mechanism of translational control that contributes to oncogenesis and underlies the anticancer effects of drug silvestrol [ 2 ]. Inhibition of eIF4A with silvestrol has powerful therapeutic effects in vitro and in vivo . In this study, we developed novel computational tools, specifically be tailored to study high throughput ribosome footprint data (Ribo-seq) [ 3 ], to identify the genes featuring either one of the two changes between two experiment conditions: 1) translational efficiency (TE), and 2) ribosome occupancy distribution profile (ROD) on mRNA. In the parametric test of TE, we take RNA abundance and ribosome occupancy density into account in order to expeditiously identify differential translation efficiency. Whereas the non-parametric test of ROD [ 4 ] aims to identify differential occupancy profiles, such as ribosome stalling at specific sites even if overall translation efficiency remain unchanged. Using transcriptome-scale ribosome footprinting data of leukemia cell line, we defined drug-sensitive genes showing both decrease of translational efficiency (Figure 1A ) and accumulation of ribosome occupancy at 5'UTR (Figure 1B ). Among the most eIF4A-dependent transcripts are a number of oncogenes, super-enhancer associated transcription factors and epigenetic regulators. Computational methods revealed drug effects on protein translation . A Histogram of the ratio of TE in control and drug-treated samples. Red: genes with significant TE down and up regulation were identified based on the read count of Ribo-seq data. Blue and green: TE up and down genes defined by |Z score| > 2 as often used in other analyses. B Averaged distribution profile of ribosome occupancy of 62 drug-sensitive genes. Ribosome footprint coverages and transcript lengths were normalized. C Twelve-nucleotide motif that is highly enriched in 5' UTR of TE down and ROD positive genes. We suggested that the GQ structure is responsible for ribosome stalling in the 5' UTR [ 2 ]. Computational and statistical methodologies facilitate the discovery of the hallmark of eIF4A-dependent transcripts, namely 5'UTR sequence harbors the 12-mer guanine quartet (CGG) 4 motif associated with RNA G-quadruplex (GQ) structures (Figure 1C ). Our novel computational tools provide a fast, accurate solution to gain biological insights from Ribo-seq and RNA-seq data.

We present Oqtans, an open-source workbench for quantitative transcriptome analysis, that is integrated in Galaxy. Its distinguishing features include customizable computational workflows and a modular pipeline architecture that facilitates comparative assessment of tool and data quality. Oqtans integrates an assortment of machine learning-powered tools into Galaxy, which show superior or equal performance to state-of-the-art tools. Implemented tools comprise a complete transcriptome analysis workflow: short-read alignment, transcript identification/quantification and differential expression analysis. Oqtans and Galaxy facilitate persistent storage, data exchange and documentation of intermediate results and analysis workflows. We illustrate how Oqtans aids the interpretation of data from different experiments in easy to understand use cases. Users can easily create their own workflows and extend Oqtans by integrating specific tools. Oqtans is available as (i) a cloud machine image with a demo instance at cloud.oqtans.org, (ii) a public Galaxy instance at galaxy.cbio.mskcc.org, (iii) a git repository containing all installed software (oqtans.org/git); most of which is also available from (iv) the Galaxy Toolshed and (v) a share string to use along with Galaxy CloudMan.

The current revolution in sequencing technologies allows us to obtain a much more detailed picture of transcriptomes via deep RNA Sequencing (RNA-Seq). In considering the full complement of RNA transcripts that comprise the transcriptome, two important analytical questions emerge: what is the abundance of RNA transcripts and which genes or transcripts are differentially expressed. In parallel with developing sequencing technologies, data analysis software is also constantly updated to improve accuracy and sensitivity while minimizing run times. The abundance of software programs, however, can be prohibitive and confusing for researchers evaluating RNA-Seq analysis pipelines. We present an open-source workbench, Oqtans , that can be integrated into the Galaxy framework that enables researchers to set up a computational pipeline for quantitative transcriptome analysis. Its distinguishing features include a modular pipeline architecture, which facilitates comparative assessment of tool and data quality. Within Oqtans , the Galaxy ’s workflow architecture enables direct comparison of several tools. Furthermore, it is straightforward to compare the performance of different programs and parameter settings on the same data and choose the best suited for the task. Oqtans analysis pipelines are easy to set up, modify, and (re-)use without significant computational skill. Oqtans integrates more than twenty sophisticated tools that perform very well compared to the state-of-the-art for transcript identification, quantification and differential expression analysis. The toolsuite contains several tools developed in the Rätsch Laboratory, but the majority of the tools were developed by other groups. In particular, we provide tools for read alignment (bwa, STAR, TopHat, PALMapper, …), transcript prediction (cufflinks, Trinity, Scripture, …) and quantitative analyses (DESeq2, edgeR, rDiff, rQuant, …). In addition, we provide tools for alignment filtering (RNA-geeq toolbox), GFF file processing (GFF toolbox) and tools for predictive sequence analysis (EasySVM, ASP, ARTS, …). See http://oqtans.org/tools for more details on included tools. Oqtans is integrated into the publicly available Galaxy server http://galaxy.cbio.mskcc.org which is maintained by the Rätsch Laboratory. It is also available as source code in a public GitHub repository http://bioweb.me/oqtans/git and as a machine image (managed by Galaxy CloudMan) for the Amazon Web Service cloud environment (instructions available at http://oqtans.org ). Oqtans sets a new standard in terms of reproducibility and builds upon Galaxy’s features to facilitate persistent storage, exchange and documentation of intermediate results and analysis workflows. Support: [email protected] Contact: [email protected] Details: http://oqtans.org Public Computing Server: http://galaxy.cbio.mskcc.org oqtans Demo Server: http://cloud.oqtans.org oqtans Amazon Machine Image: ami-65376a0c License: GPL http://www.gnu.org/licenses/gpl.html

MOTIVATION: High-throughput sequencing of mRNA (RNA-Seq) has led to tremendous improvements in the detection of expressed genes and reconstruction of RNA transcripts. However, the extensive dynamic range of gene expression, technical limitations and biases, as well as the observed complexity of the transcriptional landscape, pose profound computational challenges for transcriptome reconstruction. RESULTS: We present the novel framework MITIE (Mixed Integer Transcript IdEntification) for simultaneous transcript reconstruction and quantification. We define a likelihood function based on the negative binomial distribution, use a regularization approach to select a few transcripts collectively explaining the observed read data and show how to find the optimal solution using Mixed Integer Programming. MITIE can (i) take advantage of known transcripts, (ii) reconstruct and quantify transcripts simultaneously in multiple samples, and (iii) resolve the location of multi-mapping reads. It is designed for genome- and assembly-based transcriptome reconstruction. We present an extensive study based on realistic simulated RNA-Seq data. When compared with state-of-the-art approaches, MITIE proves to be significantly more sensitive and overall more accurate. Moreover, MITIE yields substantial performance gains when used with multiple samples. We applied our system to 38 Drosophila melanogaster modENCODE RNA-Seq libraries and estimated the sensitivity of reconstructing omitted transcript annotations and the specificity with respect to annotated transcripts. Our results corroborate that a well-motivated objective paired with appropriate optimization techniques lead to significant improvements over the state-of-the-art in transcriptome reconstruction. AVAILABILITY: MITIE is implemented in C++ and is available from http://bioweb.me/mitie under the GPL license.

The intestinal microbiota is a microbial ecosystem of crucial importance to human health. Understanding how the microbiota confers resistance against enteric pathogens and how antibiotics disrupt that resistance is key to the prevention and cure of intestinal infections. We present a novel method to infer microbial community ecology directly from time-resolved metagenomics. This method extends generalized Lotka-Volterra dynamics to account for external perturbations. Data from recent experiments on antibiotic-mediated Clostridium difficile infection is analyzed to quantify microbial interactions, commensal-pathogen interactions, and the effect of the antibiotic on the community. Stability analysis reveals that the microbiota is intrinsically stable, explaining how antibiotic perturbations and C. difficile inoculation can produce catastrophic shifts that persist even after removal of the perturbations. Importantly, the analysis suggests a subnetwork of bacterial groups implicated in protection against C. difficile. Due to its generality, our method can be applied to any high-resolution ecological time-series data to infer community structure and response to external stimuli.

We present a novel regularization-based Multitask Learning (MTL) formulation for Structured Output (SO) prediction for the case of hierarchical task relations. Structured output learning often results in difficult inference problems and requires large amounts of training data to obtain accurate models. We propose to use MTL to exploit information available for related structured output learning tasks by means of hierarchical regularization. Due to the combination of example sets, the cost of training models for structured output prediction can easily become infeasible for real world applications. We thus propose an efficient algorithm based on bundle methods to solve the optimization problems resulting from MTL structured output learning. We demonstrate the performance of our approach on gene finding problems from the application domain of computational biology. We show that 1) our proposed solver achieves much faster convergence than previous methods and 2) that the Hierarchical SO-MTL approach clearly outperforms considered non-MTL methods.

BACKGROUND: Alternative splicing (AS) is a process which generates several distinct mRNA isoforms from the same gene by splicing different portions out of the precursor transcript. Due to the (patho-)physiological importance of AS, a complete inventory of AS is of great interest. While this is in reach for human and mammalian model organisms, our knowledge of AS in plants has remained more incomplete. Experimental approaches for monitoring AS are either based on transcript sequencing or rely on hybridization to DNA microarrays. Among the microarray platforms facilitating the discovery of AS events, tiling arrays are well-suited for identifying intron retention, the most prevalent type of AS in plants. However, analyzing tiling array data is challenging, because of high noise levels and limited probe coverage. RESULTS: In this work, we present a novel method to detect intron retentions (IR) and exon skips (ES) from tiling arrays. While statistical tests have typically been proposed for this purpose, our method instead utilizes support vector machines (SVMs) which are appreciated for their accuracy and robustness to noise. Existing EST and cDNA sequences served for supervised training and evaluation. Analyzing a large collection of publicly available microarray and sequence data for the model plant A. thaliana, we demonstrated that our method is more accurate than existing approaches. The method was applied in a genome-wide screen which resulted in the discovery of 1,355 IR events. A comparison of these IR events to the TAIR annotation and a large set of short-read RNA-seq data showed that 830 of the predicted IR events are novel and that 525 events (39%) overlap with either the TAIR annotation or the IR events inferred from the RNA-seq data. CONCLUSIONS: The method developed in this work expands the scarce repertoire of analysis tools for the identification of alternative mRNA splicing from whole-genome tiling arrays. Our predictions are highly enriched with known AS events and complement the A. thaliana genome annotation with respect to AS. Since all predicted AS events can be precisely attributed to experimental conditions, our work provides a basis for follow-up studies focused on the elucidation of the regulatory mechanisms underlying tissue-specific and stress-dependent AS in plants.

The current revolution in sequencing technologies allows us to obtain a much more detailed picture of transcriptomes via RNA-Sequencing. We have developed the first integrative online platform, oqtans, for quantitatively analyzing RNA-Seq experiments. Our approach of providing a self-contained machine image with the accessible, transparent Galaxy framework [ 1 ] minimizes the risk of using a third-party web service for data analysis. These services often disappear a few years after publication and render results irreproducible [ 2 ]. With oqtans, bioinformatics becomes reproducible by providing analysis building blocks for a customized workflow of read mapping, transcript reconstruction and quantitation as well as differential expression analysis. Oqtans includes a comprehensive machine-learning-powered toolsuite developed by the authors for NGS data analysis. PALMapper is a short-read mapper which efficiently computes both unspliced and spliced alignments at high accuracy by taking advantage of base quality information and computational splice site predictions [ 3 ]. mTIM is a transcript reconstruction method, which exploits features derived from RNA-seq read alignments and from computational splice site predictions to infer the exon-intron structure of the corresponding transcripts. rQuant is based on quadratic programming. It simultaneously estimates biases inherent in library preparation, sequencing, and read mapping, and accurately determines the abundances of given transcripts [ 4 ]. rDiff is a set of statistical test techniques that determine significant differences between two RNA-seq experiments to find differentially expressed regions with or without knowledge of transcripts. We compare predictions to the published annotation at the intron and transcript levels. The performance of read aligners is shown in Fig. 1A from D. melanogaster data , and transcript segmentation tools in Fig. 1B, on C. elegans . Our tools, PALMapper and mTIM, outperform TopHat [ 5 ] and Cufflinks [ 6 ]. Oqtans is available free and open-source, from http://oqtans.org as a virtual machine for cloud computing environments, and ready to use on our public compute cluster at http://bioweb.me/mlb-galaxy . A) Accuracy (F-score) of intron predictions in 3-day-old adults of D. melanogaster with aligners PALMapper (green) and TopHat (blue). B) Accuracy of intron predictions with the same aligners and transcript predictions with mTIM (green) and Cufflinks (blue) on C. elegans RNA-seq transcriptome data.

An increasingly large number of novel genomes is being sequenced and the task of automatic genome annotation has never been more important.The current revolution in sequencing technologies also allows us to obtain a detailed picture of the whole complement of expressed RNA transcripts.We have developed a novel de novo gene finding system mGene.ngsthat combines the benefits of accurate ab initio gene finding with the rich information obtained in RNA sequencing (RNA-seq) experiments.The system is based on the recently developed accurate gene finding system mGene [1], which employs state-of-the-art prediction techniques and which has been shown to perform very well compared to established gene finding systems [2].In contrast to many HMM-based gene finders, mGene has the conceptual advantage of being very flexible in terms of incorporating heterogeneous input data.The employed inference techniques can exploit the transcriptome information already at the learning stage to appropriately adapt to the relevance of the different evidences.We show that these advantages can be translated into more accurate gene predictions.Moreover, we developed extensions of mGene.ngs to predict and quantify alternative RNA transcripts.To provide de novo genome annotations based on RNA-seq experiments, we first construct a preliminary, highly specific gene set for genes that are well-covered with RNA-seq reads.In a second step, we train predictors for genomic signals on the preliminary gene set.In the third step we train mGene.ngs,using the preliminary gene models while taking advantage of the RNA-seq read coverage and genomic signal predictions.

BACKGROUND: String kernels are commonly used for the classification of biological sequences, nucleotide as well as amino acid sequences. Although string kernels are already very powerful, when it comes to amino acids they have a major short coming. They ignore an important piece of information when comparing amino acids: the physico-chemical properties such as size, hydrophobicity, or charge. This information is very valuable, especially when training data is less abundant. There have been only very few approaches so far that aim at combining these two ideas. RESULTS: We propose new string kernels that combine the benefits of physico-chemical descriptors for amino acids with the ones of string kernels. The benefits of the proposed kernels are assessed on two problems: MHC-peptide binding classification using position specific kernels and protein classification based on the substring spectrum of the sequences. Our experiments demonstrate that the incorporation of amino acid properties in string kernels yields improved performances compared to standard string kernels and to previously proposed non-substring kernels. CONCLUSIONS: In summary, the proposed modifications, in particular the combination with the RBF substring kernel, consistently yield improvements without affecting the computational complexity. The proposed kernels therefore appear to be the kernels of choice for any protein sequence-based inference. AVAILABILITY: Data sets, code and additional information are available from http://www.fml.tuebingen.mpg.de/raetsch/suppl/aask. Implementations of the developed kernels are available as part of the Shogun toolbox.

BACKGROUND: The lack of sufficient training data is the limiting factor for many Machine Learning applications in Computational Biology. If data is available for several different but related problem domains, Multitask Learning algorithms can be used to learn a model based on all available information. In Bioinformatics, many problems can be cast into the Multitask Learning scenario by incorporating data from several organisms. However, combining information from several tasks requires careful consideration of the degree of similarity between tasks. Our proposed method simultaneously learns or refines the similarity between tasks along with the Multitask Learning classifier. This is done by formulating the Multitask Learning problem as Multiple Kernel Learning, using the recently published q-Norm MKL algorithm. RESULTS: We demonstrate the performance of our method on two problems from Computational Biology. First, we show that our method is able to improve performance on a splice site dataset with given hierarchical task structure by refining the task relationships. Second, we consider an MHC-I dataset, for which we assume no knowledge about the degree of task relatedness. Here, we are able to learn the task similarities ab initio along with the Multitask classifiers. In both cases, we outperform baseline methods that we compare against. CONCLUSIONS: We present a novel approach to Multitask Learning that is capable of learning task similarity along with the classifiers. The framework is very general as it allows to incorporate prior knowledge about tasks relationships if available, but is also able to identify task similarities in absence of such prior information. Both variants show promising results in applications from Computational Biology.

MOTIVATION: Understanding transcriptional regulation is one of the main challenges in computational biology. An important problem is the identification of transcription factor (TF) binding sites in promoter regions of potential TF target genes. It is typically approached by position weight matrix-based motif identification algorithms using Gibbs sampling, or heuristics to extend seed oligos. Such algorithms succeed in identifying single, relatively well-conserved binding sites, but tend to fail when it comes to the identification of combinations of several degenerate binding sites, as those often found in cis-regulatory modules. RESULTS: We propose a new algorithm that combines the benefits of existing motif finding with the ones of support vector machines (SVMs) to find degenerate motifs in order to improve the modeling of regulatory modules. In experiments on microarray data from Arabidopsis thaliana, we were able to show that the newly developed strategy significantly improves the recognition of TF targets. AVAILABILITY: The python source code (open source-licensed under GPL), the data for the experiments and a Galaxy-based web service are available at http://www.fml.mpg.de/raetsch/suppl/kirmes/.

We shed light on the discrimination between patterns belonging to two different classes by casting this decoding problem into a generalized prototype framework. The discrimination process is then separated into two stages: a projection stage that reduces the dimensionality of the data by projecting it on a line and a threshold stage where the distributions of the projected patterns of both classes are separated. For this, we extend the popular mean-of-class prototype classification using algorithms from machine learning that satisfy a set of invariance properties. We report a simple yet general approach to express different types of linear classification algorithms in an identical and easy-to-visualize formal framework using generalized prototypes where these prototypes are used to express the normal vector and offset of the hyperplane. We investigate non-margin classifiers such as the classical prototype classifier, the Fisher classifier, and the relevance vector machine. We then study hard and soft margin classifiers such as the support vector machine and a boosted version of the prototype classifier. Subsequently, we relate mean-of-class prototype classification to other classification algorithms by showing that the prototype classifier is a limit of any soft margin classifier and that boosting a prototype classifier yields the support vector machine. While giving novel insights into classification per se by presenting a common and unified formalism, our generalized prototype framework also provides an efficient visualization and a principled comparison of machine learning classification.

MOTIVATION: At the heart of many important bioinformatics problems, such as gene finding and function prediction, is the classification of biological sequences. Frequently the most accurate classifiers are obtained by training support vector machines (SVMs) with complex sequence kernels. However, a cumbersome shortcoming of SVMs is that their learned decision rules are very hard to understand for humans and cannot easily be related to biological facts. RESULTS: To make SVM-based sequence classifiers more accessible and profitable, we introduce the concept of positional oligomer importance matrices (POIMs) and propose an efficient algorithm for their computation. In contrast to the raw SVM feature weighting, POIMs take the underlying correlation structure of k-mer features induced by overlaps of related k-mers into account. POIMs can be seen as a powerful generalization of sequence logos: they allow to capture and visualize sequence patterns that are relevant for the investigated biological phenomena. AVAILABILITY: All source code, datasets, tables and figures are available at http://www.fml.tuebingen.mpg.de/raetsch/projects/POIM. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We study the problem of domain transfer for a supervised classification task in mRNA splicing. We consider a number of recent domain transfer methods from machine learning, including some that are novel, and evaluate them on genomic sequence data from model organisms of varying evolutionary distance. We find that in cases where the organisms are not closely related, the use of domain adaptation methods can help improve classification performance.

Art. e1000173, 10 S.

Gunnar R¨atsch Friedrich Miescher Laboratory Max Planck Society T¨ubingen, Germany We present a novel boosting algorithm, called SoftBoost, designed for sets of bi- nary labeled examples that are not necessarily separable by convex combinations of base hypotheses. Our algorithm achieves robustness by capping the distribu- tions on the examples. Our update of the distribution is motivated by minimizing a relative entropy subject to the capping constraints and constraints on the edges of the obtained base hypotheses. The capping constraints imply a soft margin in the dual optimization problem. Our algorithm produces a convex combination of hypotheses whose soft margin is within δ of its maximum. We employ relative en- tropy projection methods to prove an O( ln N δ2 ) iteration bound for our algorithm, where N is number of examples. We compare our algorithm with other approaches including LPBoost, Brown- Boost, and SmoothBoost. We show that there exist cases where the number of iter- ations required by LPBoost grows linearly in N instead of the logarithmic growth for SoftBoost. In simulation studies we show that our algorithm converges about as fast as LPBoost, faster than BrownBoost, and much faster than SmoothBoost. In a benchmark comparison we illustrate the competitiveness of our approach.

MOTIVATION: Despite many years of research on how to properly align sequences in the presence of sequencing errors, alternative splicing and micro-exons, the correct alignment of mRNA sequences to genomic DNA is still a challenging task. RESULTS: We present a novel approach based on large margin learning that combines accurate splice site predictions with common sequence alignment techniques. By solving a convex optimization problem, our algorithm-called PALMA-tunes the parameters of the model such that true alignments score higher than other alignments. We study the accuracy of alignments of mRNAs containing artificially generated micro-exons to genomic DNA. In a carefully designed experiment, we show that our algorithm accurately identifies the intron boundaries as well as boundaries of the optimal local alignment. It outperforms all other methods: for 5702 artificially shortened EST sequences from Caenorhabditis elegans and human, it correctly identifies the intron boundaries in all except two cases. The best other method is a recently proposed method called exalin which misaligns 37 of the sequences. Our method also demonstrates robustness to mutations, insertions and deletions, retaining accuracy even at high noise levels. AVAILABILITY: Datasets for training, evaluation and testing, additional results and a stand-alone alignment tool implemented in C++ and python are available at http://www.fml.mpg.de/raetsch/projects/palma

The field of computational biology has seen dramatic growth over the past few years, both in terms of available data, scientific questions and challenges for learning and inference. These new types of scientific and clinical problems require the development of novel supervised and unsupervised learning approaches. In particular, the field is characterized by a diversity of heterogeneous data. The human genome sequence is accompanied by real-valued gene expression data, functional annotation of genes, genotyping information, a graph of interacting proteins, a set of equations describing the dynamics of a system, localization of proteins in a cell, a phylogenetic tree relating species, natural language text in the form of papers describing experiments, partial models that provide priors, and numerous other data sources. This supplementary issue consists of seven peer-reviewed papers based on the NIPS Workshop on New Problems and Methods in Computational Biology held at Whistler, British Columbia, Canada on December 8, 2006. The Neural Information Processing Systems Conference is the premier scientific meeting on neural computation, with session topics spanning artificial intelligence, learning theory, neuroscience, etc. The goal of this workshop was to present emerging problems and machine learning techniques in computational biology, with a particular emphasis on methods for computational learning from heterogeneous data. We received 37 extended abstract submissions, from which 13 were selected for oral presentation. The current supplement contains seven papers based on a subset of the 13 extended abstracts. Submitted manuscripts were rigorously reviewed by at least two referees. The quality of each paper was evaluated with respect to its contribution to biology as well as the novelty of the machine learning methods employed.

BACKGROUND: For splice site recognition, one has to solve two classification problems: discriminating true from decoy splice sites for both acceptor and donor sites. Gene finding systems typically rely on Markov Chains to solve these tasks. RESULTS: In this work we consider Support Vector Machines for splice site recognition. We employ the so-called weighted degree kernel which turns out well suited for this task, as we will illustrate in several experiments where we compare its prediction accuracy with that of recently proposed systems. We apply our method to the genome-wide recognition of splice sites in Caenorhabditis elegans, Drosophila melanogaster, Arabidopsis thaliana, Danio rerio, and Homo sapiens. Our performance estimates indicate that splice sites can be recognized very accurately in these genomes and that our method outperforms many other methods including Markov Chains, GeneSplicer and SpliceMachine. We provide genome-wide predictions of splice sites and a stand-alone prediction tool ready to be used for incorporation in a gene finder. AVAILABILITY: Data, splits, additional information on the model selection, the whole genome predictions, as well as the stand-alone prediction tool are available for download at http://www.fml.mpg.de/raetsch/projects/splice.

For modern biology, precise genome annotations are of prime importance, as they allow the accurate definition of genic regions. We employ state-of-the-art machine learning methods to assay and improve the accuracy of the genome annotation of the nematode Caenorhabditis elegans. The proposed machine learning system is trained to recognize exons and introns on the unspliced mRNA, utilizing recent advances in support vector machines and label sequence learning. In 87% (coding and untranslated regions) and 95% (coding regions only) of all genes tested in several out-of-sample evaluations, our method correctly identified all exons and introns. Notably, only 37% and 50%, respectively, of the presently unconfirmed genes in the C. elegans genome annotation agree with our predictions, thus we hypothesize that a sizable fraction of those genes are not correctly annotated. A retrospective evaluation of the Wormbase WS120 annotation [] of C. elegans reveals that splice form predictions on unconfirmed genes in WS120 are inaccurate in about 18% of the considered cases, while our predictions deviate from the truth only in 10%-13%. We experimentally analyzed 20 controversial genes on which our system and the annotation disagree, confirming the superiority of our predictions. While our method correctly predicted 75% of those cases, the standard annotation was never completely correct. The accuracy of our system is further corroborated by a comparison with two other recently proposed systems that can be used for splice form prediction: SNAP and ExonHunter. We conclude that the genome annotation of C. elegans and other organisms can be greatly enhanced using modern machine learning technology.

We consider boosting algorithms that maintain a distribution over a set of examples. At each iteration a weak hypothesis is received and the distribution is updated. We motivate these updates as minimizing the relative entropy subject to linear constraints. For example AdaBoost constrains the edge of the last hypothesis w.r.t. the updated distribution to be at most γ = 0. In some sense, AdaBoost is "corrective" w.r.t. the last hypothesis. A cleaner boosting method is to be "totally corrective": the edges of all past hypotheses are constrained to be at most γ, where γ is suitably adapted.Using new techniques, we prove the same iteration bounds for the totally corrective algorithms as for their corrective versions. Moreover with adaptive γ, the algorithms provably maximizes the margin. Experimentally, the totally corrective versions return smaller convex combinations of weak hypotheses than the corrective ones and are competitive with LPBoost, a totally corrective boosting algorithm with no regularization, for which there is no iteration bound known.

We describe Hidden Semi-Markov Support Vector Machines (SHM SVMs), an extension of HM SVMs to semi-Markov chains. This allows us to predict segmentations of sequences based on segment-based features measuring properties such as the length of the segment. We propose a novel technique to partition the problem into sub-problems. The independently obtained partial solutions can then be recombined in an efficient way, which allows us to solve label sequence learning problems with several thousands of labeled sequences. We have tested our algorithm for predicting gene structures, an important problem in computational biology. Results on a well-known model organism illustrate the great potential of SHM SVMs in computational biology.

BACKGROUND: Support Vector Machines (SVMs)--using a variety of string kernels--have been successfully applied to biological sequence classification problems. While SVMs achieve high classification accuracy they lack interpretability. In many applications, it does not suffice that an algorithm just detects a biological signal in the sequence, but it should also provide means to interpret its solution in order to gain biological insight. RESULTS: We propose novel and efficient algorithms for solving the so-called Support Vector Multiple Kernel Learning problem. The developed techniques can be used to understand the obtained support vector decision function in order to extract biologically relevant knowledge about the sequence analysis problem at hand. We apply the proposed methods to the task of acceptor splice site prediction and to the problem of recognizing alternatively spliced exons. Our algorithms compute sparse weightings of substring locations, highlighting which parts of the sequence are important for discrimination. CONCLUSION: The proposed method is able to deal with thousands of examples while combining hundreds of kernels within reasonable time, and reliably identifies a few statistically significant positions.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm works for hundred thousands of examples or hundreds of kernels to be combined, and helps for automatic model selection, improving the interpretability of the learning result. In a second part we discuss general speed up mechanism for SVMs, especially when used with sparse feature maps as appear for string kernels, allowing us to train a string kernel SVM on a 10 million real-world splice data set from computational biology. We integrated multiple kernel learning in our machine learning toolbox SHOGUN for which the source code is publicly available at http://www.fml.tuebingen.mpg.de/raetsch/projects/shogun.

In genomic sequence analysis tasks like splice site recognition or promoter identification, large amounts of training sequences are available, and indeed needed to achieve sufficiently high classification performances. In this work we study two recently proposed and successfully used kernels, namely the Spectrum kernel and the Weighted Degree kernel (WD). In particular, we suggest several extensions using Suffix Trees and modifications of an SMO-like SVM training algorithm in order to accelerate the training of the SVMs and their evaluation on test sequences. Our simulations show that for the spectrum kernel and WD kernel, large scale SVM training can be accelerated by factors of 20 and 4 times, respectively, while using much less memory (e.g. no kernel caching). The evaluation on new sequences is often several thousand times faster using the new techniques (depending on the number of Support Vectors). Our method allows us to train on sets as large as one million sequences.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classi- fication, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementa- tions. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classifica- tion. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learn- ing result and works for hundred thousands of examples or hundreds of kernels to be combined. f (x) = sign N Xi=1 αiyik(xi, x) + b! ,

AdaBoost produces a linear combination of base hypotheses and predicts with the sign of this linear combination. The linear combination may be viewed as a hyperplane in feature space where the base hypotheses form the features. It has been observed that the generalization error of the algorithm continues to improve even after all examples are on the correct side of the current hyperplane. The improvement is attributed to the experimental observation that the distances (margins) of the examples to the separating hyperplane are increasing even after all examples are on the correct side. We introduce a new version of AdaBoost, called AdaBoost*ν, that explicitly maximizes the minimum margin of the examples up to a given precision. The algorithm incorporates a current estimate of the achievable margin into its calculation of the linear coefficients of the base hypotheses. The bound on the number of iterations needed by the new algorithms is the same as the number needed by a known version of AdaBoost that must have an explicit estimate of the achievable margin as a parameter. We also illustrate experimentally that our algorithm requires considerably fewer iterations than other algorithms that aim to maximize the margin.

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: on-line learning with a simple square loss, and finding a symmetric positive definite matrix subject to linear constraints. The updates generalize the exponentiated gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponentials to preserve positive definiteness. Most importantly, we show how the derivation and the analyses of the original EG update and AdaBoost generalize to the non-diagonal case. We apply the resulting matrix exponentiated gradient (MEG) update and DefiniteBoost to the problem of learning a kernel matrix from distance measurements.

One way of image denoising is to project a noisy image to the subspace of admissible images derived, for instance, by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion. We propose a new method to identify the noisy pixels by l1-norm penalization and to update the identified pixels only. The identification and updating of noisy pixels are formulated as one linear program which can be efficiently solved. In particular, one can apply the upsilon trick to directly specify the fraction of pixels to be reconstructed. Moreover, we extend the linear program to be able to exploit prior knowledge that occlusions often appear in contiguous blocks (e.g., sunglasses on faces). The basic idea is to penalize boundary points and interior points of the occluded area differently. We are also able to show the upsilon property for this extended LP leading to a method which is easy to use. Experimental results demonstrate the power of our approach.

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann diver- gence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positive definite matrix subject to symmetric linear constraints. The updates generalize the Exponentiated Gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponen- tials to preserve positive definiteness. Most importantly, we show how the analysis of each algorithm generalizes to the non-diagonal case. We apply both new algorithms, called the Matrix Exponentiated Gradient (MEG) update and DefiniteBoost, to learn a kernel matrix from distance measurements. 1 Introduction Most learning algorithms have been developed to learn a vector of parameters from data. However, an increasing number of papers are now dealing with more structured parame- ters. More specifically, when learning a similarity or a distance function among objects, the parameters are defined as a symmetric positive definite matrix that serves as a kernel (e.g. [14, 11, 13]). Learning is typically formulated as a parameter updating procedure to optimize a loss function. The gradient descent update [6] is one of the most commonly used algorithms, but it is not appropriate when the parameters form a positive definite matrix, because the updated parameter is not necessarily positive definite. Xing et al. [14] solved this problem by always correcting the updated matrix to be positive. However no bound has been proven for this update-and-correction approach. In this paper, we introduce the Matrix Exponentiated Gradient update which works as follows: First, the matrix logarithm of the current parameter matrix is computed. Then a step is taken in the direction of the steepest descent. Finally, the parameter matrix is updated to the exponential of the modified log-matrix. Our update preserves symmetry and positive definiteness because the matrix exponential maps any symmetric matrix to a positive definite matrix. Bregman divergences play a central role in the motivation and the analysis of on-line learn- ing algorithms [5]. A learning problem is essentially defined by a loss function, and a di- vergence that measures the discrepancy between parameters. More precisely, the updates are motivated by minimizing the sum of the loss function and the Bregman divergence, where the loss function is multiplied by a positive learning rate. Different divergences lead to radically different updates [6]. For example, the gradient descent is derived from the squared Euclidean distance, and the exponentiated gradient from the Kullback-Leibler di- vergence. We use the von Neumann divergence (also called quantum relative entropy) for measuring the discrepancy between two positive definite matrices [8]. We derive a new Matrix Exponentiated Gradient update from this divergence (which is a Bregman diver- gence for positive definite matrices). Finally we prove relative loss bounds using the von Neumann divergence as a measure of progress. Also the following related key problem has received a lot of attention recently [14, 11, 13]: Find a symmetric positive definite matrix that satisfies a number of symmetric linear inequality constraints. The new DefiniteBoost algorithm greedily chooses the most violated constraint and performs an approximated Bregman projection. In the diagonal case, we recover AdaBoost [9]. We also show how the convergence proof of AdaBoost generalizes to the non-diagonal case. 2 von Neumann Divergence or Quantum Relative Entropy If F is a real convex differentiable function on the parameter domain (symmetric d d positive definite matrices) and f (W) := F(W), then the Bregman divergence between two parameters W and W is defined as F(W, W) = F(W) - F(W) - tr[(W - W)f(W)]. When choosing F(W) = tr(W log W -W), then f(W) = log W and the corresponding Bregman divergence becomes the von Neumann divergence [8]: F(W, W) = tr(W log W - W log W - W + W). (1) In this paper, we are primarily interested in the normalized case (when tr(W) = 1). In this case, the positive symmetric definite matrices are related to density matrices commonly used in Statistical Physics and the divergence simplifies to F(W, W) = tr(W log W - W log W). If W = i ivivi is our notation for the eigenvalue decomposition, then we can rewrite the normalized divergence as ~ ~ F(W, W) = i ln ~ i + i ln j(~ vi vj )2. i i,j So this divergence quantifies the difference in the eigenvalues as well as the eigenvectors. 3 On-line Learning In this section, we present a natural extension of the Exponentiated Gradient (EG) up- date [6] to an update for symmetric positive definite matrices. At the t-th trial, the algorithm receives a symmetric instance matrix Xt Rdd. It then produces a prediction ^ yt = tr(WtXt) based on the algorithm's current symmetric positive definite parameter matrix Wt. Finally it incurs for instance1 a quadratic loss (^ yt - yt)2, 1For the sake of simplicity, we use the simple quadratic loss: L W t (W) = (tr(Xt ) - yt)2. For the general update, the gradient Lt(Wt) is exponentiated in the update (4) and this gradient must be symmetric. Following [5], more general loss functions (based on Bregman divergences) are amenable to our techniques. and updates its parameter matrix Wt. In the update we aim to solve the following problem: Wt+1 = argmin W F(W, Wt) + (tr(WXt) - yt)2 , (2) where the convex function F defines the Bregman divergence. Setting the derivative with respect to W to zero, we have f (Wt+1) - f(Wt) + [(tr(Wt+1Xt) - yt)2] = 0. (3) The update rule is derived by solving (3) with respect to Wt+1, but it is not solvable in closed form. A common way to avoid this problem is to approximate tr(Wt+1Xt) by tr(WtXt) [5]. Then, we have the following update: Wt+1 = f -1(f (Wt) - 2(^yt - yt)Xt). In our case, F(W) = tr(W log W - W) and thus f(W) = log W and f-1(W) = exp W. We also augment (2) with the constraint tr(W) = 1, leading to the following Matrix Exponential Gradient (MEG) Update: 1 Wt+1 = exp(log W Z t - 2(^yt - yt)Xt), (4) t where the normalization factor Zt is tr[exp(log Wt - 2(^yt - yt)Xt)]. Note that in the above update, the exponent log Wt - 2(^yt - yt)Xt is an arbitrary symmetric matrix and the matrix exponential converts this matrix back into a symmetric positive definite matrix. A numerically stable version of the MEG update is given in Section 3.2. 3.1 Relative Loss Bounds We now begin with the definitions needed for the relative loss bounds. Let S = (X1, y1), . . . , (XT , yT ) denote a sequence of examples, where the instance matrices Xt Rdd are symmetric and the labels yt R. For any symmetric positive semi-definite ma- trix U with tr(U) = 1, define its total loss as LU(S) = T (tr(UX t=1 t ) - yt)2. The total loss of the on-line algorithm is LMEG(S) = T (tr(W t=1 tXt) - yt)2. We prove a bound on the relative loss LMEG(S) -LU(S) that holds for any U. The proof generalizes a sim- ilar bound for the Exponentiated Gradient update (Lemmas 5.8 and 5.9 of [6]). The relative loss bound is derived in two steps: Lemma 3.1 bounds the relative loss for an individual trial and Lemma 3.2 for a whole sequence (Proofs are given in the full paper). Lemma 3.1 Let Wt be any symmetric positive definite matrix. Let Xt be any symmetric matrix whose smallest and largest eigenvalues satisfy max - min r. Assume Wt+1 is produced from Wt by the MEG update and let U be any symmetric positive semi-definite matrix. Then for any constants a and b such that 0 < a 2b/(2 + r2b) and any learning rate = 2b/(2 + r2b), we have a(yt - tr(WtXt))2 - b(yt - tr(UXt))2 (U,Wt) - (U,Wt+1) (5) In the proof, we use the Golden-Thompson inequality [3], i.e., tr[exp(A + B)] tr[exp(A) exp(B)] for symmetric matrices A and B. We also needed to prove the fol- lowing generalization of Jensen's inequality to matrices: exp(1A + 2(I - A)) exp(1)A + exp(2)(I - A) for finite 1,2 R and any symmetric matrix A with 0 < A I. These two key inequalities will also be essential for the analysis of Definite- Boost in the next section. Lemma 3.2 Let W1 and U be arbitrary symmetric positive definite initial and comparison matrices, respectively. Then for any c such that = 2c/(r2(2 + c)), c 1 1 LMEG(S) 1 + LU(S) + + r2(U, W 2 2 c 1). (6) Proof For the maximum tightness of (5), a should be chosen as a = = 2b/(2 + r2b). Let b = c/r2, and thus a = 2c/(r2(2 + c)). Then (5) is rewritten as 2c (y 2 + c t - tr(WtXt))2 - c(yt - tr(UXt))2 r2((U, Wt) - (U, Wt+1)) Adding the bounds for t = 1, , T, we get 2c L 2 + c MEG(S) - cLU(S) r2((U, W1) - (U, Wt+1)) r2(U, W1), which is equivalent to (6). Assuming LU(S) max and (U, W1) dmax, the bound (6) is tightest when c = r 2dmax/ max. Then we have LMEG(S) - LU(S) r2 maxdmax + r2(U,W 2 1). 3.2 Numerically stable MEG update The MEG update is numerically unstable when the eigenvalues of Wt are around zero. However we can "unwrap" Wt+1 as follows: 1 t Wt+1 = exp(c (^ y ~ tI + log W1 s Z - 2 - ys)Xs), (7) t s=1 where the constant ~ Zt normalizes the trace of Wt+1 to one. As long as the eigen values of W1 are not too small then the computation of log Wt is stable. Note that the update is inde- pendent of the choice of ct R. We incrementally maintain an eigenvalue decomposition of the matrix in the exponent (O(n3) per iteration): t VttVTt = ctI + log W1 - 2 (^ys - ys)Xs), s=1 where the constant ct is chosen so that the maximum eigenvalue of the above is zero. Now Wt+1 = Vt exp(t)VTt /tr(exp(t)). 4 Bregman Projection and DefiniteBoost In this section, we address the following Bregman projection problem2 W = argmin W F (W, W1), tr(W) = 1, tr(WCj ) 0, for j = 1, . . . , n, (8) where the symmetric positive definite matrix W1 of trace one is the initial parameter ma- trix, and C1, . . . , Cn are arbitrary symmetric matrices. Prior knowledge about W is en- coded in the constraints, and the matrix closest to W1 is chosen among the matrices satis- fying all constraints. Tsuda and Noble [13] employed this approach for learning a kernel matrix among graph nodes, and this method can be potentially applied to learn a kernel matrix in other settings (e.g. [14, 11]). The problem (8) is a projection of W1 to the intersection of convex regions defined by the constraints. It is well known that the Bregman projection into the intersection of convex regions can be solved by sequential projections to each region [1]. In the original papers only asymptotic convergence was shown. More recently a connection [4, 7] was made to the AdaBoost algorithm which has an improved convergence analysis [2, 9]. We generalize the latter algorithm and its analysis to symmetric positive definite matrices and call the new algorithm DefiniteBoost. As in the original setting, only approximate projections (Figure 1) are required to show fast convergence. 2Note that if is large then the on-line update (2) becomes a Bregman projection subject to a single equality constraint tr(WXt) = yt. Approximate Figure 1: In (exact) Bregman projections, the intersection Projection of convex sets (i.e., two lines here) is found by iterating pro- jections to each set. We project only approximately, so the projected point does not satisfy the current constraint. Nev- ertheless, global convergence to the optimal solution is guar- anteed via our proofs. Exact Projection Before presenting the algorithm, let us derive the dual problem of (8) by means of Lagrange multipliers , n = argmin log trexp(logW1- jCj), j 0. (9) j=1 See [13] for a detailed derivation of the dual problem. When (8) is feasible, the opti- mal solution is described as W = 1 exp(log W C ) = Z( 1 j ), where Z( ) - nj=1 j tr[exp(log W1 - n C j=1 j j )]. 4.1 Exact Bregman Projections First, let us present the exact Bregman projection algorithm to solve (8). We start from the initial parameter W1. At the t-th step, the most unsatisfied constraint is chosen, jt = argmaxj=1, ,n tr(WtCj). Let us use Ct as the short notation for Cj . Then, the t following Bregman projection with respect to the chosen constraint is solved. Wt+1 = argmin (W, W W t), tr(W) = 1, tr(WCt) 0. (10) By means of a Lagrange multiplier , the dual problem is described as t = argmin tr[exp(log Wt - Ct)], 0. (11) Using the solution of the dual problem, Wt is updated as 1 Wt+1 = exp(log W Z t - tCt) (12) t(t) where the normalization factor is Zt(t) = tr[exp(log Wt -tCt)]. Note that we can use the same numerically stable update as in the previous section. 4.2 Approximate Bregman Projections The solution of (11) cannot be obtained in closed form. However, one can use the following approximate solution: 1 1 + r t/max t t = log , (13) max t - min t 1 + rt/min t when the eigenvalues of Ct lie in the interval [min t , max t ] and rt = tr(WtCt). Since the most unsatisfied constraint is chosen, rt 0 and thus t 0. Although the projection is done only approximately,3 the convergence of the dual objective (9) can be shown using the following upper bound. 3The approximate Bregman projection (with t as in (13) can also be motivated as an online algorithm based on an entropic loss and learning rate one (following Section 3 and [4]). Theorem 4.1 The dual objective (9) is bounded as n T tr explogW1- jCj (rt) (14) j=1 t=1 max min t -t rt max max t -min t rt t -min t where (rt) = 1 - 1 . max - t min t The dual objective is monotonically decreasing, because (rt) 1. Also, since rt corre- sponds to the maximum value among all constraint violations {rj}nj=1, we have (rt) = 1 only if rt = 0. Thus the dual objective continues to decrease until all constraints are satisfied. 4.3 Relation to Boosting When all matrices are diagonal, the DefiniteBoost degenerates to AdaBoost [9]: Let {xi,yi}di=1 be the training samples, where xi Rm and yi {-1,1}. Let h1(x), . . . , hn(x) [-1,1] be the weak hypotheses. For the j-th hypothesis hj(x), let us define Cj = diag(y1hj(x1), . . . , ydhj(xd)). Since |yhj(x)| 1, max/min t = 1 for any t. Setting W1 = I/d, the dual objective (14) is rewritten as d n 1 exp d -yi jhj(xi), i=1 j=1 which is equivalent to the exponential loss function used in AdaBoost. Since Cj and W1 are diagonal, the matrix Wt stays diagonal after the update. If wti = [Wt]ii, the updating formula (12) becomes the AdaBoost update: wt+1,i = wti exp(-tyiht(xi))/Zt(t). The approximate solution of t (13) is described as t = 1 log 1+rt , where r 2 1-r t is the weighted t training error of the t-th hypothesis, i.e. rt = d w i=1 tiyiht(xi). 5 Experiments on Learning Kernels In this section, our technique is applied to learning a kernel matrix from a set of distance measurements. This application is not on-line per se, but it shows nevertheless that the theoretical bounds can be reasonably tight on natural data. When K is a d d kernel matrix among d objects, then the Kij characterizes the similarity between objects i and j. In the feature space, Kij corresponds to the inner product between object i and j, and thus the Euclidean distance can be computed from the entries of the kernel matrix [10]. In some cases, the kernel matrix is not given explicitly, but only a set of distance measurements is available. The data are represented either as (i) quantitative distance values (e.g., the distance between i and j is 0.75), or (ii) qualitative evaluations (e.g., the distance between i and j is small) [14, 13]. Our task is to obtain a positive definite kernel matrix which fits well to the given distance data. On-line kernel learning In the first experiment, we consider the on-line learning scenario in which only one distance example is shown to the learner at each time step. The distance example at time t is described as {at, bt, yt}, which indicates that the squared Euclidean distance between objects at and bt is yt. Let us define a time-developing sequence of kernel matrices as {Wt}Tt=1, and the corresponding points in the feature space as {xti}di=1 (i.e. [Wt]ab = xtaxtb). Then, the total loss incurred by this sequence is T T 2 2 xta = (tr(W t - xtbt - yt tXt) - yt)2, t=1 t=1 1.8 0.45 1.6 0.4 1.4 0.35 1.2 0.3 1 0.25 0.8 Total Loss 0.2 0.6 Classification Error 0.4 0.15 0.2 0.1 0 0.05 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 5 Iterations 5 Iterations x 10 x 10 Figure 2: Numerical results of on-line learning. (Left) total loss against the number of iterations. The dashed line shows the loss bound. (Right) classification error of the nearest neighbor classifier using the learned kernel. The dashed line shows the error by the target kernel. where Xt is a symmetric matrix whose (at, at) and (bt, bt) elements are 0.5, (at, bt) and (bt, at) elements are -0.5, and all the other elements are zero. We consider a controlled experiment in which the distance examples are created from a known target kernel matrix. We used a 52 52 kernel matrix among gyrB proteins of bacteria (d = 52). This data contains three bacteria species (see [12] for details). Each distance example is created by randomly choosing one element of the target kernel. The initial parameter was set as W1 = I/d. When the comparison matrix U is set to the target matrix, LU (S) = 0 and max = 0, because all the distance examples are derived from the target matrix. Therefore we choose learning rate = 2, which minimizes the relative loss bound of Lemma 3.2. The total loss of the kernel matrix sequence obtained by the matrix exponential update is shown in Figure 2 (left). In the plot, we have also shown the relative loss bound. The bound seems to give a reasonably tight performance guarantee--it is about twice the actual total loss. To evaluate the learned kernel matrix, the prediction accuracy of bacteria species by the nearest neighbor classifier is calculated (Figure 2, right), where the 52 proteins are randomly divided into 50% training and 50% testing data. The value shown in the plot is the test error averaged over 10 different divisions. It took a large number of iterations ( 2 105) for the error rate to converge to the level of the target kernel. In practice one can often increase the learning rate for faster convergence, but here we chose the small rate suggested by our analysis to check the tightness of the bound. Kernel learning by Bregman projection Next, let us consider a batch learning sce- nario where we have a set of qualitative distance evaluations (i.e. inequality constraints). Given n pairs of similar objects {aj, bj}nj=1, the inequality constraints are constructed as xaj - xbj , j = 1, . . ., n, where is a predetermined constant. If Xj is de- fined as in the previous section and Cj = Xj - I, the inequalities are then rewritten as tr(WCj) 0,j = 1,...,n. The largest and smallest eigenvalues of any Cj are 1 - and -, respectively. As in the previous section, distance examples are generated from the target kernel matrix between gyrB proteins. Setting = 0.2/d, we collected all object pairs whose distance in the feature space is less than to yield 980 inequalities (n = 980). Figure 3 (left) shows the convergence of the dual objective function as proven in Theo- rem 4.1. The convergence was much faster than the previous experiment, because, in the batch setting, one can choose the most unsatisfied constraint, and optimize the step size as well. Figure 3 (right) shows the classification error of the nearest neighbor classifier. As opposed to the previous experiment, the error rate is higher than that of the target kernel matrix, because substantial amount of information is lost by the conversion to inequality constraints. 55 0.8 50 0.7 45 0.6 40 0.5 35 0.4 Dual Obj 30 0.3 Classification Error 25 0.2 20 0.1 15 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Iterations Iterations Figure 3: Numerical results of Bregman projection. (Left) convergence of the dual objective function. (Right) classification error of the nearest neighbor classifier using the learned kernel. 6 Conclusion We motivated and analyzed a new update for symmetric positive matrices using the von Neumann divergence. We showed that the standard bounds for on-line learning and Boost- ing generalize to the case when the parameters are a symmetric positive definite matrix (of trace one) instead of a probability vector. As in quantum physics, the eigenvalues act as probabilities. Acknowledgment We would like to thank B. Sch olkopf, M. Kawanabe, J. Liao and W.S. Noble for fruitful discussions. M.W. was supported by NSF grant CCR 9821087 and UC Discovery grant LSIT02-10110. K.T. and G.R. gratefully acknowledge partial support from the PASCAL Network of Excellence (EU #506778). Part of this work was done while all three authors were visiting the National ICT Australia in Canberra.

Boosting approaches are based on the idea that high-quality learning algorithms can be formed by repeated use of a "weak-learner", which is required to perform only slightly better than random guessing. It is known that Boosting can lead to drastic improvements compared to the individual weak-learner. For two-class problems it has been shown that the original Boosting algorithm, called AdaBoost, is quite unaffected by overfitting. However, for the case of noisy data, it is also understood that AdaBoost can be improved considerably by introducing some regularization technique. In speech-related problems one often considers multi-class problems and Boosting formulations have been used successfully to solve them. I review existing multi-class boosting algorithms, which have been much less analyzed and explored than the twoclass pendants. In this work I extend these methods to derive new boosting algorithms which are more robust against outliers and noise in the data and are able to exploit prior knowledge about relationships between the classes.

A common way of image denoising is to project a noisy image to the sub- space of admissible images made for instance by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion. We pro- pose a new method to identify the noisy pixels by (cid:1) 1-norm penalization and update the identified pixels only. The identification and updating of noisy pixels are formulated as one linear program which can be solved efficiently. Especially, one can apply the ν-trick to directly specify the fraction of pixels to be reconstructed. Moreover, we extend the linear program to be able to exploit prior knowledge that occlusions often ap- pear in contiguous blocks (e.g. sunglasses on faces). The basic idea is to penalize boundary points and interior points of the occluded area dif- ferently. We are able to show the ν-property also for this extended LP leading a method which is easy to use. Experimental results impressively demonstrate the power of our approach.

We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher's discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.

In this paper we consider formulations of multi-class problems based on a generalized notion of a margin and using output coding. This includes, but is not restricted to, standard multi-class SVM formulations. Differ- ently from many previous approaches we learn the code as well as the embedding function. We illustrate how this can lead to a formulation that allows for solving a wider range of problems with for instance many classes or even “missing classes”. To keep our optimization problems tractable we propose an algorithm capable of solving them using two- class classifiers, similar in spirit to Boosting.

Recently, Jaakkola and Haussler (1999) proposed a method for constructing kernel functions from probabilistic models. Their so-called Fisher kernel has been combined with discriminative classifiers such as support vector machines and applied successfully in, for example, DNA and protein analysis. Whereas the Fisher kernel is calculated from the marginal log-likelihood, we propose the TOP kernel derived; from tangent vectors of posterior log-odds. Furthermore, we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing the TOP kernel. In experiments, our new discriminative TOP kernel compares favorably to the Fisher kernel.

We show via an equivalence of mathematical programs that a support vector (SV) algorithm can be translated into an equivalent boosting-like algorithm and vice versa. We exemplify this translation procedure for a new algorithm: one-class leveraging, starting from the one-class support vector machine (1-SVM). This is a first step toward unsupervised learning in a boosting framework. Building on so-called barrier methods known from the theory of constrained optimization, it returns a function, written as a convex combination of base hypotheses, that characterizes whether a given test point is likely to have been generated from the distribution underlying the training data. Simulations on one-class classification problems demonstrate the usefulness of our approach.

We give an unified convergence analysis of ensemble learning meth- ods including e.g. AdaBoost, Logistic Regression and the Least-Square- Boost algorithm for regression. These methods have in common that they iteratively call a base learning algorithm which returns hypotheses that are then linearly combined. We show that these methods are related to the Gauss-Southwell method known from numerical optimization and state non-asymptotical convergence results for all these methods. Our analysis includes ` 1 -norm regularized cost functions leading to a clean and general way to regularize ensemble learning. 1 Introduction We show convergence rates of ensemble learning methods such as AdaBoost [10], Logistic Regression (LR) [11, 5] and the Least-Square (LS) regression algorithm called LS-Boost [12]. These algorithms have in common that they iteratively call a base learning algorithm L (also called weak learner) on a weighted training sample. The base learner is expected to return in each iteration t a hypothesis ^ h t from some hypothesis set of weak hypotheses H that has small weighted training error. This is the weighted number of false predictions in classification and weighted estimation error in regression. These hypotheses are then linearly combined to form the final hypothesis f ^ (x) =

Recently, Jaakkola and Haussler proposed a method for construct(cid:173) ing kernel functions from probabilistic models. Their so called "Fisher kernel" has been combined with discriminative classifiers such as SVM and applied successfully in e.g. DNA and protein analysis. Whereas the Fisher kernel (FK) is calculated from the marginal log-likelihood, we propose the TOP kernel derived from Tangent vectors Of Posterior log-odds. Furthermore we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing FK and TOP. In experiments our new discriminative TOP kernel compares favorably to the Fisher kernel.

We investigate the following data mining problem from Computational Chemistry: From a large data set of compounds, find those that bind to a target molecule in as few iterations of biological testing as possible. In each iteration a comparatively small batch of compounds is screened for binding to the target. We apply active learning techniques for selecting the successive batches. One selection strategy picks unlabeled examples closest to the maximum margin hyperplane. Another produces many weight vectors by running perceptrons over multiple permutations of the data. Each weight vector prediction and we pick the unlabeled examples for which votes with its the prediction is most evenly split between . For a third selec- tion strategy note that each unlabeled example bisects the version space of consistent weight vectors. We estimate the volume on both sides of the split by bouncing a billiard through the version space and select un- labeled examples that cause the most even split of the version space. We demonstrate that on two data sets provided by DuPont Pharmaceu- ticals that all three selection strategies perform comparably well and are much better than selecting random batches for testing. and

This paper provides an introduction to support vector machines, kernel Fisher discriminant analysis, and kernel principal component analysis, as examples for successful kernel-based learning methods. We first give a short background about Vapnik-Chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations. We illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and DNA analysis.

We investigate a new kernel-based classifier: the Kernel Fisher Discrim(cid:173) inant (KFD). A mathematical programming formulation based on the ob(cid:173) servation that KFD maximizes the average margin permits an interesting modification of the original KFD algorithm yielding the sparse KFD. We find that both, KFD and the proposed sparse KFD, can be understood in an unifying probabilistic context. Furthermore, we show connections to Support Vector Machines and Relevance Vector Machines. From this understanding, we are able to outline an interesting kernel-regression technique based upon the KFD algorithm. Simulations support the use(cid:173) fulness of our approach.

MOTIVATION: In order to extract protein sequences from nucleotide sequences, it is an important step to recognize points at which regions start that code for proteins. These points are called translation initiation sites (TIS). RESULTS: The task of finding TIS can be modeled as a classification problem. We demonstrate the applicability of support vector machines for this task, and show how to incorporate prior biological knowledge by engineering an appropriate kernel function. With the described techniques the recognition performance can be improved by 26% over leading existing approaches. We provide evidence that existing related methods (e.g. ESTScan) could profit from advanced TIS recognition.

This paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector (SV) kernel functions. We first discuss the geometry of feature space. In particular, we review what is known about the shape of the image of input space under the feature space map, and how this influences the capacity of SV methods. Following this, we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel, using the example of the class of inhomogeneous polynomial kernels, which are often used in SV pattern recognition. We then discuss the connection between feature space and input space by dealing with the question of how one can, given some vector in feature space, find a preimage (exact or approximate) in input space. We describe algorithms to tackle this issue, and show their utility in two applications of kernel methods. First, we use it to reduce the computational complexity of SV decision functions; second, we combine it with the Kernel PCA algorithm, thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real-world data.