BACKGROUND: Accurate identification of translation initiation sites is essential for the proper translation of mRNA into functional proteins. In eukaryotes, the choice of the translation initiation site is influenced by multiple factors, including its proximity to the 5[Formula: see text] end and the local start codon context. Translation initiation sites mark the transition from non-coding to coding regions. This fact motivates the expectation that the upstream sequence, if translated, would assemble a nonsensical order of amino acids, while the downstream sequence would correspond to the structured beginning of a protein. This distinction suggests potential for predicting translation initiation sites using a protein language model. RESULTS: We present NetStart 2.0, a deep learning-based model that integrates the ESM-2 protein language model with the local sequence context to predict translation initiation sites across a broad range of eukaryotic species. NetStart 2.0 was trained as a single model across multiple species, and despite the broad phylogenetic diversity represented in the training data, it consistently relied on features marking the transition from non-coding to coding regions. CONCLUSION: By leveraging "protein-ness", NetStart 2.0 achieves state-of-the-art performance in predicting translation initiation sites across a diverse range of eukaryotic species. This success underscores the potential of protein language models to bridge transcript- and peptide-level information in complex biological prediction tasks. The NetStart 2.0 webserver is available at: https://services.healthtech.dtu.dk/services/NetStart-2.0/ .

The genome sequence contains the blueprint for governing cellular processes. While the availability of genomes has vastly increased over the last decades, experimental annotation of the various functional, non-coding and regulatory elements encoded in the DNA sequence remains both expensive and challenging. This has sparked interest in unsupervised language modeling of genomic DNA, a paradigm that has seen great success for protein sequence data. Although various DNA language models have been proposed, evaluation tasks often differ between individual works, and might not fully recapitulate the fundamental challenges of genome annotation, including the length, scale and sparsity of the data. In this study, we introduce **BEND**, a **BEN**chmark for **D**NA language models, featuring a collection of realistic and biologically meaningful downstream tasks defined on the human genome. We find that embeddings from current DNA LMs can approach performance of expert methods on some tasks, but only capture limited information about long-range features. BEND is available at https://github.com/frederikkemarin/BEND.

Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditionals in the generative process and efficient computation of the loss as independent terms over the hierarchy. We consider two changes to the diffusion model that retain these advantages while adding flexibility to the model. Firstly, we introduce a data and depth-dependent mean function in the diffusion process, which leads to a modified diffusion loss. Our proposed framework, DiffEnc, achieves a statistically significant improvement in likelihood on CIFAR-10. Secondly, we let the ratio of the noise variance of the reverse encoder process and the generative process be a free weight parameter rather than being fixed to one. This leads to theoretical insights: For a finite depth hierarchy, the evidence lower bound (ELBO) can be used as an objective for a weighted diffusion loss approach and for optimizing the noise schedule specifically for inference. For the infinite-depth hierarchy, on the other hand, the weight parameter has to be one to have a well-defined ELBO.

MOTIVATION: Protein subcellular location prediction is a widely explored task in bioinformatics because of its importance in proteomics research. We propose DeepLocPro, an extension to the popular method DeepLoc, tailored specifically to archaeal and bacterial organisms. RESULTS: DeepLocPro is a multiclass subcellular location prediction tool for prokaryotic proteins, trained on experimentally verified data curated from UniProt and PSORTdb. DeepLocPro compares favorably to the PSORTb 3.0 ensemble method, surpassing its performance across multiple metrics in our benchmark experiment. AVAILABILITY AND IMPLEMENTATION: The DeepLocPro prediction tool is available online at https://ku.biolib.com/deeplocpro and https://services.healthtech.dtu.dk/services/DeepLocPro-1.0/.

MOTIVATION: Accurate prediction of RNA subcellular localization plays an important role in understanding cellular processes and functions. Although post-transcriptional processes are governed by trans-acting RNA binding proteins (RBPs) through interaction with cis-regulatory RNA motifs, current methods do not incorporate RBP-binding information. RESULTS: In this article, we propose DeepLocRNA, an interpretable deep-learning model that leverages a pre-trained multi-task RBP-binding prediction model to predict the subcellular localization of RNA molecules via fine-tuning. We constructed DeepLocRNA using a comprehensive dataset with variant RNA types and evaluated it on the held-out dataset. Our model achieved state-of-the-art performance in predicting RNA subcellular localization in mRNA and miRNA. It has also demonstrated great generalization capabilities, performing well on both human and mouse RNA. Additionally, a motif analysis was performed to enhance the interpretability of the model, highlighting signal factors that contributed to the predictions. The proposed model provides general and powerful prediction abilities for different RNA types and species, offering valuable insights into the localization patterns of RNA molecules and contributing to our understanding of cellular processes at the molecular level. A user-friendly web server is available at: https://biolib.com/KU/DeepLocRNA/.

Zero-shot learning models achieve remarkable results on image classification for samples from classes that were not seen during training. However, such models must be trained from scratch with specialised methods: therefore, access to a training dataset is required when the need for zero-shot classification arises. In this paper, we aim to equip pre-trained models with zero-shot classification capabilities without the use of image data. We achieve this with our proposed Image-free Classifier Injection with Semantics (ICIS) that injects classifiers for new, unseen classes into pre-trained classification models in a post-hoc fashion without relying on image data. Instead, the existing classifier weights and simple class-wise descriptors, such as class names or attributes, are used. ICIS has two encoder-decoder networks that learn to reconstruct classifier weights from descriptors (and vice versa), exploiting (cross-)reconstruction and cosine losses to regularise the decoding process. Notably, ICIS can be cheaply trained and applied directly on top of pre-trained classification models. Experiments on benchmark ZSL datasets show that ICIS produces unseen classifier weights that achieve strong (generalised) zero-shot classification performance. Code is available at https://github.com/ExplainableML/ImageFreeZSL.

The recent advances in neural language models have also been successfully applied to the field of chemistry, offering generative solutions for classical problems in molecular design and synthesis planning. These new methods have the potential to fuel a new era of data-driven automation in scientific discovery. However, specialized models are still typically required for each task, leading to the need for problem-specific fine-tuning and neglecting task interrelations. The main obstacle in this field is the lack of a unified representation between natural language and chemical representations, complicating and limiting human-machine interaction. Here, we propose the first multi-domain, multi-task language model that can solve a wide range of tasks in both the chemical and natural language domains. Our model can handle chemical and natural language concurrently, without requiring expensive pre-training on single domains or task-specific models. Interestingly, sharing weights across domains remarkably improves our model when benchmarked against state-of-the-art baselines on single-domain and cross-domain tasks. In particular, sharing information across domains and tasks gives rise to large improvements in cross-domain tasks, the magnitude of which increase with scale, as measured by more than a dozen of relevant metrics. Our work suggests that such models can robustly and efficiently accelerate discovery in physical sciences by superseding problem-specific fine-tuning and enhancing human-model interactions.

Retrieval-augmented models have proven to be effective in natural language processing tasks, yet there remains a lack of research on their optimization using variational inference. We introduce the Variational Open-Domain (VOD) framework for end-to-end training and evaluation of retrieval-augmented models, focusing on open-domain question answering and language modelling. The VOD objective, a self-normalized estimate of the Rényi variational bound, approximates the task marginal likelihood and is evaluated under samples drawn from an auxiliary sampling distribution (cached retriever and/or approximate posterior). It remains tractable, even for retriever distributions defined on large corpora. We demonstrate VOD's versatility by training reader-retriever BERT-sized models on multiple-choice medical exam questions. On the MedMCQA dataset, we outperform the domain-tuned Med-PaLM by +5.3% despite using 2.500$\times$ fewer parameters. Our retrieval-augmented BioLinkBERT model scored 62.9% on the MedMCQA and 55.0% on the MedQA-USMLE. Last, we show the effectiveness of our learned retriever component in the context of medical semantic search.

Generative models have significantly influenced both vision and language domains, ushering in innovative multimodal applications. Although these achievements have motivated exploration in scientific and engineering fields, challenges emerge, particularly in constrained settings with limited data where precision is crucial. Traditional engineering optimization methods rooted in physics often surpass generative models in these contexts. To address these challenges, we introduce Diffusion Optimization Models (DOM) and Trajectory Alignment (TA), a learning framework that demonstrates the efficacy of aligning the sampling trajectory of diffusion models with the trajectory derived from physics-based iterative optimization methods. This alignment ensures that the sampling process remains grounded in the underlying physical principles. This alignment eliminates the need for costly preprocessing, external surrogate models, or extra labeled data, generating feasible and high-performance designs efficiently. We apply our framework to structural topology optimization, a fundamental problem in mechanical design, evaluating its performance on in- and out-of-distribution configurations. Our results demonstrate that TA outperforms state-of-the-art deep generative models on in-distribution configurations and halves the inference computational cost. When coupled with a few steps of optimization, it also improves manufacturability for out-of-distribution conditions. DOM's efficiency and performance improvements significantly expedite design processes and steer them toward optimal and manufacturable outcomes, highlighting the potential of generative models in data-driven design.

Computing properties of molecular systems rely on estimating expectations of the (unnormalized) Boltzmann distribution. Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities. However, stable simulations rely on very small integration time-steps ($10^{-15}\,\mathrm{s}$), whereas convergence of some moments, e.g. binding free energy or rates, might rely on sampling processes on time-scales as long as $10^{-1}\, \mathrm{s}$, and these simulations must be repeated for every molecular system independently. Here, we present Implicit Transfer Operator (ITO) Learning, a framework to learn surrogates of the simulation process with multiple time-resolutions. We implement ITO with denoising diffusion probabilistic models with a new SE(3) equivariant architecture and show the resulting models can generate self-consistent stochastic dynamics across multiple time-scales, even when the system is only partially observed. Finally, we present a coarse-grained CG-SE3-ITO model which can quantitatively model all-atom molecular dynamics using only coarse molecular representations. As such, ITO provides an important step towards multiple time- and space-resolution acceleration of MD. Code is available at \href{https://github.com/olsson-group/ito}{https://github.com/olsson-group/ito}.

RNA localization is essential for regulating spatial translation, where RNAs are trafficked to their target locations via various biological mechanisms. In this review, we discuss RNA localization in the context of molecular mechanisms, experimental techniques and machine learning-based prediction tools. Three main types of molecular mechanisms that control the localization of RNA to distinct cellular compartments are reviewed, including directed transport, protection from mRNA degradation, as well as diffusion and local entrapment. Advances in experimental methods, both image and sequence based, provide substantial data resources, which allow for the design of powerful machine learning models to predict RNA localizations. We review the publicly available predictive tools to serve as a guide for users and inspire developers to build more effective prediction models. Finally, we provide an overview of multimodal learning, which may provide a new avenue for the prediction of RNA localization.

MOTIVATION: Peptides are ubiquitous throughout life and involved in a wide range of biological processes, ranging from neural signaling in higher organisms to antimicrobial peptides in bacteria. Many peptides are generated post-translationally by cleavage of precursor proteins and can thus not be detected directly from genomics data, as the specificities of the responsible proteases are often not completely understood. RESULTS: We present DeepPeptide, a deep learning model that predicts cleaved peptides directly from the amino acid sequence. DeepPeptide shows both improved precision and recall for peptide detection compared to previous methodology. We show that the model is capable of identifying peptides in underannotated proteomes. AVAILABILITY AND IMPLEMENTATION: DeepPeptide is available online at ku.biolib.com/DeepPeptide.

Dermatological diagnosis automation is essential in addressing the high prevalence of skin diseases and critical shortage of dermatologists. Despite approaching expert-level diagnosis performance, convolutional neural network (ConvNet) adoption in clinical practice is impeded by their limited explainability, and by subjective, expensive explainability validations. We introduce DermX, an end-to-end framework for explainable automated dermatological diagnosis. DermX is a clinically-inspired explainable dermatological diagnosis ConvNet, trained using DermXDB, a 554 image dataset annotated by eight dermatologists with diagnoses, supporting explanations, and explanation attention maps. DermX+ extends DermX with guided attention training for explanation attention maps. Both methods achieve near-expert diagnosis performance, with DermX, DermX+, and dermatologist F1 scores of 0.79, 0.79, and 0.87, respectively. We assess the explanation performance in terms of identification and localization by comparing model-selected with dermatologist-selected explanations, and gradient-weighted class-activation maps with dermatologist explanation maps, respectively. DermX obtained an identification F1 score of 0.77, while DermX+ obtained 0.79. The localization F1 score is 0.39 for DermX and 0.35 for DermX+. These results show that explainability does not necessarily come at the expense of predictive power, as our high-performance models provide expert-inspired explanations for their diagnoses without lowering their diagnosis performance.

The idea behind object-centric representation learning is that natural scenes can better be modeled as compositions of objects and their relations as opposed to distributed representations. This inductive bias can be injected into neural networks to potentially improve systematic generalization and performance of downstream tasks in scenes with multiple objects. In this paper, we train state-of-the-art unsupervised models on five common multi-object datasets and evaluate segmentation metrics and downstream object property prediction. In addition, we study generalization and robustness by investigating the settings where either a single object is out of distribution – e.g., having an unseen color, texture, or shape – or global properties of the scene are altered – e.g., by occlusions, cropping, or increasing the number of objects. From our experimental study, we find object-centric representations to be useful for downstream tasks and generally robust to most distribution shifts affecting objects. However, when the distribution shift affects the input in a less structured manner, robustness in terms of segmentation and downstream task performance may vary significantly across models and distribution shifts.

A few-shot generative model should be able to generate data from a novel distribution by only observing a limited set of examples. In few-shot learning the model is trained on data from many sets from distributions sharing some underlying properties such as sets of characters from different alphabets or objects from different categories. We extend current latent variable models for sets to a fully hierarchical approach with an attention-based point to set-level aggregation and call our method SCHA-VAE for Set-Context-Hierarchical-Aggregation Variational Autoencoder. We explore likelihood-based model comparison, iterative data sampling, and adaptation-free out-of-distribution generalization. Our results show that the hierarchical formulation better captures the intrinsic variability within the sets in the small data regime. This work generalizes deep latent variable approaches to few-shot learning, taking a step toward large-scale few-shot generation with a formulation that readily works with current state-of-the-art deep generative models.

This paper introduces novel results for the score-function gradient estimator of the importance-weighted variational bound (IWAE). We prove that in the limit of large $K$ (number of importance samples) one can choose the control variate such that the Signal-to-Noise ratio (SNR) of the estimator grows as $\sqrt{K}$. This is in contrast to the standard pathwise gradient estimator where the SNR decreases as $1/\sqrt{K}$. Based on our theoretical findings we develop a novel control variate that extends on VIMCO. Empirically, for the training of both continuous and discrete generative models, the proposed method yields superior variance reduction, resulting in an SNR for IWAE that increases with $K$ without relying on the reparameterization trick. The novel estimator is competitive with state-of-the-art reparameterization-free gradient estimators such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective (TVO) when training generative models.

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model densities whereas VAEs learn stochastic transformations that are non-invertible and thus typically do not provide tractable estimates of the marginal likelihood. In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows. SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations, wherein the transformations are deterministic in one direction -- thereby allowing exact likelihood computation, and stochastic in the reverse direction -- hence providing a lower bound on the corresponding likelihood. We show that several recently proposed methods, including dequantization and augmented normalizing flows, can be expressed as SurVAE Flows. Finally, we introduce common operations such as the max value, the absolute value, sorting and stochastic permutation as composable layers in SurVAE Flows.

Flow models have recently made great progress at modeling ordinal discrete data such as images and audio. Due to the continuous nature of flow models, dequantization is typically applied when using them for such discrete data, resulting in lower bound estimates of the likelihood. In this paper, we introduce subset flows, a class of flows that can tractably transform finite volumes and thus allow exact computation of likelihoods for discrete data. Based on subset flows, we identify ordinal discrete autoregressive models, including WaveNets, PixelCNNs and Transformers, as single-layer flows. We use the flow formulation to compare models trained and evaluated with either the exact likelihood or its dequantization lower bound. Finally, we study multilayer flows composed of PixelCNNs and non-autoregressive coupling layers and demonstrate state-of-the-art results on CIFAR-10 for flow models trained with dequantization.

MOTIVATION: Models for analysing and making relevant biological inferences from massive amounts of complex single-cell transcriptomic data typically require several individual data-processing steps, each with their own set of hyperparameter choices. With deep generative models one can work directly with count data, make likelihood-based model comparison, learn a latent representation of the cells and capture more of the variability in different cell populations. RESULTS: We propose a novel method based on variational auto-encoders (VAEs) for analysis of single-cell RNA sequencing (scRNA-seq) data. It avoids data preprocessing by using raw count data as input and can robustly estimate the expected gene expression levels and a latent representation for each cell. We tested several count likelihood functions and a variant of the VAE that has a priori clustering in the latent space. We show for several scRNA-seq datasets that our method outperforms recently proposed scRNA-seq methods in clustering cells and that the resulting clusters reflect cell types. AVAILABILITY AND IMPLEMENTATION: Our method, called scVAE, is implemented in Python using the TensorFlow machine-learning library, and it is freely available at https://github.com/scvae/scvae. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Document information extraction tasks performed by humans create data consisting of a PDF or document image input, and extracted string outputs. This end-to-end data is naturally consumed and produced when performing the task because it is valuable in and of itself. It is naturally available, at no additional cost. Unfortunately, state-of-the-art word classification methods for information extraction cannot use this data, instead requiring word-level labels which are expensive to create and consequently not available for many real life tasks. In this paper we propose the Attend, Copy, Parse architecture, a deep neural network model that can be trained directly on end-to-end data, bypassing the need for word-level labels. We evaluate the proposed architecture on a large diverse set of invoices, and outperform a state-of-the-art production system based on word classification. We believe our proposed architecture can be used on many real life information extraction tasks where word classification cannot be used due to a lack of the required word-level labels.

With the introduction of the variational autoencoder (VAE), probabilistic latent variable models have received renewed attention as powerful generative models. However, their performance in terms of test likelihood and quality of generated samples has been surpassed by autoregressive models without stochastic units. Furthermore, flow-based models have recently been shown to be an attractive alternative that scales well to high-dimensional data. In this paper we close the performance gap by constructing VAE models that can effectively utilize a deep hierarchy of stochastic variables and model complex covariance structures. We introduce the Bidirectional-Inference Variational Autoencoder (BIVA), characterized by a skip-connected generative model and an inference network formed by a bidirectional stochastic inference path. We show that BIVA reaches state-of-the-art test likelihoods, generates sharp and coherent natural images, and uses the hierarchy of latent variables to capture different aspects of the data distribution. We observe that BIVA, in contrast to recent results, can be used for anomaly detection. We attribute this to the hierarchy of latent variables which is able to extract high-level semantic features. Finally, we extend BIVA to semi-supervised classification tasks and show that it performs comparably to state-of-the-art results by generative adversarial networks.

BACKGROUND: Unsupervised machine learning methods (deep learning) have shown their usefulness with noisy single cell mRNA-sequencing data (scRNA-seq), where the models generalize well, despite the zero-inflation of the data. A class of neural networks, namely autoencoders, has been useful for denoising of single cell data, imputation of missing values and dimensionality reduction. RESULTS: Here, we present a striking feature with the potential to greatly increase the usability of autoencoders: With specialized training, the autoencoder is not only able to generalize over the data, but also to tease apart biologically meaningful modules, which we found encoded in the representation layer of the network. Our model can, from scRNA-seq data, delineate biological meaningful modules that govern a dataset, as well as give information as to which modules are active in each single cell. Importantly, most of these modules can be explained by known biological functions, as provided by the Hallmark gene sets. CONCLUSIONS: We discover that tailored training of an autoencoder makes it possible to deconvolute biological modules inherent in the data, without any assumptions. By comparisons with gene signatures of canonical pathways we see that the modules are directly interpretable. The scope of this discovery has important implications, as it makes it possible to outline the drivers behind a given effect of a cell. In comparison with other dimensionality reduction methods, or supervised models for classification, our approach has the benefit of both handling well the zero-inflated nature of scRNA-seq, and validating that the model captures relevant information, by establishing a link between input and decoded data. In perspective, our model in combination with clustering methods is able to provide information about which subtype a given single cell belongs to, as well as which biological functions determine that membership.

Human brain activity as measured by fMRI exhibits strong correlations between brain regions which are believed to vary over time. Importantly, dynamic connectivity has been linked to individual differences in physiology, psychology and behavior, and has shown promise as a biomarker for disease. The state of the art in computational neuroimaging is to estimate the brain networks as relatively short sliding window covariance matrices, which leads to high variance estimates, thereby resulting in high overall error. This manuscript proposes a novel Bayesian model for dynamic brain connectivity. Motivated by the underlying neuroscience, the model estimates covariances which vary smoothly over time, with an instantaneous decomposition into a collection of spatially sparse components – resulting in parsimonious and highly interpretable estimates of dynamic brain connectivity. Simulated results are presented to illustrate the performance of the model even when it is mis-specified. For real brain imaging data with unknown ground truth, in addition to qualitative evaluation, we devise a simple classification task which suggests that the estimated brain networks better capture the underlying structure.

This paper is concerned with learning to solve tasks that require a chain of interde- pendent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational net- work, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]’s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the art results on the bAbI textual question-answering dataset with the recurrent relational network, consistently solving 20/20 tasks. As bAbI is not particularly challenging from a relational reasoning point of view, we introduce Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the Pretty- CLEVR set-up, we can vary the question to control for the number of relational reasoning steps that are required to obtain the answer. Using Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational and recurrent relational networks. Finally, we show how recurrent relational networks can learn to solve Sudoku puzzles from supervised training data, a challenging task requiring upwards of 64 steps of relational reasoning. We achieve state-of-the-art results amongst comparable methods by solving 96.6% of the hardest Sudoku puzzles.

We present CloudScan; an invoice analysis system that requires zero configuration or upfront annotation. In contrast to previous work, CloudScan does not rely on templates of invoice layout, instead it learns a single global model of invoices that naturally generalizes to unseen invoice layouts. The model is trained using data automatically extracted from end-user provided feedback. This automatic training data extraction removes the requirement for users to annotate the data precisely. We describe a recurrent neural network model that can capture long range context and compare it to a baseline logistic regression model corresponding to the current CloudScan production system. We train and evaluate the system on 8 important fields using a dataset of 326,471 invoices. The recurrent neural network and baseline model achieve 0.891 and 0.887 average F1 scores respectively on seen invoice layouts. For the harder task of unseen invoice layouts, the recurrent neural network model outperforms the baseline with 0.840 average F1 compared to 0.788.

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By design, the fixed points of the algorithm obey the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way that the resulting fields become Gaussian random variables allowing for an explicit analysis. The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.

This paper takes a step towards temporal reasoning in a dynamically changing video, not in the pixel space that constitutes its frames, but in a latent space that describes the non-linear dynamics of the objects in its world. We introduce the Kalman variational auto-encoder, a framework for unsupervised learning of sequential data that disentangles two latent representations: an object's representation, coming from a recognition model, and a latent state describing its dynamics. As a result, the evolution of the world can be imagined and missing data imputed, both without the need to generate high dimensional frames at each time step. The model is trained end-to-end on videos of a variety of simulated physical systems, and outperforms competing methods in generative and missing data imputation tasks.

We present hash embeddings, an efficient method for representing words in a continuous vector form. A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function (the hashing trick). In hash embeddings each token is represented by $k$ $d$-dimensional embeddings vectors and one $k$ dimensional weight vector. The final $d$ dimensional representation of the token is the product of the two. Rather than fitting the embedding vectors for each token these are selected by the hashing trick from a shared pool of $B$ embedding vectors. Our experiments show that hash embeddings can easily deal with huge vocabularies consisting of millions tokens. When using a hash embedding there is no need to create a dictionary before training nor to perform any kind of vocabulary pruning after training. We show that models trained using hash embeddings exhibit at least the same level of performance as models trained using regular embeddings across a wide range of tasks. Furthermore, the number of parameters needed by such an embedding is only a fraction of what is required by a regular embedding. Since standard embeddings and embeddings constructed using the hashing trick are actually just special cases of a hash embedding, hash embeddings can be considered an extension and improvement over the existing regular embedding types.

MOTIVATION: The prediction of eukaryotic protein subcellular localization is a well-studied topic in bioinformatics due to its relevance in proteomics research. Many machine learning methods have been successfully applied in this task, but in most of them, predictions rely on annotation of homologues from knowledge databases. For novel proteins where no annotated homologues exist, and for predicting the effects of sequence variants, it is desirable to have methods for predicting protein properties from sequence information only. RESULTS: Here, we present a prediction algorithm using deep neural networks to predict protein subcellular localization relying only on sequence information. At its core, the prediction model uses a recurrent neural network that processes the entire protein sequence and an attention mechanism identifying protein regions important for the subcellular localization. The model was trained and tested on a protein dataset extracted from one of the latest UniProt releases, in which experimentally annotated proteins follow more stringent criteria than previously. We demonstrate that our model achieves a good accuracy (78% for 10 categories; 92% for membrane-bound or soluble), outperforming current state-of-the-art algorithms, including those relying on homology information. AVAILABILITY AND IMPLEMENTATION: The method is available as a web server at http://www.cbs.dtu.dk/services/DeepLoc. Example code is available at https://github.com/JJAlmagro/subcellular_localization. The dataset is available at http://www.cbs.dtu.dk/services/DeepLoc/data.php. CONTACT: [email protected].

Bioinformatics (2017) doi: 10.1093/bioinformatics/btx431 The authors of the above article wish to inform readers that the following change has been made post-publication: Sentence “If the Gorodkin measure is squared, the ‘generalized squared correlation’ (GC2) of Baldi et al. (2000) is obtained” has now been corrected to: “For K = 2, the Gorodkin measure squared is the ‘generalized squared correlation’ (GC2) of Baldi et al. (2000).”

MOTIVATION: Deep neural network architectures such as convolutional and long short-term memory networks have become increasingly popular as machine learning tools during the recent years. The availability of greater computational resources, more data, new algorithms for training deep models and easy to use libraries for implementation and training of neural networks are the drivers of this development. The use of deep learning has been especially successful in image recognition; and the development of tools, applications and code examples are in most cases centered within this field rather than within biology. RESULTS: Here, we aim to further the development of deep learning methods within biology by providing application examples and ready to apply and adapt code templates. Given such examples, we illustrate how architectures consisting of convolutional and long short-term memory neural networks can relatively easily be designed and trained to state-of-the-art performance on three biological sequence problems: prediction of subcellular localization, protein secondary structure and the binding of peptides to MHC Class II molecules. AVAILABILITY AND IMPLEMENTATION: All implementations and datasets are available online to the scientific community at https://github.com/vanessajurtz/lasagne4bio. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In this work, we address the problem of solving a series of underdetermined linear inverse problemblems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets.

Bayesian generalised ensemble (BayesGE) is a new method that addresses two major drawbacks of standard Markov chain Monte Carlo algorithms for inference in high-dimensional probability models: inapplicability to estimate the partition function and poor mixing properties. BayesGE uses a Bayesian approach to iteratively update the belief about the density of states (distribution of the log likelihood under the prior) for the model, with the dual purpose of enhancing the sampling efficiency and making the estimation of the partition function tractable. We benchmark BayesGE on Ising and Potts systems and show that it compares favourably to existing state-of-the-art methods.

We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder (VAE) with a generative adversarial network (GAN) we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic.

Deep generative models parameterized by neural networks have recently achieved state-of-the-art performance in unsupervised and semi-supervised learning. We extend deep generative models with auxiliary variables which improves the variational approximation. The auxiliary variables leave the generative model unchanged but make the variational distribution more expressive. Inspired by the structure of the auxiliary variable we also propose a model with two stochastic layers and skip connections. Our findings suggest that more expressive and properly specified deep generative models converge faster with better results. We show state-of-the-art performance within semi-supervised learning on MNIST, SVHN and NORB datasets.

How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model’s posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over the uncertainty in a latent path, like a state space model, we improve the state of the art results on the Blizzard and TIMIT speech modeling data sets by a large margin, while achieving comparable performances to competing methods on polyphonic music modeling.

Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch-normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several Bayesian leave-one-out (LOO) cross-validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data. Our main objective is to assess the accuracy of the approximative LOO cross-validation estimators. That is, for each method (Laplace and EP) we compare the approximate fast computation with the exact brute force LOO computation. Secondarily, we evaluate the accuracy of the Laplace and EP approximations themselves against a ground truth established through extensive Markov chain Monte Carlo simulation. Our empirical results show that the approach based upon a Gaussian approximation to the LOO marginal distribution (the so-called cavity distribution) gives the most accurate and reliable results among the fast methods.

Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.

We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.

BACKGROUND: A central question in molecular biology is how transcriptional regulatory elements (TREs) act in combination. Recent high-throughput data provide us with the location of multiple regulatory regions for multiple regulators, and thus with the possibility of analyzing the multivariate distribution of the occurrences of these TREs along the genome. RESULTS: We present a model of TRE occurrences known as the Hawkes process. We illustrate the use of this model by analyzing two different publically available data sets. We are able to model, in detail, how the occurrence of one TRE is affected by the occurrences of others, and we can test a range of natural hypotheses about the dependencies among the TRE occurrences. In contrast to earlier efforts, pre-processing steps such as clustering or binning are not needed, and we thus retain information about the dependencies among the TREs that is otherwise lost. For each of the two data sets we provide two results: first, a qualitative description of the dependencies among the occurrences of the TREs, and second, quantitative results on the favored or avoided distances between the different TREs. CONCLUSIONS: The Hawkes process is a novel way of modeling the joint occurrences of multiple TREs along the genome that is capable of providing new insights into dependencies among elements involved in transcriptional regulation. The method is available as an R package from http://www.math.ku.dk/~richard/ppstat/.

In this paper we present a novel approach to learn directed acyclic graphs (DAG) and factor models within the same framework while also allowing for model comparison between them. For this purpose, we exploit the connection between factor models and DAGs to propose Bayesian hierarchies based on spike and slab priors to promote sparsity, heavy-tailed priors to ensure identifiability and predictive densities to perform the model comparison. We require identifiability to be able to produce variable orderings leading to valid DAGs and sparsity to learn the structures. The effectiveness of our approach is demonstrated through extensive experiments on artificial and biological data showing that our approach outperform a number of state of the art methods.

A major goal in post-genome biology is the complete mapping of the gene regulatory networks for every organism. Identification of regulatory elements is a prerequisite for realizing this ambitious goal. A common problem is finding regulatory patterns in promoters of a group of co-expressed genes, but contemporary methods are challenged by the size and diversity of regulatory regions in higher metazoans. Two key issues are the small amount of information contained in a pattern compared to the large promoter regions and the repetitive characteristics of genomic DNA, which both lead to "pattern drowning". We present a new computational method for identifying transcription factor binding sites in promoters using a discriminatory approach with a large negative set encompassing a significant sample of the promoters from the relevant genome. The sequences are described by a probabilistic model and the most discriminatory motifs are identified by maximizing the probability of the sets given the motif model and prior probabilities of motif occurrences in both sets. Due to the large number of promoters in the negative set, an enhanced suffix array is used to improve speed and performance. Using our method, we demonstrate higher accuracy than the best of contemporary methods, high robustness when extending the length of the input sequences and a strong correlation between our objective function and the correct solution. Using a large background set of real promoters instead of a simplified model leads to higher discriminatory power and markedly reduces the need for repeat masking; a common pre-processing step for other pattern finders.

We develop as series of corrections to Expectation Propagation (EP), which is one of the most popular methods for approximate probabilistic inference. These corrections can lead to improvements of the inference approximation or serve as a sanity check, indicating when EP yields unrealiable results.

In this paper, prefiltering techniques for sphere detection (SD) in frequency-selective channels are examined. It is shown that a link between QL-factorization of the channel matrix and minimum-phase prefiltering exists. As a result, it is possible to regard SD as a generalization of traditional reduced- state sequence estimation, providing a unifying framework for the two detection methods. It is illustrated how minimum-phase prefiltering or the linear minimum mean-square error decision feedback equalization (LMMSE-DFE) forward filter is capable of reducing the complexity of sphere detectors significantly, while still obtaining near-optimal performance. The significant reduction in complexity is obtained as prefiltering enables earlier decision making in SD. Simulations carried out in an EDGE system confirm that prefiltering leads to a considerable complexity reduction for sphere detectors.

A speech model parameterized by formant frequencies, formant bandwidths, and formant gains is proposed. Inference in the model is made by particle filtering for the application of speech enhancement. The advantage of the proposed parameterization over existing parameterizations based on auto-regressive (AR) coefficients or reflection coefficients is the smooth time-varying behavior of the parameters and their loose coupling. Experiments confirm this advantage both in terms of parameter estimation and SNR improvement.

MOTIVATION: Hierarchical and relocation clustering (e.g. K-means and self-organizing maps) have been successful tools in the display and analysis of whole genome DNA microarray expression data. However, the results of hierarchical clustering are sensitive to outliers, and most relocation methods give results which are dependent on the initialization of the algorithm. Therefore, it is difficult to assess the significance of the results. We have developed a consensus clustering algorithm, where the final result is averaged over multiple clustering runs, giving a robust and reproducible clustering, capable of capturing small signal variations. The algorithm preserves valuable properties of hierarchical clustering, which is useful for visualization and interpretation of the results. RESULTS: We show for the first time that one can take advantage of multiple clustering runs in DNA microarray analysis by collecting re-occurring clustering patterns in a co-occurrence matrix. The results show that consensus clustering obtained from clustering multiple times with Variational Bayes Mixtures of Gaussians or K-means significantly reduces the classification error rate for a simulated dataset. The method is flexible and it is possible to find consensus clusters from different clustering algorithms. Thus, the algorithm can be used as a framework to test in a quantitative manner the homogeneity of different clustering algorithms. We compare the method with a number of state-of-the-art clustering methods. It is shown that the method is robust and gives low classification error rates for a realistic, simulated dataset. The algorithm is also demonstrated for real datasets. It is shown that more biological meaningful transcriptional patterns can be found without conservative statistical or fold-change exclusion of data. AVAILABILITY: Matlab source code for the clustering algorithm ClusterLustre, and the simulated dataset for testing are available upon request from T.G. and O.W.

We investigate two techniques for independent component analysis which use the expectation-maximization algorithm. Analysis and simulations show that convergence becomes extraordinarily slow for almost all cases, compared to other optimization techniques. The two alternatives considered are "adaptive overrelaxed EM" and Ucminf (a BFGS with soft line search), which both improves the convergence dramatically with little or no extra analytical work. We discuss the generality and perspectives of the findings.

We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood as replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability distributions which are made consistent on a set of moments and encode different features of the original intractable distribution. In this way we are able to use Gaussian approximations for models with discrete or bounded variables which allow us to include non-trivial correlations. These are neglected in many other methods. We test the framework on toy benchmark problems for binary variables on fully connected graphs and 2D grids and compare with other methods, such as loopy belief propagation. Good performance is already achieved by using single nodes as tractable substructures. Significant improvements are obtained when a spanning tree is used instead.

We analyze convergence of the expectation maximization (EM) and variational Bayes EM (VBEM) schemes for parameter estimation in noisy linear models. The analysis shows that both schemes are inefficient in the low-noise limit. The linear model with additive noise includes as special cases independent component analysis, probabilistic principal component analysis, factor analysis, and Kalman filtering. Hence, the results are relevant for many practical applications.

We propose a simple Bayesian model for performing single channel speech separation using factorized source priors in a sliding window linearly transformed domain. Using a one dimensional mixture of Gaussians to model each band source leads to fast tractable inference for the source signals. Simulations with separation of a male and a female speaker using priors trained on the same speakers show comparable performance with the blind separation approach of G.-J. Jang and T.-W. Lee (see NIPS, vol.15, 2003) with a SNR improvement of 4.9 dB for both the male and female speaker. Mixing coefficients can be estimated quite precisely using ML-II, but the estimation is quite sensitive to the accuracy of the priors as opposed to the source separation quality for known mixing coefficients, which is quite insensitive to the accuracy of the priors. Finally, we discuss how to improve our approach while keeping the complexity low using machine learning and CASA (computational auditory scene analysis) approaches (Jang and Lee, 2003; Roweis, S.T., 2001; Wang, D.L. and Brown, G.J., 1999; Hu, G. and Wang, D., 2003).

We propose a novel a framework for deriving approximations for in- tractable probabilistic models. This framework is based on a free energy (negative log marginal likelihood) and can be seen as a generalization of adaptive TAP [1, 2, 3] and expectation propagation (EP) [4, 5]. The free energy is constructed from two approximating distributions which encode different aspects of the intractable model such a single node con- straints and couplings and are by construction consistent on a chosen set of moments. We test the framework on a difficult benchmark problem with binary variables on fully connected graphs and 2D grid graphs. We find good performance using sets of moments which either specify fac- torized nodes or a spanning tree on the nodes (structured approximation). Surprisingly, the Bethe approximation gives very inferior results even on grids.

A general linear response method for deriving improved estimates of cor- relations in the variational Bayes framework is presented. Three applica- tions are given and it is discussed how to use linear response as a general principle for improving mean field approximations.

In this paper, we consider Tipping’s relevance vector machine (RVM) [1] and formalize an incremental training strategy as a variant of the expectation-maximization (EM) algorithm that we call Subspace EM (SSEM). Working with a subset of active basis functions, the sparsity of the RVM solution will ensure that the number of basis functions and thereby the computational complexity is kept low. We also introduce a mean field approach to the intractable classification model that is ex- pected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case. We test the algorithms on two large data sets with O(103 (cid:0) 104) examples. The re- sults indicate that Bayesian learning of large data sets, e.g. the MNIST database is realistic.

We develop mean-field approaches for probabilistic independent component analysis (ICA). The sources are estimated from the mean of their posterior distribution and the mixing matrix (and noise level) is estimated by maximum a posteriori (MAP). The latter requires the computation of (a good approximation to) the correlations between sources. For this purpose, we investigate three increasingly advanced mean-field methods: the variational (also known as naive mean field) approach, linear response corrections, and an adaptive version of the Thouless, Anderson and Palmer (1977) (TAP) mean-field approach, which is due to Opper and Winther (2001). The resulting algorithms are tested on a number of problems. On synthetic data, the advanced mean-field approaches are able to recover the correct mixing matrix in cases where the variational meanfield theory fails. For handwritten digits, sparse encoding is achieved using nonnegative source and mixing priors. For speech, the mean-field method is able to separate in the underdetermined (overcomplete) case of two sensors and three sources. One major advantage of the proposed method is its generality and algorithmic simplicity. Finally, we point out several possible extensions of the approaches developed here.

The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka’s expectation propa- gation. Lastly, we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classifica- tion and density estimation with Gaussian processes and on an indepen- dent component analysis problem.

We propose a general Bayesian framework for performing independent component analysis (leA) which relies on ensemble learning and lin(cid:173) ear response theory known from statistical physics. We apply it to both discrete and continuous sources. For the continuous source the underde(cid:173) termined (overcomplete) case is studied. The naive mean-field approach fails in this case whereas linear response theory-which gives an improved estimate of covariances-is very efficient. The examples given are for sources without temporal correlations. However, this derivation can eas(cid:173) ily be extended to treat temporal correlations. Finally, the framework offers a simple way of generating new leA algorithms without needing to define the prior distribution of the sources explicitly.

Using statistical mechanics results, I calculate learning curves (average generalization error) for Gaussian processes (GPs) and Bayesian neural networks (NNs) used for regression. Applying the results to learning a teacher defined by a two-layer network, I can directly compare GP and Bayesian NN learning. I find that a GP in general requires CJ (d S )-training examples to learn input features of order s (d is the input dimension), whereas a NN can learn the task with order the number of adjustable weights training examples. Since a GP can be considered as an infinite NN, the results show that even in the Bayesian approach, it is important to limit the complexity of the learning machine. The theoretical findings are confirmed in simulations with analytical GP learning and a NN mean field algorithm.

We derive a mean-field algorithm for binary classification with gaussian processes that is based on the TAP approach originally proposed in statistical physics of disordered systems. The theory also yields an approximate leave-one-out estimator for the generalization error, which is computed with no extra computational cost. We show that from the TAP approach, it is possible to derive both a simpler "naive" mean-field theory and support vector machines (SVMs) as limiting cases. For both mean-field algorithms and support vector machines, simulation results for three small benchmark data sets are presented. They show that one may get state-of-the-art performance by using the leave-one-out estimator for model selection and the built-in leave-one-out estimators are extremely precise when compared to the exact leave-one-out estimate. The second result is taken as strong support for the internal consistency of the mean-field approach.

The optimal brain damage (OBD) scheme of Le Cun, Denker and Solla for pruning of feedforward networks has been implemented and applied to the contiguity classification problem. It is shown that OBD improves the learning curve (the test error as a function of the number of examples). By inspecting the architectures obtained through pruning, it is found that the networks with less parameters have the smallest test error in agreement with "Ockhams Razor". Based on this, we propose a heuristic which selects the smallest successful architecture among a group of pruned networks and we show that it leads to very efficient optimization of the architecture. The validity of the approximations involved in OBD are discussed and it is found that they are surprisingly accurate for the problem studied.