In antimicrobial peptide development, red-blood-cell lysis ($\text{HC}_{50}$) is the principal safety barrier, but existing in silico tools stop at a binary toxicity classification. Here we propose a new method, AmpLyze, that closes this gap by predicting the actual$\text{HC}_{50}$value from protein sequence alone and explaining the residues that drive toxicity. The model couples residue-level ProtT5/ESM2 embeddings with sequence-level descriptors in dual local and global branches, aligned by a cross-attention module and trained with log-cosh loss for robustness to assay noise. The optimal AmpLyze model reaches a PCC of 0.756 and an MSE of 0.987, outperforming classical regressors and the state-of-the-art. Ablations confirm that both branches are essential, and cross-attention adds a further$1 \% \text{PCC}$and 3% MSE improvement. Expected-Gradients attributions reveal known toxicity hotspots and suggest safer substitutions. By turning hemolysis assessment into a quantitative, sequence-based, and interpretable prediction, AmpLyze facilitates AMP design and offers a practical tool for early-stage toxicity screening.

Graph Neural Networks (GNNs) have become important tools for machine learning on graph-structured data. In this paper, we explore the synergistic combination of graph encoding, graph rewiring, and graph attention, by introducing Graph Attention with Stochastic Structures (GRASS), a novel GNN architecture. GRASS utilizes relative random walk probabilities (RRWP) encoding and a novel decomposed variant (D-RRWP) to efficiently capture structural information. It rewires the input graph by superimposing a random regular graph to enhance long-range information propagation. It also employs a novel additive attention mechanism tailored for graph-structured data. Our empirical evaluations demonstrate that GRASS achieves state-of-the-art performance on multiple benchmark datasets, including a 20.3% reduction in mean absolute error on the ZINC dataset.

Recent advances in diffusion models have shown remarkable potential in the conditional generation of novel molecules. These models can be guided in two ways: (i) explicitly, through additional features representing the condition, or (ii) implicitly, using a property predictor. However, training property predictors or conditional diffusion models requires an abundance of labeled data and is inherently challenging in real-world applications. We propose a novel approach that attenuates the limitations of acquiring large labeled datasets by leveraging domain knowledge from quantum chemistry as a non-differentiable oracle to guide an unconditional diffusion model. Instead of relying on neural networks, the oracle provides accurate guidance in the form of estimated gradients, allowing the diffusion process to sample from a conditional distribution specified by quantum chemistry. We show that this results in more precise conditional generation of novel and stable molecular structures. Our experiments demonstrate that our method: (1) significantly reduces atomic forces, enhancing the validity of generated molecules when used for stability optimization; (2) is compatible with both explicit and implicit guidance in diffusion models, enabling joint optimization of molecular properties and stability; and (3) generalizes effectively to molecular optimization tasks beyond stability optimization. Our implementation is available at https://github.com/A-Chicharito-S/ChemGuide.

MOTIVATION: Gene regulation is a dynamic process that underlies all aspects of human development, disease response, and other biological processes. The reconstruction of temporal gene regulatory networks has conventionally relied on regression analysis, graphical models, or other types of relevance networks. With the large increase in time series single-cell data, new approaches are needed to address the unique scale and nature of these data for reconstructing such networks. RESULTS: Here, we develop a deep neural network, Marlene, to infer dynamic graphs from time series single-cell gene expression data. Marlene constructs directed gene networks using a self-attention mechanism where the weights evolve over time using recurrent units. By employing meta learning, the model is able to recover accurate temporal networks even for rare cell types. In addition, Marlene can identify gene interactions relevant to specific biological responses, including COVID-19 immune response, fibrosis, and aging, paving the way for potential treatments. AVAILABILITY AND IMPLEMENTATION: The code used to train Marlene is available at https://github.com/euxhenh/Marlene.

TACRED is one of the largest and most widely used sentence-level relation extraction datasets. Proposed models that are evaluated using this dataset consistently set new state-of-the-art performance. However, they still exhibit large error rates despite leveraging external knowledge and unsupervised pretraining on large text corpora. A recent study suggested that this may be due to poor dataset quality. The study observed that over 50% of the most challenging sentences from the development and test sets are incorrectly labeled and account for an average drop of 8% f1-score in model performance. However, this study was limited to a small biased sample of 5k (out of a total of 106k) sentences, substantially restricting the generalizability and broader implications of its findings. In this paper, we address these shortcomings by: (i) performing a comprehensive study over the whole TACRED dataset, (ii) proposing an improved crowdsourcing strategy and deploying it to re-annotate the whole dataset, and (iii) performing a thorough analysis to understand how correcting the TACRED annotations affects previously published results. After verification, we observed that 23.9% of TACRED labels are incorrect. Moreover, evaluating several models on our revised dataset yields an average f1-score improvement of 14.3% and helps uncover significant relationships between the different models (rather than simply offsetting or scaling their scores by a constant factor). Finally, aside from our analysis we also release Re-TACRED, a new completely re-annotated version of the TACRED dataset that can be used to perform reliable evaluation of relation extraction models.

Yiwei Lyu, Paul Pu Liang, Hai Pham, Eduard Hovy, Barnabás Póczos, Ruslan Salakhutdinov, Louis-Philippe Morency. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

Program synthesis has emerged as a successful approach to the image parsing task. Most prior works rely on a two-step scheme involving supervised pretraining of a Seq2Seq model with synthetic programs followed by reinforcement learning (RL) for fine-tuning with real reference images. Fully unsupervised approaches promise to train the model directly on the target images without requiring curated pretraining datasets. However, they struggle with the inherent sparsity of meaningful programs in the search space. In this paper, we present the first unsupervised algorithm capable of parsing constructive solid geometry (CSG) images into context-free grammar (CFG) without pretraining. To tackle the non-Markovian sparse reward problem, we combine three key ingredients—(i) a grammar-encoded tree LSTM ensuring program validity (ii) entropy regularization and (iii) sampling without replacement from the CFG syntax tree. Empirically, our algorithm recovers meaningful programs in large search spaces (up to $3.8 \times 10^{28}$). Further, even though our approach is fully unsupervised, it generalizes better than supervised methods on the synthetic 2D CSG dataset. On the 2D computer aided design (CAD) dataset, our approach significantly outperforms the supervised pretrained model and is competitive to the refined model.

We consider the task of knowledge graph link prediction. Given a question consisting of a source entity and a relation (e.g., Shakespeare and BornIn), the objective is to predict the most likely answer entity (e.g., England). Recent approaches tackle this problem by learning entity and relation embeddings. However, they often constrain the relationship between these embeddings to be additive (i.e., the embeddings are concatenated and then processed by a sequence of linear functions and element-wise non-linearities). We show that this type of interaction significantly limits representational power. For example, such models cannot handle cases where a different projection of the source entity is used for each relation. We propose to use contextual parameter generation to address this limitation. More specifically, we treat relations as the context in which source entities are processed to produce predictions, by using relation embeddings to generate the parameters of a model operating over source entity embeddings. This allows models to represent more complex interactions between entities and relations. We apply our method on two existing link prediction methods, including the current state-of-the-art, resulting in significant performance gains and establishing a new state-of-the-art for this task. These gains are achieved while also reducing convergence time by up to 28 times.

Aman Madaan, Amrith Setlur, Tanmay Parekh, Barnabas Poczos, Graham Neubig, Yiming Yang, Ruslan Salakhutdinov, Alan W Black, Shrimai Prabhumoye. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 2020.

In applications such as molecule design or drug discovery, it is desirable to have an algorithm which recommends new candidate molecules based on the results of past tests. These molecules first need to be synthesized and then tested for objective properties. We describe ChemBO, a Bayesian optimization framework for generating and optimizing organic molecules for desired molecular properties. While most existing data-driven methods for this problem do not account for sample efficiency or fail to enforce realistic constraints on synthesizability, our approach explores synthesis graphs in a sample-efficient way and produces synthesizable candidates. We implement ChemBO as a Gaussian process model and explore existing molecular kernels for it. Moreover, we propose a novel optimal-transport based distance and kernel that accounts for graphical information explicitly. In our experiments, we demonstrate the efficacy of the proposed approach on several molecular optimization problems.

Current natural language processing models work well on a single task, yet they often fail to continuously learn new tasks without forgetting previous ones as they are re-trained throughout their lifetime, a challenge known as lifelong learning.State-of-the-art lifelong language learning methods store past examples in episodic memory and replay them at both training and inference time.However, as we show later in our experiments, there are three significant impediments: (1) needing unrealistically large memory module to achieve good performance, (2) suffering from negative transfer, (3) requiring multiple local adaptation steps for each test example that significantly slows down the inference speed.In this paper, we identify three common principles of lifelong learning methods and propose an efficient meta-lifelong framework that combines them in a synergistic fashion.To achieve sample efficiency, our method trains the model in a manner that it learns a better initialization for local adaptation.Extensive experiments on text classification and question answering benchmarks demonstrate the effectiveness of our framework by achieving state-of-the-art performance using merely 1% memory size and narrowing the gap with multi-task learning.We further show that our method alleviates both catastrophic forgetting and negative transfer at the same time.

Despite the advent of deep learning in computer vision, the general handwriting recognition problem is far from solved. Most existing approaches focus on handwriting datasets that have clearly written text and carefully segmented labels. In this paper, we instead focus on learning handwritten characters from maintenance logs, a constrained setting where data is very limited and noisy. We break the problem into two consecutive stages of word segmentation and word recognition respectively, and utilize data augmentation techniques to train both stages. Extensive comparisons with popular baselines for scene-text detection and word recognition show that our system achieves a lower error rate and is more suited to handle noisy and difficult documents.

Deep Neural Networks (DNNs) achieve the state-of-the-art results on a wide range of image processing tasks, however, the majority of such solutions are problem-specific, like most AI algorithms. The One Network to Solve Them All (OneNet) procedure has been suggested to resolve this issue by exploiting a DNN as the proximal operator in Alternating Direction Method of Multipliers (ADMM) solvers for various imaging problems. In this work, we make two contributions, both facilitating end-to-end learning using backpropagation. First, we generalize OneNet to videos by augmenting its convolutional prior network with bidirectional recurrent connections; second, we extend the fixed fully connected linear ADMM data step with another trainable bidirectional convolutional recurrent network. In our computational experiments on the Rotated MNIST, Scanned CIFAR-10 and UCF-101 data sets, the proposed modifications improve performance by a large margin compared to end-to-end convolutional OneNet and 3D Wavelet sparsity on several video processing problems: pixelwise inpainting-denoising, blockwise inpainting, scattered inpainting, super resolution, compressive sensing, deblurring, frame interpolation, frame prediction and colorization. Our two contributions are complementary, and using them together yields the best results.

This paper extends recent work on nonlinear Independent Component Analysis (ICA) by introducing a theoretical framework for nonlinear Independent Subspace Analysis (ISA) in the presence of auxiliary variables. Observed high dimensional acoustic features like log Mel spectrograms can be considered as surface level manifestations of nonlinear transformations over individual multivariate sources of information like speaker characteristics, phonological content etc. Under assumptions of energy based models we use the theory of nonlinear ISA to propose an algorithm that learns unsupervised speech representations whose subspaces are independent and potentially highly correlated with the original non-stationary multivariate sources. We show how nonlinear ICA with auxiliary variables can be extended to a generic identifiable model for subspaces as well while also providing sufficient conditions for the identifiability of these high dimensional subspaces. Our proposed methodology is generic and can be integrated with standard unsupervised approaches to learn speech representations with subspaces that can theoretically capture independent higher order speech signals. We evaluate the gains of our algorithm when integrated with the Autoregressive Predictive Decoding (APC) model by showing empirical results on the speaker verification and phoneme recognition tasks.

How meaning is represented in the brain is still one of the big open questions in neuroscience. Does a word (e.g., bird) always have the same representation, or does the task under which the word is processed alter its representation (answering can you eat it?" versuscan it fly?")? The brain activity of subjects who read the same word while performing different semantic tasks has been shown to differ across tasks. However, it is still not understood how the task itself contributes to this difference. In the current work, we study Magnetoencephalography (MEG) brain recordings of participants tasked with answering questions about concrete nouns. We investigate the effect of the task (i.e. the question being asked) on the processing of the concrete noun by predicting the millisecond-resolution MEG recordings as a function of both the semantics of the noun and the task. Using this approach, we test several hypotheses about the task-stimulus interactions by comparing the zero-shot predictions made by these hypotheses for novel tasks and nouns not seen during training. We find that incorporating the task semantics significantly improves the prediction of MEG recordings, across participants. The improvement occurs 475-550ms after the participants first see the word, which corresponds to what is considered to be the ending time of semantic processing for a word. These results suggest that only the end of semantic processing of a word is task-dependent, and pose a challenge for future research to formulate new hypotheses for earlier task effects as a function of the task and stimuli.

We study minimax convergence rates of nonparametric density estimation under the Huber contamination model, in which a ``contaminated'' proportion of the data comes from an unknown outlier distribution. We provide the first results for this problem under a large family of losses, called Besov integral probability metrics (IPMs), that include L^p, Wasserstein, Kolmogorov-Smirnov, Cramer-von Mises, and other commonly used metrics. Under a range of smoothness assumptions on the population and outlier distributions, we show that a re-scaled thresholding wavelet estimator converges at the minimax optimal rate under a wide variety of losses and also exhibits optimal dependence on the contamination proportion. We also provide a purely data-dependent extension of the estimator that adapts to both an unknown contamination proportion and the unknown smoothness of the true density. Finally, based on connections shown recently between density estimation under IPM losses and generative adversarial networks (GANs), we show that certain GAN architectures are robustly minimax optimal.

Bayesian Optimisation (BO) refers to a suite of techniques for global optimisation of expensive black box functions, which use introspective Bayesian models of the function to efficiently search for the optimum. While BO has been applied successfully in many applications, modern optimisation tasks usher in new challenges where conventional methods fail spectacularly. In this work, we present Dragonfly, an open source Python library for scalable and robust BO. Dragonfly incorporates multiple recently developed methods that allow BO to be applied in challenging real world settings; these include better methods for handling higher dimensional domains, methods for handling multi-fidelity evaluations when cheap approximations of an expensive function are available, methods for optimising over structured combinatorial spaces, such as the space of neural network architectures, and methods for handling parallel evaluations. Additionally, we develop new methodological improvements in BO for selecting the Bayesian model, selecting the acquisition function, and optimising over complex domains with different variable types and additional constraints. We compare Dragonfly to a suite of other packages and algorithms for global optimisation and demonstrate that when the above methods are integrated, they enable significant improvements in the performance of BO. The Dragonfly library is available at dragonfly.github.io.

Multimodal sentiment analysis is a core research area that studies speaker sentiment expressed from the language, visual, and acoustic modalities. The central challenge in multimodal learning involves inferring joint representations that can process and relate information from these modalities. However, existing work learns joint representations by requiring all modalities as input and as a result, the learned representations may be sensitive to noisy or missing modalities at test time. With the recent success of sequence to sequence (Seq2Seq) models in machine translation, there is an opportunity to explore new ways of learning joint representations that may not require all input modalities at test time. In this paper, we propose a method to learn robust joint representations by translating between modalities. Our method is based on the key insight that translation from a source to a target modality provides a method of learning joint representations using only the source modality as input. We augment modality translations with a cycle consistency loss to ensure that our joint representations retain maximal information from all modalities. Once our translation model is trained with paired multimodal data, we only need data from the source modality at test time for final sentiment prediction. This ensures that our model remains robust from perturbations or missing information in the other modalities. We train our model with a coupled translationprediction objective and it achieves new state-of-the-art results on multimodal sentiment analysis datasets: CMU-MOSI, ICTMMMO, and YouTube. Additional experiments show that our model learns increasingly discriminative joint representations with more input modalities while maintaining robustness to missing or perturbed modalities.

Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While learning the kernel in a data driven way has been investigated, in this paper we explore learning the spectral distribution of kernel via implicit generative models parametrized by deep neural networks. We called our method Implicit Kernel Learning (IKL). The proposed framework is simple to train and inference is performed via sampling random Fourier features. We investigate two applications of the proposed IKL as examples, including generative adversarial networks with MMD (MMD GAN) and standard supervised learning. Empirically, MMD GAN with IKL outperforms vanilla predefined kernels on both image and text generation benchmarks; using IKL with Random Kitchen Sinks also leads to substantial improvement over existing state-of-the-art kernel learning algorithms on popular supervised learning benchmarks. Theory and conditions for using IKL in both applications are also studied as well as connections to previous state-of-the-art methods.

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity models. We find simple but realistic examples showing that this phenomenon exists even when learning linear classifiers — between two linear networks with the same capacity, the one with a convolutional layer can generalize better than the other when the data distribution has some underlying spatial structure. We argue that this difference results from a combination of the convolution architecture, data distribution and gradient descent, all of which are necessary to be included in a meaningful analysis. We analyze of the generalization performance as a function of data distribution and convolutional filter size, given gradient descent as the optimization algorithm, then interpret the results using concrete examples. Experimental results show that our analysis is able to explain what happens in our introduced examples.

We present LBS-AE; a self-supervised autoencoding algorithm for fitting articulated mesh models to point clouds. As input, we take a sequence of point clouds to be registered as well as an artist-rigged mesh, i.e. a template mesh equipped with a linear-blend skinning (LBS) deformation space parameterized by a skeleton hierarchy. As output, we learn an LBS-based autoencoder that produces registered meshes from the input point clouds. To bridge the gap between the artist-defined geometry and the captured point clouds, our autoencoder models pose-dependent deviations from the template geometry. During training, instead of us- ing explicit correspondences, such as key points or pose supervision, our method leverages LBS deformations to boot- strap the learning process. To avoid poor local minima from erroneous point-to-point correspondences, we utilize a structured Chamfer distance based on part-segmentations, which are learned concurrently using self-supervision. We demonstrate qualitative results on real captured hands, and report quantitative evaluations on the FAUST benchmark for body registration. Our method achieves performance that is superior to other unsupervised approaches and com- parable to methods using supervised examples.

When labeled data is scarce for a specific target task, transfer learning often offers an effective solution by utilizing data from a related source task. However, when transferring knowledge from a less related source, it may inversely hurt the target performance, a phenomenon known as negative transfer. Despite its pervasiveness, negative transfer is usually described in an informal manner, lacking rigorous definition, careful analysis, or systematic treatment. This paper proposes a formal definition of negative transfer and analyzes three important aspects thereof. Stemming from this analysis, a novel technique is proposed to circumvent negative transfer by filtering out unrelated source data. Based on adversarial networks, the technique is highly generic and can be applied to a wide range of transfer learning algorithms. The proposed approach is evaluated on six state-of-the-art deep transfer methods via experiments on four benchmark datasets with varying levels of difficulty. Empirically, the proposed method consistently improves the performance of all baseline methods and largely avoids negative transfer, even when the source data is degenerate.

Bayesian methods for adaptive decision-making, such as Bayesian optimisation, active learning, and active search have seen great success in relevant applications. However, real world data collection tasks are more broad and complex, as we may need to achieve a combination of the above goals and/or application specific goals. In such scenarios, specialised methods have limited applicability. In this work, we design a new myopic strategy for a wide class of adaptive design of experiment (DOE) problems, where we wish to collect data in order to fulfil a given goal. Our approach, Myopic Posterior Sampling (MPS), which is inspired by the classical posterior sampling algorithm for multi-armed bandits, enables us to address a broad suite of DOE tasks where a practitioner may incorporate domain expertise about the system and specify her desired goal via a reward function. Empirically, this general-purpose strategy is competitive with more specialised methods in a wide array of synthetic and real world DOE tasks. More importantly, it enables addressing complex DOE goals where no existing method seems applicable. On the theoretical side, we leverage ideas from adaptive submodularity and reinforcement learning to derive conditions under which MPS achieves sublinear regret against natural benchmark policies.

In this paper we propose Group k-Sparse Temporal Convolutional Neural Networks for unsupervised pretraining using video data. Our work is the first to consider the recurrent extension of structured sparsity, thus enhancing representational power and explainability. We show that our architecture is able to outperform several state-of-the-art baselines on Rotated MNIST, Scanned CIFAR-10, COIL-100 and NEC Animal pretraining benchmarks for video classification using limited labeled data.

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to \emph{infinitely wide} multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.

We study the problem of estimating a nonparametric probability distribution under a family of losses called Besov IPMs. This family is quite large, including, for example, L^p distances, total variation distance, and generalizations of both Wasserstein (earthmover's) and Kolmogorov-Smirnov distances. For a wide variety of settings, we provide both lower and upper bounds, identifying precisely how the choice of loss function and assumptions on the data distribution interact to determine the mini-max optimal convergence rate. We also show that, in many cases, linear distribution estimates, such as the empirical distribution or kernel density estimator, cannot converge at the optimal rate. These bounds generalize, unify, or improve on several recent and classical results. Moreover, IPMs can be used to formalize a statistical model of generative adversarial networks (GANs). Thus, we show how our results imply bounds on the statistical error of a GAN, showing, for example, that, in many cases, GANs can strictly outperform the best linear estimator.

We present an approach to learn SAT solver heuristics from scratch through deep reinforcement learning with a curriculum. In particular, we incorporate a graph neural network in a stochastic local search algorithm to act as the variable selection heuristic. We consider Boolean satisfiability problems from different classes and learn specialized heuristics for each class. Although we do not aim to compete with the state-of-the-art SAT solvers in run time, we demonstrate that the learned heuristics allow us to find satisfying assignments in fewer steps compared to a generic heuristic, and we provide analysis of our results through experiments.

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

We design and analyse variations of the classical Thompson sampling (TS) procedure for Bayesian optimisation (BO) in settings where function evaluations are expensive but can be performed in parallel. Our theoretical analysis shows that a direct application of the sequential Thompson sampling algorithm in either synchronous or asynchronous parallel settings yields a surprisingly powerful result: making $n$ evaluations distributed among $M$ workers is essentially equivalent to performing $n$ evaluations in sequence. Further, by modelling the time taken to complete a function evaluation, we show that, under a time constraint, asynchronous parallel TS achieves asymptotically lower regret than both the synchronous and sequential versions. These results are complemented by an experimental analysis, showing that asynchronous TS outperforms a suite of existing parallel BO algorithms in simulations and in an application involving tuning hyper-parameters of a convolutional neural network. In addition to these, the proposed procedure is conceptually much simpler than existing work for parallel BO.

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from saddles one has to use second-order methods. However, most works on second-order methods rely extensively on expensive Hessian-based computations, making them impractical in large-scale settings. To tackle this challenge, we introduce a generic framework that minimizes Hessian-based computations while at the same time provably converging to second-order critical points. Our framework carefully alternates between a first-order and a second-order subroutine, using the latter only close to saddle points, and yields convergence results competitive to the state-of-the-art. Empirical results suggest that our strategy also enjoys a good practical performance.

Sparse dictionary learning (SDL) has become a popular method for learning parsimonious representations of data, a fundamental problem in machine learning and signal processing. While most work on SDL assumes a training dataset of independent and identically distributed (IID) samples, a variant known as convolutional sparse dictionary learning (CSDL) relaxes this assumption to allow dependent, non-stationary sequential data sources. Recent work has explored statistical properties of IID SDL; however, the statistical properties of CSDL remain largely unstudied. This paper identifies minimax rates of CSDL in terms of reconstruction risk, providing both lower and upper bounds in a variety of settings. Our results make minimal assumptions, allowing arbitrary dictionaries and showing that CSDL is robust to dependent noise. We compare our results to similar results for IID SDL and verify our theory with synthetic experiments.

We consider the problem of learning an one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation function, i.e., $f(Z; w, a) = \sum_j a_j\sigma(w^\top Z_j)$, in which both the convolutional weights $w$ and the output weights $a$ are parameters to be learned. We prove that with Gaussian input $\mathbf{Z}$ there is a spurious local minimizer. Surprisingly, in the presence of the spurious local minimizer, starting from randomly initialized weights, gradient descent with weight normalization can still be proven to recover the true parameters with constant probability (which can be boosted to probability $1$ with multiple restarts). We also show that with constant probability, the same procedure could also converge to the spurious local minimum, showing that the local minimum plays a non-trivial role in the dynamics of gradient descent. Furthermore, a quantitative analysis shows that the gradient descent dynamics has two phases: it starts off slow, but converges much faster after several iterations.

The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods can be categorized into either using: a) autoregressive models to estimate the conditional factors of the chain rule, $p(x_{i}\, |\, x_{i-1}, \ldots)$; or b) non-linear transformations of variables of a simple base distribution. Based on the study of the characteristics of these categories, we propose multiple novel methods for each category. For example we propose RNN based transformations to model non-Markovian dependencies. Further, through a comprehensive study over both real world and synthetic data, we show that jointly leveraging transformations of variables and autoregressive conditional models, results in a considerable improvement in performance. We illustrate the use of our models in outlier detection and image modeling. Finally we introduce a novel data driven framework for learning a family of distributions.

Plant phenotyping is the measurement of observable plant traits. Current methods for phenotyping in the field are labour intensive and error prone. High throughput plant phenotyping in an automated and noninvasive manner is crucial to accelerating plant breeding methods. Occlusions and non-ideal sensing conditions is a major problem for high throughput plant phenotyping with most state-of-the-art 3D phenotyping algorithms relying heavily on heuristics or hand-tuned parameters. To address this problem, we present a novel model-based optimization approach for estimating plant physical traits from plant units called phytomers. The proposed approach involves sampling parameterized 3D plant models from an underlying probability distribution. It then optimizes, making the mass of this probability distribution approach true parameters of the model. Reformulating the phenotyping objective as a search in the space of plant models lets us reason about the plant structure in a holistic manner without having to rely on hand-tuned parameters. This makes our approach robust to noise and occlusions as frequently encountered in real world environments. We evaluate our approach for plant units taken across simulated, greenhouse and field environments. This work furthers field-based robotic phenotyping capabilities paving the way for plant biologists to study the coupled effect of genetics and environment on improving crop yields.

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called ``adversarial losses'', which, besides classical L^p losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.

Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function f which is only accessible via point evaluations. It is typically used in settings where f is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network architectures. In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks.

Understanding the nature of dark energy, the mysterious force driving the accelerated expansion of the Universe, is a major challenge of modern cosmology. The next generation of cosmological surveys, specifically designed to address this issue, rely on accurate measurements of the apparent shapes of distant galaxies. However, shape measurement methods suffer from various unavoidable biases and therefore will rely on a precise calibration to meet the accuracy requirements of the science analysis. This calibration process remains an open challenge as it requires large sets of high quality galaxy images. To this end, we study the application of deep conditional generative models in generating realistic galaxy images. In particular we consider variations on conditional variational autoencoder and introduce a new adversarial objective for training of conditional generative networks. Our results suggest a reliable alternative to the acquisition of expensive high quality observations for generating the calibration data needed by the next generation of cosmological surveys.

While deep learning methods have achieved state-of-theart performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach, each inverse problem requires its own dedicated network. In scenarios where we need to solve a wide variety of problems, e.g., on a mobile camera, it is inefficient and expensive to use these problem-specific networks. On the other hand, traditional methods using analytic signal priors can be used to solve any linear inverse problem; this often comes with a performance that is worse than learning-based methods. In this work, we provide a middle ground between the two kinds of methods - we propose a general framework to train a single deep neural network that solves arbitrary linear inverse problems. We achieve this by training a network that acts as a quasi-projection operator for the set of natural images and show that any linear inverse problem involving natural images can be solved using iterative methods. We empirically show that the proposed framework demonstrates superior performance over traditional methods using wavelet sparsity prior while achieving performance comparable to specially-trained networks on tasks including compressive sensing and pixel-wise inpainting.

We study the problem of using i.i.d. samples from an unknown multivariate probability distribution p to estimate the mutual information of p. This problem has recently received attention in two settings: (1) where p is assumed to be Gaussian and (2) where p is assumed only to lie in a large nonparametric smoothness class. Estimators proposed for the Gaussian case converge in high dimensions when the Gaussian assumption holds, but are brittle, failing dramatically when p is not Gaussian, while estimators proposed for the nonparametric case fail to converge with realistic sample sizes except in very low dimension. Hence, there is a lack of robust mutual information estimators for many realistic data. To address this, we propose estimators for mutual information when p is assumed to be a nonparanormal (or Gaussian copula) model, a semiparametric compromise between Gaussian and nonparametric extremes. Using theoretical bounds and experiments, we show these estimators strike a practical balance between robustness and scalability.

Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, multi-fidelity methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. On the other hand, in many practical applications, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data $N$ and/or few training iterations $T$. Here, the approximations are best viewed as arising out of a continuous two dimensional space $(N,T)$. In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.

Sophisticated gated recurrent neural network architectures like LSTMs and GRUs have been shown to be highly effective in a myriad of applications. We develop an un-gated unit, the statistical recurrent unit (SRU), that is able to learn long term dependencies in data by only keeping moving averages of statistics. The SRU’s architecture is simple, un-gated, and contains a comparable number of parameters to LSTMs; yet, SRUs perform favorably to more sophisticated LSTM and GRU alternatives, often outperforming one or both in various tasks. We show the efficacy of SRUs as compared to LSTMs and GRUs in an unbiased manner by optimizing respective architectures’ hyperparameters for both synthetic and real-world tasks.

We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group G that acts discretely on the input and output of a standard neural network layer, we show that its equivariance is linked to the symmetry group of network parameters. We then propose two parameter-sharing scheme to induce the desirable symmetry on the parameters of the neural network. Under some conditions on the action of G, our procedure for tying the parameters achieves G-equivariance and guarantees sensitivity to all other permutation groups outside of G.

Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular \cite{Rahimi_NIPS_07}, where kernel approximation is treated as empirical mean estimation via Monte Carlo (MC) or Quasi-Monte Carlo (QMC) integration \cite{Yang_ICML_14}. A limitation of the current approaches is that all the features receive an equal weight summing to 1. In this paper, we propose a novel shrinkage estimator from "Stein effect", which provides a data-driven weighting strategy for random features and enjoys theoretical justifications in terms of lowering the empirical risk. We further present an efficient randomized algorithm for large-scale applications of the proposed method. Our empirical results on six benchmark data sets demonstrate the advantageous performance of this approach over representative baselines in both kernel approximation and supervised learning tasks.

Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape. On the other hand, gradient descent with perturbations [Ge et al., 2015, Jin et al., 2017] is not slowed down by saddle points—it can find an approximate local minimizer in polynomial time. This result implies that GD is inherently slower than perturbed GD, and justifies the importance of adding perturbations for efficient non-convex optimization. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

We consider the Hypothesis Transfer Learning (HTL) problem where one incorporates a hypothesis trained on the source domain into the learning procedure of the target domain. Existing theoretical analysis either only studies specific algorithms or only presents upper bounds on the generalization error but not on the excess risk. In this paper, we propose a unified algorithm-dependent framework for HTL through a novel notion of transformation functions, which characterizes the relation between the source and the target domains. We conduct a general risk analysis of this framework and in particular, we show for the first time, if two domains are related, HTL enjoys faster convergence rates of excess risks for Kernel Smoothing and Kernel Ridge Regression than those of the classical non-transfer learning settings. We accompany this framework with an analysis of cross-validation for HTL to search for the best transfer technique and gracefully reduce to non-transfer learning when HTL is not helpful. Experiments on robotics and neural imaging data demonstrate the effectiveness of our framework.

Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD). Although some theoretical guarantees of MMD have been studied, the empirical performance of GMMN is still not as competitive as that of GAN on challenging and large benchmark datasets. The computational efficiency of GMMN is also less desirable in comparison with GAN, partially due to its requirement for a rather large batch size during the training. In this paper, we propose to improve both the model expressiveness of GMMN and its computational efficiency by introducing {\it adversarial kernel learning} techniques, as the replacement of a fixed Gaussian kernel in the original GMMN. The new approach combines the key ideas in both GMMN and GAN, hence we name it MMD-GAN. The new distance measure in MMD-GAN is a meaningful loss that enjoys the advantage of weak$^*$ topology and can be optimized via gradient descent with relatively small batch sizes. In our evaluation on multiple benchmark datasets, including MNIST, CIFAR-10, CelebA and LSUN, the performance of MMD-GAN significantly outperforms GMMN, and is competitive with other representative GAN works.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to the traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets and are invariant to permutations. Such problems are widespread, ranging from the estimation of population statistics, to anomaly detection in piezometer data of embankment dams, to cosmology. Our main theorem characterizes the permutation invariant objective functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

How close can we zoom in to observe brain activity? Our understanding is limited by the resolution of imaging modalities that exhibit good spatial but poor temporal resolution, or vice-versa. In this paper, we propose BrainZoom, an efficient imaging algorithm that cross-leverages multi-modal brain signals. BrainZoom (a) constructs high resolution brain images from multi-modal signals, (b) is scalable, and (c) is flexible in that it can easily incorporate various priors on the brain activities, such as sparsity, low rank, or smoothness. We carefully formulate the problem to tackle nonlinearity in the measurements (via variable splitting) and auto-scale between different modal signals, and judiciously design an inexact alternating optimization-based algorithmic framework to handle the problem with provable convergence guarantees. Our experiments using a popular realistic brain signal simulator to generate fMRI and MEG demonstrate that high spatio-temporal resolution brain imaging is possible from these two modalities. The experiments also suggest that smoothness seems to be the best prior, among several we tried.

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Most previous work devoted to machine learning tasks with distributional inputs has done so through pairwise kernel evaluations between pdfs (or sample sets). While such an approach is fine for smaller datasets, the computation of an N × N Gram matrix is prohibitive in large datasets. Recent scalable estimators that work over pdfs have done so only with kernels that use Euclidean metrics, like the L2 distance. However, there are a myriad of other useful metrics available, such as total variation, Hellinger distance, and the Jensen-Shannon divergence. This work develops the first random features for pdfs whose dot product approximates kernels using these non-Euclidean metrics. These random features allow estimators to scale to large datasets by working in a primal space, without computing large Gram matrices. We provide an analysis of the approximation error in using our proposed random features, and show empirically the quality of our approximation both in estimating a Gram matrix and in solving learning tasks in real-world and synthetic data.

Bayesian Optimization (BO) is commonly used to optimize blackbox objective functions which are expensive to evaluate. A common approach is based on using Gaussian Process (GP) to model the objective function. Applying GP to higher dimensional settings is generally difficult due to the curse of dimensionality for nonparametric regression. Existing works makes strong assumptions such as the function is low-dimensional embedding (Wang et al., 2013) or is axis-aligned additive (Kandasamy et al., 2015). In this pa- per, we generalize the existing assumption to a projected-additive assumption. Our generalization provides the benefits of i) greatly increasing the space of functions that can be modeled by our approach, which covers the previous works (Wang et al., 2013; Kandasamy et al., 2015) as special cases, and ii) efficiently handling the learning in a larger model space. We prove that the regret for projected-additive functions has only linear dependence on the number of dimensions in this general setting. Directly using projected-additive GP (Gilboa et al., 2013) to BO results in a non-box constraint, which is not easy to optimize. We tackle this problem by proposing a restricted-projection-pursuit GP for BO. We conduct experiments on synthetic examples and scientific and hyper-parameter tuning tasks in many cases. Our method outperforms existing approaches even when the function does not meet the projected additive assumption. Last, we study the validity of the additive and projected-additive assumption in practice.

Kernel methods are ubiquitous tools in machine learning. They have proven to be effective in many domains and tasks. Yet, kernel methods often require the user to select a predefined kernel to build an estimator with. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when directly applying kernel methods, one typically needs to compute a N \times N Gram matrix of pairwise kernel evaluations to work with a dataset of N instances. The computation of this Gram matrix precludes the direct application of kernel methods on large datasets, and makes kernel learning especially difficult. In this paper we introduce Bayesian nonparmetric kernel-learning (BaNK), a generic, data-driven framework for scalable learning of kernels. BaNK places a nonparametric prior on the spectral distribution of random frequencies allowing it to both learn kernels and scale to large datasets. We show that this framework can be used for large scale regression and classification tasks. Furthermore, we show that BaNK outperforms several other scalable approaches for kernel learning on a variety of real world datasets.

We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences. This family, that we call exponential family RBM (Exp-RBM), is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearity for each neuron. Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBM can learn useful representations using novel stochastic units.

A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach in estimating the cosmological parameters is to use the large scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in three dimensions. Information about galaxy locations is typically summarized in a "single" function of scale, such as the galaxy correlation function or power-spectrum. We show that it is possible to estimate these cosmological parameters directly from the distribution of matter. This paper presents the application of deep 3D convolutional networks to volumetric representation of dark matter simulations as well as the results obtained using a recently proposed distribution regression framework, showing that machine learning techniques are comparable to, and can sometimes outperform, maximum-likelihood point estimates using "cosmological models". This opens the way to estimating the parameters of our Universe with higher accuracy.

Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message passing approach that scales linearly with the number of observations and factors. Our empirical study demonstrates that message passing is able to recover low-rank Boolean matrices, in the boundaries of theoretically possible recovery and compares favorably with state-of-the-art in real-world applications, such collaborative filtering with large-scale Boolean data.

We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient descent (SGD); but their theoretical analysis almost exclusively assumes convexity. In contrast, we prove non-asymptotic rates of convergence (to stationary points) of SVRG for nonconvex optimization, and show that it is provably faster than SGD and gradient descent. We also analyze a subclass of nonconvex problems on which SVRG attains linear convergence to the global optimum. We extend our analysis to mini-batch variants of SVRG, showing (theoretical) linear speedup due to minibatching in parallel settings.

Sensor models, which specify the distribution of sensor observations, are a widely used and integral part of robotics algorithms. Observation distributions are commonly approximated by parametric models, which are limited in their expressiveness, and may require careful design to suit an application. In this paper, we propose nonparametric distribution regression as a procedure to model sensors. It is a data-driven procedure to predict distributions that makes few assumptions. We apply the procedure to model raw distributions from real sensors, and also demonstrate its utility to a mobile robot state estimation task. We show that nonparametric distribution regression adapts to characteristics in the training data, leading to realistic predictions. The same procedure competes favorably with baseline parametric models across applications. The results also help develop intuition for different sensor modeling situations. Our procedure is useful when distributions are inherently noisy, and sufficient data is available.

Stochastic gradient-based Monte Carlo methods such as stochastic gradient Langevin dynamics are useful tools for posterior inference on large scale datasets in many machine learning applications. These methods scale to large datasets by using noisy gradients calculated using a mini-batch or subset of the dataset. However, the high variance inherent in these noisy gradients degrades performance and leads to slower mixing. In this paper, we present techniques for reducing variance in stochastic gradient Langevin dynamics, yielding novel stochastic Monte Carlo methods that improve performance by reducing the variance in the stochastic gradient. We show that our proposed method has better theoretical guarantees on convergence rate than stochastic Langevin dynamics. This is complemented by impressive empirical results obtained on a variety of real world datasets, and on four different machine learning tasks (regression, classification, independent component analysis and mixture modeling). These theoretical and empirical contributions combine to make a compelling case for using variance reduction in stochastic Monte Carlo methods.

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function $\func$. Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations to $\func$ may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of $\func$ in a small but promising region and speedily identify the optimum. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop \mfgpucb, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information. \mfgpucbs outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

We study a variant of the classical stochastic $K$-armed bandit where observing the outcome of each arm is expensive, but cheap approximations to this outcome are available. For example, in online advertising the performance of an ad can be approximated by displaying it for shorter time periods or to narrower audiences. We formalise this task as a \emph{multi-fidelity} bandit, where, at each time step, the forecaster may choose to play an arm at any one of $M$ fidelities. The highest fidelity (desired outcome) expends cost $\costM$. The $m$\ssth fidelity (an approximation) expends $\costm < \costM$ and returns a biased estimate of the highest fidelity. We develop \mfucb, a novel upper confidence bound procedure for this setting and prove that it naturally adapts to the sequence of available approximations and costs thus attaining better regret than naive strategies which ignore the approximations. For instance, in the above online advertising example, \mfucbs would use the lower fidelities to quickly eliminate suboptimal ads and reserve the larger expensive experiments on a small set of promising candidates. We complement this result with a lower bound and show that \mfucbs is nearly optimal under certain conditions.

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem is very limited. For example, it is not known whether the proximal stochastic gradient method with constant minibatch converges to a stationary point. To tackle this issue, we develop fast stochastic algorithms that provably converge to a stationary point for constant minibatches. Furthermore, using a variant of these algorithms, we obtain provably faster convergence than batch proximal gradient descent. Our results are based on the recent variance reduction techniques for convex optimization but with a novel analysis for handling nonconvex and nonsmooth functions. We also prove global linear convergence rate for an interesting subclass of nonsmooth nonconvex functions, which subsumes several recent works.

Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They also include, as special cases, L^2 quantities which are used in many applications. We propose and analyze a family of estimators for Sobolev quantities of unknown probability density functions. We bound the finite-sample bias and variance of our estimators, finding that they are generally minimax rate-optimal. Our estimators are significantly more computationally tractable than previous estimators, and exhibit a statistical/computational trade-off allowing them to adapt to computational constraints. We also draw theoretical connections to recent work on fast two-sample testing and empirically validate our estimators on synthetic data.

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k → ∞ as the sample size n → ∞) into the functional of interest, the estimators we consider fix k and perform a bias correction. This can be more efficient computationally, and, as we show, statistically, leading to faster convergence rates. Our framework unifies several previous estimators, for most of which ours are the first finite sample guarantees.

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point estimation problems without analytical solution (such as hyperparameter or entropy estimation). Despite the large number of available heuristics in the literature, the inherent two-stage sampled nature of the problem makes the theoretical analysis quite challenging, since in practice only samples from sampled distributions are observable, and the estimates have to rely on similarities computed between sets of points. To the best of our knowledge, the only existing technique with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step (which often performs poorly in practice), and the domain of the distributions to be compact Euclidean. In this paper, we study a simple, analytically computable, ridge regression-based alternative to distribution regression, where we embed the distributions to a reproducing kernel Hilbert space, and learn the regressor from the embeddings to the outputs. Our main contribution is to prove that this scheme is consistent in the two-stage sampled setup under mild conditions (on separable topological domains enriched with kernels): we present an exact computational-statistical efficiency trade-off analysis showing that our estimator is able to match the one-stage sampled minimax optimal rate (Caponnetto and De Vito, 2007; Steinwart et al., 2009). This result answers a $17 $-year-old open question, establishing the consistency of the classical set kernel (Haussler, 1999; Gärtner et al., 2002) in regression. We also cover consistency for more recent kernels on distributions, including those due to Christmann and Steinwart (2010).

Quantifying differences or similarities in connectomes has been a challenge due to the immense complexity of global brain networks. Here we introduce a noninvasive method that uses diffusion MRI to characterize whole-brain white matter architecture as a single local connectome fingerprint that allows for a direct comparison between structural connectomes. In four independently acquired data sets with repeated scans (total N = 213), we show that the local connectome fingerprint is highly specific to an individual, allowing for an accurate self-versus-others classification that achieved 100% accuracy across 17,398 identification tests. The estimated classification error was approximately one thousand times smaller than fingerprints derived from diffusivity-based measures or region-to-region connectivity patterns for repeat scans acquired within 3 months. The local connectome fingerprint also revealed neuroplasticity within an individual reflected as a decreasing trend in self-similarity across time, whereas this change was not observed in the diffusivity measures. Moreover, the local connectome fingerprint can be used as a phenotypic marker, revealing 12.51% similarity between monozygotic twins, 5.14% between dizygotic twins, and 4.51% between none-twin siblings, relative to differences between unrelated subjects. This novel approach opens a new door for probing the influence of pathological, genetic, social, or environmental factors on the unique configuration of the human connectome.

This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave well in high-dimensional settings. We identify different sources of misconception that give rise to the above belief. Specifically, we differentiate the hardness of estimation of test statistics from the hardness of testing whether these statistics are zero or not, and explicitly discuss a notion of "fair" alternative hypotheses for these problems as dimension increases. We then demonstrate that the power of these tests actually drops polynomially with increasing dimension against fair alternatives. We end with some theoretical insights and shed light on the median heuristic for kernel bandwidth selection. Our work advances the current understanding of the power of modern nonparametric hypothesis tests in high dimensions.

Covariate shift correction allows one to perform supervised learning even when the distribution of the covariates on the training set does not match that on the test set. This is achieved by re-weighting observations. Such a strategy removes bias, potentially at the expense of greatly increased variance. We propose a simple strategy for removing bias while retaining small variance. It uses a biased, low variance estimate as a prior and corrects the final estimate relative to the prior. We prove that this yields an efficient estimator and demonstrate good experimental performance.

We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their generalization performance in specific learning tasks. Learning problems formulated on distributions have an inherent two-stage sampled difficulty: in practice only samples from sampled distributions are observable, and one has to build an estimate on similarities computed between sets of points. To the best of our knowledge, the only existing method with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step (which suffers from slow convergence issues in high dimensions), and the domain of the distributions to be compact Euclidean. In this paper, we provide theoretical guarantees for a remarkably simple algorithmic alternative to solve the distribution regression problem: embed the distributions to a reproducing kernel Hilbert space, and learn a ridge regressor from the embeddings to the outputs. Our main contribution is to prove the consistency of this technique in the two-stage sampled setting under mild conditions (on separable, topological domains endowed with kernels). As a special case, we answer a 15-year-old open question: we establish the consistency of the classical set kernel [Haussler, 1999; Gaertner et. al, 2002] in regression, and cover more recent kernels on distributions, including those due to [Christmann and Steinwart, 2010].

We give a comprehensive theoretical characterization of a nonparametric estimator for the L_2^2 divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is \sqrtn-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically normal, construct asymptotic confidence intervals, and establish a Berry-Esséen style inequality characterizing the rate of convergence to normality. We also show that this estimator is minimax optimal.

We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping between two separate types of distributions. However, previous nonparametric estimators for FFR type problems scale badly computationally with the number of input/output pairs in a data-set. Given the complexity of a mapping between general functions it may be necessary to consider large data-sets in order to achieve a low estimation risk. To address this issue, we develop a novel scalable nonparametric estimator, the Triple-Basis Estimator (3BE), which is capable of operating over datasets with many instances. To the best of our knowledge, the 3BE is the first nonparametric FFR estimator that can scale to massive data-sets. We analyze the 3BE’s risk and derive an upperbound rate. Furthermore, we show an improvement of several orders of magnitude in terms of prediction speed and a reduction in error over previous estimators in various real-world data-sets.

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any assumptions about how the distributions may differ (\textitgeneral alternatives), and those which are designed to specifically test easier alternatives, like a difference in means (\textitmean-shift alternatives). The main contribution of this paper is to explicitly characterize the power of a popular nonparametric two sample test, designed for general alternatives, under a mean-shift alternative in the high-dimensional setting. Specifically, we explicitly derive the power of the linear-time Maximum Mean Discrepancy statistic using the Gaussian kernel, where the dimension and sample size can both tend to infinity at any rate, and the two distributions differ in their means. As a corollary, we find that if the signal-to-noise ratio is held constant, then the test’s power goes to one if the number of samples increases faster than the dimension increases. This is the first explicit power derivation for a general nonparametric test in the high-dimensional setting, and the first analysis of how tests designed for general alternatives perform against easier ones.

Bayesian Optimisation (BO) is a technique used in optimising a D-dimensional function which is typically expensive to evaluate. While there have been many successes for BO in low dimensions, scaling it to high dimensions has been notoriously difficult. Existing literature on the topic are under very restrictive settings. In this paper, we identify two key challenges in this endeavour. We tackle these challenges by assuming an additive structure for the function. This setting is substantially more expressive and contains a richer class of functions than previous work. We prove that, for additive functions the regret has only linear dependence on D even though the function depends on all D dimensions. We also demonstrate several other statistical and computational benefits in our framework. Via synthetic examples, a scientific simulation and a face detection problem we demonstrate that our method outperforms naive BO on additive functions and on several examples where the function is not additive.

We propose and analyse estimators for statistical functionals of one or moredistributions under nonparametric assumptions.Our estimators are derived from the von Mises expansion andare based on the theory of influence functions, which appearin the semiparametric statistics literature.We show that estimators based either on data-splitting or a leave-one-out techniqueenjoy fast rates of convergence and other favorable theoretical properties.We apply this framework to derive estimators for several popular informationtheoretic quantities, and via empirical evaluation, show the advantage of thisapproach over existing estimators.

We study optimization algorithms based on variance reduction for stochastic gradientdescent (SGD). Remarkable recent progress has been made in this directionthrough development of algorithms like SAG, SVRG, SAGA. These algorithmshave been shown to outperform SGD, both theoretically and empirically. However,asynchronous versions of these algorithms—a crucial requirement for modernlarge-scale applications—have not been studied. We bridge this gap by presentinga unifying framework that captures many variance reduction techniques.Subsequently, we propose an asynchronous algorithm grounded in our framework,with fast convergence rates. An important consequence of our general approachis that it yields asynchronous versions of variance reduction algorithms such asSVRG, SAGA as a byproduct. Our method achieves near linear speedup in sparsesettings common to machine learning. We demonstrate the empirical performanceof our method through a concrete realization of asynchronous SVRG.

We study the problem of distribution to real regression, where one aims to regress a mapping f that takes in a distribution input covariate P∈\mathcalI (for a non-parametric family of distributions \mathcalI) and outputs a real-valued response Y=f(P) + ε. This setting was recently studied in Pózcos et al. (2013), where the “Kernel-Kernel” estimator was introduced and shown to have a polynomial rate of convergence. However, evaluating a new prediction with the Kernel-Kernel estimator scales as Ω(N). This causes the difficult situation where a large amount of data may be necessary for a low estimation risk, but the computation cost of estimation becomes infeasible when the data-set is too large. To this end, we propose the Double-Basis estimator, which looks to alleviate this big data problem in two ways: first, the Double-Basis estimator is shown to have a computation complexity that is independent of the number of of instances N when evaluating new predictions after training; secondly, the Double-Basis estimator is shown to have a fast rate of convergence for a general class of mappings f∈\mathcalF.

We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric assumptions about the nature of input functional covariates and assuming a linear form to the mapping of functional covariates to the response. We provide a statistical backing for use of the FuSSO via proof of asymptotic sparsistency under various conditions. Furthermore, we observe good results on both synthetic and real-world data.

In active learning, the user sequentially chooses values for feature X and an oracle returns the corresponding label Y. In this paper, we consider the effect of feature noise in active learning, which could arise either because X itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as“errors in variables” and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width σ. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a + label crosses half). We deal with regression functions that are antisymmetric in a region of size σaround the threshold and also satisfy Tsybakov’s margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when σis smaller than the minimiax active/passive noiseless error derived in Castro & Nowak (2007), then noise has no effect on the rates and one achieves the same noiseless rates. For larger σ, the \textitunflattening of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textitappears to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise.

We consider nonparametric estimation of L_2, Renyi-αand Tsallis-αdivergences between continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them into divergence estimators. For the integral functionals, our estimators are based on corrections of a preliminary plug-in estimator. We show that these estimators achieve the parametric convergence rate of n^-1/2 when the densities’ smoothness, s, are both at least d/4 where d is the dimension. We also derive minimax lower bounds for this problem which confirm that s > d/4 is necessary to achieve the n^-1/2 rate of convergence. We validate our theoretical guarantees with a number of simulations.

Estimating divergences between probability distributions in a consistent way is of great importance in many machine learning tasks. Although this is a fundamental problem in nonparametric statistics, to the best of our knowledge there has been no finite sample exponential inequality convergence bound derived for any divergence estimators. The main contribution of our work is to provide such a bound for an estimator of Renyi divergence for a smooth Holder class of densities on the d-dimensional unit cube. We also illustrate our theoretical results with a numerical experiment.

Distribution regression refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + e where f is an unknown regression function and e is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P. In this paper we develop theory and methods for distribution-free versions of distribution regression. This means that we do not make strong distributional assumptions about the error term e and covariate P. We prove that when the effective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.

Recently several methods have been proposed to learn from data that are represented as sets of multidimensional vectors. Such algorithms usually suffer from the high demand of computational resources, making them impractical on large-scale problems. We propose to solve this problem by condensing i.e. reducing the sizes of the sets while maintaining the learning performance. Three methods are examined and evaluated with a wide spectrum of set learning algorithms on several large-scale image data sets. We discover that k-Means can successfully achieve the goal of condensing. In many cases, k-Means condensing can improve the algorithms' speed, space requirements, and surprisingly, learning performances simultaneously.

We analyze ’Distribution to Distribution regression’ where one is regressing a mapping where both the covariate (inputs) and response (outputs) are distributions. No parameters on the input or output distributions are assumed, nor are any strong assumptions made on the measure from which input distributions are drawn from. We develop an estimator and derive an upper bound for the L2 risk; also, we show that when the effective dimension is small enough (as measured by the doubling dimension), then the risk converges to zero with a polynomial rate.

In this paper we develop new dependence and conditional dependence measures and provide their estimators. An attractive property of these measures and estimators is that they are invariant to any monotone increasing transformations of the random variables, which is important in many applications including feature selection. Under certain conditions we show the consistency of these estimators, derive upper bounds on their convergence rates, and show that the estimators do not suffer from the curse of dimensionality. However, when the conditions are less restrictive, we derive a lower bound which proves that in the worst case the convergence can be arbitrarily slow similarly to some other estimators. Numerical illustrations demonstrate the applicability of our method.

Collaborative prediction is a powerful technique, useful in domains from recommender systems to guiding the scientific discovery process. Low-rank matrix factorization is one of the most powerful tools for collaborative prediction. This work presents a general approach for active collaborative prediction with the Probabilistic Matrix Factorization model. Using variational approximations or Markov chain Monte Carlo sampling to estimate the posterior distribution over models, we can choose query points to maximize our understanding of the model, to best predict unknown elements of the data matrix, or to find as many "positive" data points as possible. We evaluate our methods on simulated data, and also show their applicability to movie ratings prediction and the discovery of drug-target interactions.

We introduce a new discriminative learning method for image classification. We assume that the images are represented by unordered, multi-dimensional, finite sets of feature vectors, and that these sets might have different cardinality. This allows us to use consistent nonparametric divergence estimators to define new kernels over these sets, and then apply them in kernel classifiers. Our numerical results demonstrate that in many cases this approach can outperform state-of-the-art competitors on both simulated and challenging real-world datasets.

We develop a dictionary learning method which is (i) online, (ii) enables overlapping group structures with (iii) non-convex sparsity-inducing regularization and (iv) handles the partially observable case. Structured sparsity and the related group norms have recently gained widespread attention in group-sparsity regularized problems in the case when the dictionary is assumed to be known and fixed. However, when the dictionary also needs to be learned, the problem is much more difficult. Only a few methods have been proposed to solve this problem, and they can handle two of these four desirable properties at most. To the best of our knowledge, our proposed method is the first one that possesses all of these properties. We investigate several interesting special cases of our framework, such as the online, structured, sparse non-negative matrix factorization, and demonstrate the efficiency of our algorithm with several numerical experiments.

An important task in exploring and analyzing real-world data sets is to detect unusual and interesting phenomena. In this paper, we study the group anomaly detection problem. Unlike traditional anomaly detection research that focuses on data points, our goal is to discover anomalous aggregated behaviors of groups of points. For this purpose, we propose the Flexible Genre Model (FGM). FGM is designed to characterize data groups at both the point level and the group level so as to detect various types of group anomalies. We evaluate the effectiveness of FGM on both synthetic and real data sets including images and turbulence data, and show that it is superior to existing approaches in detecting group anomalies.

Some real-world problems are partially decomposable, in that they can be decomposed into a set of coupled sub- problems, that are each relatively easy to solve. However, when these sub-problem share some common variables, it is not sufficient to simply solve each sub-problem in isolation. We develop a technology for such problems, and use it to address the challenge of finding the concentrations of the chemicals that appear in a complex mixture, based on its one-dimensional 1H Nuclear Magnetic Resonance (NMR) spectrum. As each chemical involves clusters of spatially localized peaks, this requires finding the shifts for the clusters and the concentrations of the chemicals, that collectively pro- duce the best match to the observed NMR spectrum. Here, each sub-problem requires finding the chemical concentrations and cluster shifts that can appear within a limited spectrum range; these are coupled as these limited regions can share many chemicals, and so must agree on the concentrations and cluster shifts of the common chemicals. This task motivates CEED: a novel extension to the Cross-Entropy stochastic optimization method constructed to address such partially decomposable problems. Our experimental results in the NMR task show that our CEED system is superior to other well-known optimization methods, and indeed produces the best-known results in this important, real-world application.

An anytime algorithm is capable of returning a response to the given task at essentially any time; typically the quality of the response improves as the time increases. Here, we consider the challenge of learning when we should terminate such algorithms on each of a sequence of iid tasks, to optimize the expected average reward per unit time. We provide a system for addressing this challenge, which combines the global optimizer Cross-Entropy method with local gradient ascent. This paper theoretically investigates how far the estimated gradient is from the true gradient, then empirically demonstrates that this system is effective by applying it to a toy problem, as well as on a real-world face detection task.

We propose a new algorithm for independent component and independent subspace analysis problems. This algorithm uses a contrast based on the Schweizer-Wolff measure of pairwise dependence (Schweizer & Wolff, 1981), a non-parametric measure computed on pairwise ranks of the variables. Our algorithm frequently outperforms state of the art ICA methods in the normal setting, is significantly more robust to outliers in the mixed signals, and performs well even in the presence of noise. Our method can also be used to solve independent subspace analysis (ISA) problems by grouping signals recovered by ICA methods. We provide an extensive empirical evaluation using simulated, sound, and image data.

A novel algorithm for performing Independent Subspace Analysis, the estimation of hidden independent subspaces is introduced. This task is a generalization of Independent Component Analysis. The algorithm works by estimating the multi-dimensional differential entropy. The estimation utilizes minimal geodesic spanning trees matched to the sample points. Numerical studies include (i) illustrative examples, (ii) a generalization of the cocktail-party problem to songs played by bands, and (iii) an example on mixed independent subspaces, where subspaces have dependent sources, which are pairwise independent.

We studied user behaviors when the cursor is directed by a head in a simple control task. We used an intelligent writing tool called Dasher. Hidden Markov models (HMMs) were applied to separate behavioral patterns. We found that similar interpretations can be given to the hidden states upon learning. It is argued that the recognition of such general application specific behavioral patterns should be of help for adaptive human-computer interfaces.

In optimizations the dimension of the problem may severely, sometimes exponentially increase optimization time. Parametric function approximatiors (FAPPs) have been suggested to overcome this problem. Here, a novel FAPP, cost component analysis (CCA) is described. In CCA, the search space is resampled according to the Boltzmann distribution generated by the energy landscape. That is, CCA converts the optimization problem to density estimation. Structure of the induced density is searched by independent component analysis (ICA). The advantage of CCA is that each independent ICA component can be optimized separately. In turn, (i) CCA intends to partition the original problem into subproblems and (ii) separating (partitioning) the original optimization problem into subproblems may serve interpretation. Most importantly, (iii) CCA may give rise to high gains in optimization time. Numerical simulations illustrate the working of the algorithm.