Deep convolutional neural networks comprise a subclass of deep neural networks (DNN) with a constrained architecture that leverages the spatial and temporal structure of the domain they model. Convolutional networks achieve the best predictive performance in areas such as speech and image recognition by hierarchically composing simple local features into complex models. Although DNNs have been used in drug discovery for QSAR and ligand-based bioactivity predictions, none of these models have benefited from this powerful convolutional architecture. This paper introduces AtomNet, the first structure-based, deep convolutional neural network designed to predict the bioactivity of small molecules for drug discovery applications. We demonstrate how to apply the convolutional concepts of feature locality and hierarchical composition to the modeling of bioactivity and chemical interactions. In further contrast to existing DNN techniques, we show that AtomNet's application of local convolutional filters to structural target information successfully predicts new active molecules for targets with no previously known modulators. Finally, we show that AtomNet outperforms previous docking approaches on a diverse set of benchmarks by a large margin, achieving an AUC greater than 0.9 on 57.8% of the targets in the DUDE benchmark.

In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is crucial to select the appropriate number of states. We propose a new model selection technique based on the Gap statistics, which uses a null reference distribution on the stable AR filters to check whether adding a new AR state significantly improves the performance of the model. To that end, we define a new distance measure between AR filters based on mean squared prediction error (MSPE), and propose an efficient method to generate random stable filters that are uniformly distributed in the coefficient space. Numerical results are provided to evaluate the performance of the proposed approach.

Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set of information, community structure across layers can be collectively utilized to discover and quantify underlying relational patterns between nodes. To concisely extract information from a multilayer network, we propose to identify and combine sets of layers with meaningful similarities in community structure. In this paper, we describe the "strata multilayer stochastic block model'' (sMLSBM), a probabilistic model for multilayer community structure. The central extension of the model is that there exist groups of layers, called "strata'', which are defined such that all layers in a given stratum have community structure described by a common stochastic block model (SBM). That is, layers in a stratum exhibit similar node-to-community assignments and SBM probability parameters. Fitting the sMLSBM to a multilayer network provides a joint clustering that yields node-to-community and layer-to-stratum assignments, which cooperatively aid one another during inference. We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the SBM parameters for each stratum. We demonstrate our method using synthetic networks and a multilayer network inferred from data collected in the Human Microbiome Project.

We compare and contrast two approaches to validating a trained classifier while using all in-sample data for training. One is simultaneous validation over an organized set of hypotheses (SVOOSH), the well-known method that began with VC theory. The other is withhold and gap (WAG). WAG withholds a validation set, trains a holdout classifier on the remaining data, uses the validation data to validate that classifier, then adds the rate of disagreement between the holdout classifier and one trained using all in-sample data, which is an upper bound on the difference in error rates. We show that complex hypothesis classes and limited training data can make WAG a favorable alternative.

A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method can be viewed as a hybrid of SVM and DWD that finds the classification direction by minimizing mainly the DWD loss, and determines the intercept term in the SVM manner. We show that our method inheres the merit of DWD, and hence, overcomes the data-piling and overfitting issue of SVM. On the other hand, the new method is not subject to imbalanced data issue which was a main advantage of SVM over DWD. It uses an unusual loss which combines the Hinge loss (of SVM) and the DWD loss through a trick of axillary hyperplane. Several theoretical properties, including Fisher consistency and asymptotic normality of the DWSVM solution are developed. We use some simulated examples to show that the new method can compete DWD and SVM on both classification performance and interpretability. A real data application further establishes the usefulness of our approach.

The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is very difficult. In recent years some estimation methods are suggested for approximate computation of test log-likelihood. In this paper we present an empirical comparison of the main estimation methods, namely, the AIS algorithm for estimating the partition function, the CSL method for directly estimating the log-likelihood, and the RAISE algorithm that combines these two ideas. We use the MNIST data set to learn the RBM and then compare these methods for estimating the test log-likelihood.

Top-performing machine learning systems, such as deep neural networks, large ensembles and complex probabilistic graphical models, can be expensive to store, slow to evaluate and hard to integrate into larger systems. Ideally, we would like to replace such cumbersome models with simpler models that perform equally well. In this thesis, we study knowledge distillation, the idea of extracting the knowledge contained in a complex model and injecting it into a more convenient model. We present a general framework for knowledge distillation, whereby a convenient model of our choosing learns how to mimic a complex model, by observing the latter's behaviour and being penalized whenever it fails to reproduce it. We develop our framework within the context of three distinct machine learning applications: (a) model compression, where we compress large discriminative models, such as ensembles of neural networks, into models of much smaller size; (b) compact predictive distributions for Bayesian inference, where we distil large bags of MCMC samples into compact predictive distributions in closed form; (c) intractable generative models, where we distil unnormalizable models such as RBMs into tractable models such as NADEs. We contribute to the state of the art with novel techniques and ideas. In model compression, we describe and implement derivative matching, which allows for better distillation when data is scarce. In compact predictive distributions, we introduce online distillation, which allows for significant savings in memory. Finally, in intractable generative models, we show how to use distilled models to robustly estimate intractable quantities of the original model, such as its intractable partition function.

Currently, Markov-Gibbs random field (MGRF) image models which include high-order interactions are almost always built by modelling responses of a stack of local linear filters. Actual interaction structure is specified implicitly by the filter coefficients. In contrast, we learn an explicit high-order MGRF structure by considering the learning process in terms of general exponential family distributions nested over base models, so that potentials added later can build on previous ones. We relatively rapidly add new features by skipping over the costly optimisation of parameters. We introduce the use of local binary patterns as features in MGRF texture models, and generalise them by learning offsets to the surrounding pixels. These prove effective as high-order features, and are fast to compute. Several schemes for selecting high-order features by composition or search of a small subclass are compared. Additionally we present a simple modification of the maximum likelihood as a texture modelling-specific objective function which aims to improve generalisation by local windowing of statistics. The proposed method was experimentally evaluated by learning high-order MGRF models for a broad selection of complex textures and then performing texture synthesis, and succeeded on much of the continuum from stochastic through irregularly structured to near-regular textures. Learning interaction structure is very beneficial for textures with large-scale structure, although those with complex irregular structure still provide difficulties. The texture models were also quantitatively evaluated on two tasks and found to be competitive with other works: grading of synthesised textures by a panel of observers; and comparison against several recent MGRF models by evaluation on a constrained inpainting task.

The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically observed. Within this context, the paper proposes a probabilistic framework for the construction of "POD-Galerkin" reduced-order models. Assuming a hidden Markov chain, the inference integrates the uncertainty of the hidden states relying on their posterior distribution. Simulations show the benefits obtained by exploiting the proposed framework.

Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental non-expansiveness property of filtering maps in the space of probability distributions endowed with the Hilbert metric. This is viewed as a preliminary step towards improving the convergence analysis of filtering algorithms over general graphical models.