We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse zero-variance discriminant analysis (SZVD), for simultaneously performing linear discriminant analysis and feature selection on high dimensional data. This method combines classical zero-variance discriminant analysis, where discriminant vectors are identified in the null space of the sample within-class covariance matrix, with penalization applied to induce sparse structures in the resulting vectors. To approximately solve the resulting nonconvex problem, we develop a simple algorithm based on the alternating direction method of multipliers. Further, we show that this algorithm is applicable to a larger class of penalized generalized eigenvalue problems, including a particular relaxation of the sparse principal component analysis problem. Finally, we establish theoretical guarantees for convergence of our algorithm to stationary points of the original nonconvex problem, and empirically demonstrate the effectiveness of our heuristic for classifying simulated data and data drawn from applications in time-series classification.

Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods perform impressively well, they have a significant disadvantage, the lack of transparency, limiting the interpretability of the solution and thus the scope of application in practice. Especially DNNs act as black boxes due to their multilayer nonlinear structure. In this paper we introduce a novel methodology for interpreting generic multilayer neural networks by decomposing the network classification decision into contributions of its input elements. Although our focus is on image classification, the method is applicable to a broad set of input data, learning tasks and network architectures. Our method is based on deep Taylor decomposition and efficiently utilizes the structure of the network by backpropagating the explanations from the output to the input layer. We evaluate the proposed method empirically on the MNIST and ILSVRC data sets.

We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for the locally optimal control algorithm presented here, with objective formed from the variance trace of the expected posterior distribution. We present results for linear flows near hyperbolic fixed points. Keywords: Bayesian inverse problem, Lagrangian data assimilation, Optimal control, Ocean glider 2010 MSC: 49M, 62F, 62L, 93C, 65C 1. Introduction The need for a more accurate and better resolved estimate of oceanic flows is being driven by a number of pressing global issues, including the crisis facing many species of fish and waterborne organisms, the mitigation of pollutants resulting from spills and offshore contamination, and the important role played by ocean dynamics on climate change. Scientific efforts to estimate ocean flow began in the 1980s with the work of Robinson [1], but has enjoyed limited success due to a lack of observational data. In an effort to improve the current state of understanding of the world's oceans, autonomous vehicles (AVs) are being deployed for the collection of physical oceanography data in a growing number of projects around the globe.

At the forefront of neuroscientific research is the study of functional connectivity; defined as the statistical dependencies across spatially remote brain regions [Friston, 1994, 2011]. While traditional neuroimaging studies focused on the roles of specific brain regions, there has recently been a significant shift towards understanding the connectivity across regions [Smith, 2012]. This shift has been partially catalyzed by recent advances in imaging techniques. In particular, the introduction of functional MRI (fMRI) has played a crucial role by providing a noninvasive mechanism through which to obtain whole-brain coverage of neuronal activity [Huettel, Song and McCarthy, 2004, Poldrack, Mumford and Nichols, 2011]. The focus of this work involves estimating functional connectivity networks from fMRI data, however the methodology presented can also be used in conjunction with other imaging modalities. From a statistical perspective, Gaussian Graphical models (GGMs) are often employed to model functional connectivity [Smith et al., 2011, Varoquaux and Craddock, 2013]. In this manner, undirected connectivity networks can be inferred by studying the conditional independence structures across brain regions [Lauritzen, 1996].

Genome-wide association studies have proven to be essential for understanding the genetic basis of disease. However, many complex traits---personality traits, facial features, disease subtyping---are inherently high-dimensional, impeding simple approaches to association mapping. We developed a nonparametric Bayesian reduced rank regression model for multi-SNP, multi-trait association mapping that does not require the rank of the linear subspace to be specified. We show in simulations and real data that our model shares strength over SNPs and over correlated traits, improving statistical power to identify genetic associations with an interpretable, SNP-supervised low-dimensional linear projection of the high-dimensional phenotype. On the HapMap phase 3 gene expression QTL study data, we identify pleiotropic expression QTLs that classical univariate tests are underpowered to find and that two step approaches cannot recover. Our Python software, BERRRI, is publicly available at GitHub: https://github.com/ashlee1031/BERRRI.

Recent work has shown that optical flow estimation can be formulated as a supervised learning task and can be successfully solved with convolutional networks. Training of the so-called FlowNet was enabled by a large synthetically generated dataset. The present paper extends the concept of optical flow estimation via convolutional networks to disparity and scene flow estimation. To this end, we propose three synthetic stereo video datasets with sufficient realism, variation, and size to successfully train large networks. Our datasets are the first large-scale datasets to enable training and evaluating scene flow methods. Besides the datasets, we present a convolutional network for real-time disparity estimation that provides state-of-the-art results. By combining a flow and disparity estimation network and training it jointly, we demonstrate the first scene flow estimation with a convolutional network.

Our goal is to deploy a high-accuracy system starting with zero training examples. We consider an "on-the-job" setting, where as inputs arrive, we use real-time crowdsourcing to resolve uncertainty where needed and output our prediction when confident. As the model improves over time, the reliance on crowdsourcing queries decreases. We cast our setting as a stochastic game based on Bayesian decision theory, which allows us to balance latency, cost, and accuracy objectives in a principled way. Computing the optimal policy is intractable, so we develop an approximation based on Monte Carlo Tree Search. We tested our approach on three datasets---named-entity recognition, sentiment classification, and image classification. On the NER task we obtained more than an order of magnitude reduction in cost compared to full human annotation, while boosting performance relative to the expert provided labels. We also achieve a 8% F1 improvement over having a single human label the whole set, and a 28% F1 improvement over online learning.

Kozlenko, M.I. (2012), "Frequency resource using of the spread spectrum signals forming in the distributed computer and telecommunication systems", Kozlenko, M.I. (2012), "Time complexity of the variable entropy spread spectrum signals digital demodulation", To obtain the interference immunity of the data exchange by spread spectrum signals with variable entropy of the telemetric information data exchange with autonomous mobile robots. The results have been obtained by the theoretical investigations and have been confirmed by the modeling experiments. The interference immunity in form of dependence of bit error probability on normalized signal/noise ratio of the data exchange by spread spectrum signals with variable entropy has been obtained. It has been proved that the interference immunity fa ctor (needed normalized signal/noise ratio) is at least 2 dB better under condition of equal time complexity as compared with correlation processing methods of orthogonal signals. For the first time the interference immunity in form of dependence of bit error probability on normalized signal/noise ratio of the data exchange by spread spectrum signals with variable entropy has been obtained.

Understanding a user's motivations provides valuable information beyond the ability to recommend items. Quite often this can be accomplished by perusing both ratings and review texts, since it is the latter where the reasoning for specific preferences is explicitly expressed. Unfortunately matrix factorization approaches to recommendation result in large, complex models that are difficult to interpret and give recommendations that are hard to clearly explain to users. In contrast, in this paper, we attack this problem through succinct additive co-clustering. We devise a novel Bayesian technique for summing co-clusterings of Poisson distributions. With this novel technique we propose a new Bayesian model for joint collaborative filtering of ratings and text reviews through a sum of simple co-clusterings. The simple structure of our model yields easily interpretable recommendations. Even with a simple, succinct structure, our model outperforms competitors in terms of predicting ratings with reviews.

There is renewed interest in formulating integration as a statistical inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. An important challenge is therefore to reconcile these probabilistic integrators with rigorous convergence guarantees. In this paper, we present the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ). Under FWBQ, convergence to the true value of the integral is shown to be up to exponential and posterior contraction rates are proven to be up to super-exponential. In simulations, FWBQ is competitive with state-of-the-art methods and outperforms alternatives based on Frank-Wolfe optimisation. Our approach is applied to successfully quantify numerical error in the solution to a challenging Bayesian model choice problem in cellular biology.