Correlation matrices are omnipresent in multivariate data analysis. When the number $d$ of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case when the variables can be grouped into $K$ clusters with exchangeable dependence; an assumption often made in applications in finance and econometrics. Under this partial exchangeability condition, the corresponding correlation matrix has a block structure and the number of unknown parameters is reduced from $d(d-1)/2$ to at most $K(K+1)/2$. We propose a robust algorithm based on Kendall's rank correlation to identify the clusters without assuming the knowledge of $K$ a priori or anything about the margins except continuity. The corresponding block-structured estimator performs considerably better than the sample Kendall rank correlation matrix when $K < d$. Even in the unstructured case $K = d$, though there is no gain asymptotically, the new estimator can be much more efficient in finite samples. When the data are elliptical, the results extend to linear correlation matrices and their inverses. The procedure is illustrated on financial stock returns.

In many machine learning applications, it is important to explain the predictions of a black-box classifier. For example, why does a deep neural network assign an image to a particular class? We cast interpretability of black-box classifiers as a combinatorial maximization problem and propose an efficient streaming algorithm to solve it subject to cardinality constraints. By extending ideas from Badanidiyuru et al. [2014], we provide a constant factor approximation guarantee for our algorithm in the case of random stream order and a weakly submodular objective function. This is the first such theoretical guarantee for this general class of functions, and we also show that no such algorithm exists for a worst case stream order. Our algorithm obtains similar explanations of Inception V3 predictions $10$ times faster than the state-of-the-art LIME framework of Ribeiro et al. [2016].

The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical machine learning methods such as elastic-net regression, ridge penalized logistic regression, and sparse additive regression. Existing optimization literature has shown that for strongly convex minimization, the CBCD-type methods attain iteration complexity of $\mathcal{O}(p\log(1/\epsilon))$, where $\epsilon$ is a pre-specified accuracy of the objective value, and $p$ is the number of blocks. However, such iteration complexity explicitly depends on $p$, and therefore is at least $p$ times worse than the complexity $\mathcal{O}(\log(1/\epsilon))$ of gradient descent (GD) methods. To bridge this theoretical gap, we propose an improved convergence analysis for the CBCD-type methods. In particular, we first show that for a family of quadratic minimization problems, the iteration complexity $\mathcal{O}(\log^2(p)\cdot\log(1/\epsilon))$ of the CBCD-type methods matches that of the GD methods in term of dependency on $p$, up to a $\log^2 p$ factor. Thus our complexity bounds are sharper than the existing bounds by at least a factor of $p/\log^2(p)$. We also provide a lower bound to confirm that our improved complexity bounds are tight (up to a $\log^2 (p)$ factor), under the assumption that the largest and smallest eigenvalues of the Hessian matrix do not scale with $p$. Finally, we generalize our analysis to other strongly convex minimization problems beyond quadratic ones.

The Whittle likelihood is a widely used and computationally efficient pseudo-likelihood. However, it is known to produce biased parameter estimates for large classes of models. We propose a method for de-biasing Whittle estimates for second-order stationary stochastic processes. The de-biased Whittle likelihood can be computed in the same $\mathcal{O}(n\log n)$ operations as the standard approach. We demonstrate the superior performance of the method in simulation studies and in application to a large-scale oceanographic dataset, where in both cases the de-biased approach reduces bias by up to two orders of magnitude, achieving estimates that are close to exact maximum likelihood, at a fraction of the computational cost. We prove that the method yields estimates that are consistent at an optimal convergence rate of $n^{-1/2}$, under weaker assumptions than standard theory, where we do not require that the power spectral density is continuous in frequency. We describe how the method can be easily combined with standard methods of bias reduction, such as tapering and differencing, to further reduce bias in parameter estimates.

New KDnuggets Poll is asking: Which Data Science / Machine Learning methods and tools you used in the past 12 months for work or a real-world project? Please vote below and we will summarize the results and examine the trends in early December. Poll Which Data Science / Machine Learning methods and tools you used in the past 12 months for a real-world application? Kaggle survey asked: What data science methods are used at work? and the top answers were Gradient Boosted Machines

In this work, we consider the task of classifying the binary positive-unlabeled (PU) data. The existing discriminative learning based PU models attempt to seek an optimal re-weighting strategy for U data, so that a decent decision boundary can be found. In contrast, we provide a totally new paradigm to attack the binary PU task, from perspective of generative learning by leveraging the powerful generative adversarial networks (GANs). Our generative positive-unlabeled (GPU) learning model is devised to express P and N data distributions. It comprises of three discriminators and two generators with different roles, producing both positive and negative samples that resemble those come from the real training dataset. Even with rather limited labeled P data, our GPU framework is capable of capturing the underlying P and N data distribution with infinite realistic sample streams. In this way, an optimal classifier can be trained on those generated samples using a very deep neural networks (DNNs). Moreover, an useful variant of GPU is also introduced for semi-supervised classification.

Domain generalization is the problem of assigning class labels to an unlabeled test data set, given several labeled training data sets drawn from similar distributions. This problem arises in several applications where data distributions fluctuate because of biological, technical, or other sources of variation. We develop a distribution-free, kernel-based approach that predicts a classifier from the marginal distribution of features, by leveraging the trends present in related classification tasks. This approach involves identifying an appropriate reproducing kernel Hilbert space and optimizing a regularized empirical risk over the space. We present generalization error analysis, describe universal kernels, and establish universal consistency of the proposed methodology. Experimental results on synthetic data and three real data applications demonstrate the superiority of the method with respect to a pooling strategy.

Abstract-- Spinal cord stimulation has enabled humans with motor complete spinal cord injury (SCI) to independently stand and recover some lost autonomic function. Quantifying the quality of bipedal standing under spinal stimulation is important for spinal rehabilitation therapies and for new strategies that seek to combine spinal stimulation and rehabilitative robots (such as exoskeletons) in real time feedback. To study the potential for automated electromyography (EMG) analysis in SCI, we evaluated the standing quality of paralyzed patients undergoing electrical spinal cord stimulation using both video and multi-channel surface EMG recordings during spinal stimulation therapy sessions. The quality of standing under different stimulation settings was quantified manually by experienced clinicians. By correlating features of the recorded EMG activity with the expert evaluations, we show that multi-channel EMG recording can provide accurate, fast, and robust estimation for the quality of bipedal standing in spinally stimulated SCI patients. Moreover, our analysis shows that the total number of EMG channels needed to effectively predict standing quality can be reduced while maintaining high estimation accuracy, which provides more flexibility for rehabilitation robotic systems to incorporate EMG recordings. I. INTRODUCTION Spinal Cord Injury (SCI) is a debilitating condition that afflicts 350,000 people in the U.S., and 5 million worldwide. Electrical spinal stimulation, using multi-electrode arrays implanted in the epidural space over the lumbosacral spinal cord (see Figure 1), has enabled motor complete paralyzed SCI sufferers to achieve independent weight bearing standing, some weight-assisted stepping, and partial recovery of lost autonomic function.

Detection of protein-protein interactions (PPIs) plays a vital role in molecular biology. Particularly, infections are caused by the interactions of host and pathogen proteins. It is important to identify host-pathogen interactions (HPIs) to discover new drugs to counter infectious diseases. Conventional wet lab PPI prediction techniques have limitations in terms of large scale application and budget. Hence, computational approaches are developed to predict PPIs. This study aims to develop large margin machine learning models to predict interspecies PPIs with a special interest in host-pathogen protein interactions (HPIs). Especially, we focus on seeking answers to three queries that arise while developing an HPI predictor. 1) How should we select negative samples? 2) What should be the size of negative samples as compared to the positive samples? 3) What type of margin violation penalty should be used to train the predictor? We compare two available methods for negative sampling. Moreover, we propose a new method of assigning weights to each training example in weighted SVM depending on the distance of the negative examples from the positive examples. We have also developed a web server for our HPI predictor called HoPItor (Host Pathogen Interaction predicTOR) that can predict interactions between human and viral proteins. This webserver can be accessed at the URL: http://faculty.pieas.edu.pk/fayyaz/software.html#HoPItor.

The EM algorithm is one of many important tools in the field of statistics. While often used for imputing missing data, its widespread applications include other common statistical tasks, such as clustering. In clustering, the EM algorithm assumes a parametric distribution for the clusters, whose parameters are estimated through a novel iterative procedure that is based on the theory of maximum likelihood. However, one major drawback of the EM algorithm, that renders it impractical especially when working with large datasets, is that it often requires several passes of the data before convergence. In this paper, we introduce a new EM-style algorithm that implements a novel policy for performing partial E-steps. We call the new algorithm the EM-Tau algorithm, which can approximate the traditional EM algorithm with high accuracy but with only a fraction of the running time.