We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves typically several associated proximal subproblems that usually have a closed-form solution, until a certain progress on objective value is achieved. In contrast to the usual randomized block coordinate descent method [23,20], our method has a nonmonotone flavor and uses variable stepsizes that can partially utilize the local curvature information of the smooth component of objective function. We show that any accumulation point of the solution sequence of the method is a stationary point of the problem {\it almost surely} and the method is capable of finding an approximate stationary point with high probability. We also establish a sublinear rate of convergence for the method in terms of the minimal expected squared norm of certain proximal gradients over the iterations. When the problem under consideration is convex, we show that the expected objective values generated by RNBPG converge to the optimal value of the problem. Under some assumptions, we further establish a sublinear and linear rate of convergence on the expected objective values generated by a monotone version of RNBPG. Finally, we conduct some preliminary experiments to test the performance of RNBPG on the $\ell_1$-regularized least-squares problem and a dual SVM problem in machine learning. The computational results demonstrate that our method substantially outperforms the randomized block coordinate {\it descent} method with fixed or variable stepsizes.

In medical domain, data features often contain missing values. This can create serious bias in the predictive modeling. Typical standard data mining methods often produce poor performance measures. In this paper, we propose a new method to simultaneously classify large datasets and reduce the effects of missing values. The proposed method is based on a multilevel framework of the cost-sensitive SVM and the expected maximization imputation method for missing values, which relies on iterated regression analyses. We compare classification results of multilevel SVM-based algorithms on public benchmark datasets with imbalanced classes and missing values as well as real data in health applications, and show that our multilevel SVM-based method produces fast, and more accurate and robust classification results.

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed input results in the model outputting an incorrect answer with high confidence. Early attempts at explaining this phenomenon focused on nonlinearity and overfitting. We argue instead that the primary cause of neural networks' vulnerability to adversarial perturbation is their linear nature. This explanation is supported by new quantitative results while giving the first explanation of the most intriguing fact about them: their generalization across architectures and training sets. Moreover, this view yields a simple and fast method of generating adversarial examples. Using this approach to provide examples for adversarial training, we reduce the test set error of a maxout network on the MNIST dataset.

Estimation of response functions is an important task in dynamic medical imaging. This task arises for example in dynamic renal scintigraphy, where impulse response or retention functions are estimated, or in functional magnetic resonance imaging where hemodynamic response functions are required. These functions can not be observed directly and their estimation is complicated because the recorded images are subject to superposition of underlying signals. Therefore, the response functions are estimated via blind source separation and deconvolution. Performance of this algorithm heavily depends on the used models of the response functions. Response functions in real image sequences are rather complicated and finding a suitable parametric form is problematic. In this paper, we study estimation of the response functions using non-parametric Bayesian priors. These priors were designed to favor desirable properties of the functions, such as sparsity or smoothness. These assumptions are used within hierarchical priors of the blind source separation and deconvolution algorithm. Comparison of the resulting algorithms with these priors is performed on synthetic dataset as well as on real datasets from dynamic renal scintigraphy. It is shown that flexible non-parametric priors improve estimation of response functions in both cases. MATLAB implementation of the resulting algorithms is freely available for download.

Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront the so-called "crowding problem" that clusters tend to overlap with each other in the embedding. Previously, researchers expect to avoid that problem and seek to make clusters maximally separated in the embedding. However, the proposed in-tree (IT) based method, called IT-map, allows clusters in the embedding to be locally overlapped, while seeking to make them distinguishable by some small yet key parts. IT-map provides a simple, effective and novel solution to cluster-preserving mapping, which makes it possible to cluster the original data points interactively and thus should be of general meaning in science and engineering.

In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its dual Voronoi tessellation, we propose a nonparametric process to compute potential values by the local information. This computation, though nonparametric, is relatively very rough, and consequently, many local extreme points will be generated. However, unlike those gradient-based methods, our IT-based methods are generally insensitive to those local extremes. This positively demonstrates the superiority of these parametric (previous) and nonparametric (in this work) IT-based methods.

We propose a sequential learning policy for noisy discrete global optimization and ranking and selection (R\&S) problems with high dimensional sparse belief functions, where there are hundreds or even thousands of features, but only a small portion of these features contain explanatory power. We aim to identify the sparsity pattern and select the best alternative before the finite budget is exhausted. We derive a knowledge gradient policy for sparse linear models (KGSpLin) with group Lasso penalty. This policy is a unique and novel hybrid of Bayesian R\&S with frequentist learning. Particularly, our method naturally combines B-spline basis expansion and generalizes to the nonparametric additive model (KGSpAM) and functional ANOVA model. Theoretically, we provide the estimation error bounds of the posterior mean estimate and the functional estimate. Controlled experiments show that the algorithm efficiently learns the correct set of nonzero parameters even when the model is imbedded with hundreds of dummy parameters. Also it outperforms the knowledge gradient for a linear model.

This paper presents a novel approach to speaker subspace modelling based on Gaussian-Binary Restricted Boltzmann Machines (GRBM). The proposed model is based on the idea of shared factors as in the Probabilistic Linear Discriminant Analysis (PLDA). GRBM hidden layer is divided into speaker and channel factors, herein the speaker factor is shared over all vectors of the speaker. Then Maximum Likelihood Parameter Estimation (MLE) for proposed model is introduced. Various new scoring techniques for speaker verification using GRBM are proposed. The results for NIST i-vector Challenge 2014 dataset are presented.

Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called $l_0$ norm. In this paper we develop a Momentumized Iterative Shrinkage Thresholding (MIST) algorithm for minimizing the resulting non-convex criterion and prove its convergence to a local minimizer. Simulations on large data sets show superior performance of the proposed method to other methods.

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the de-biasing technique with the composite quantile function to construct an estimator that is asymptotically normal. Hence it can be used to construct valid confidence intervals and conduct hypothesis tests. Our estimator is robust and does not require the existence of first or second moment of the noise distribution. It also preserves efficiency in the sense that the worst case efficiency loss is less than 30\% compared to the square-loss-based de-biased Lasso estimator. In many cases our estimator is close to or better than the latter, especially when the noise is heavy-tailed. Our de-biasing procedure does not require solving the $L_1$-penalized composite quantile regression. Instead, it allows for any first-stage estimator with desired convergence rate and empirical sparsity. The paper also provides new proof techniques for developing theoretical guarantees of inferential procedures with non-smooth loss functions. To establish the main results, we exploit the local curvature of the conditional expectation of composite quantile loss and apply empirical process theories to control the difference between empirical quantities and their conditional expectations. Our results are established under weaker assumptions compared to existing work on inference for high-dimensional quantile regression. Furthermore, we consider a high-dimensional simultaneous test for the regression parameters by applying the Gaussian approximation and multiplier bootstrap theories. We also study distributed learning and exploit the divide-and-conquer estimator to reduce computation complexity when the sample size is massive. Finally, we provide empirical results to verify the theory.