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There is an overwhelmingly large literature and algorithms already available on `large scale inference problems' based on different modeling techniques and cultures. Our primary goal in this paper is \emph{not to add one more new…

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…

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…

Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…

We consider the problem of detecting sparse heterogeneous mixtures in a two-sample setting from a nonparametric perspective, where the effect manifests itself as a positive shift. We suggest a two-sample higher criticism test, and show that…

Starting from few simple examples we have proposed a general method for finding an exact analytical solution for the two state scattering problem in presence of a delta function coupling. We have also extended our model to deal with general…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…

We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…

We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…

A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…

We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization…

We propose a monotone, and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized Infinity Laplacian, which could be related to the family of so--called two--scale methods. We show that this method is…

A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…

We describe here the general mathematical approach to constructing likelihoods for fitting observed spectra in one or more dimensions with multiple sources, including the effects of systematic uncertainties represented as nuisance…

In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…

The Gauss Circle Problem concerns finding asymptotics for the number of lattice point lying inside a circle in terms of the radius of the circle. The heuristic that the number of points is very nearly the area of the circle is surprisingly…