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Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
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…
We present a general approach to visualizing uncertainty in static 2-D statistical graphics. If we treat a visualization as a function of its underlying quantities, uncertainty in those quantities induces a distribution over images. We show…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
The dynamics of systems of many degrees of freedom evolving on multiple scales are often modeled in terms of stochastic differential equations. Usually the structural form of these equations is unknown and the only manifestation of the…
Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…
This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…
This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
We study the problem of two-sample comparison with categorical data when the contingency table is sparsely populated. In modern applications, the number of categories is often comparable to the sample size, causing existing methods to have…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
One central goal of design of observational studies is to embed non-experimental data into an approximate randomized controlled trial using statistical matching. Despite empirical researchers' best intention and effort to create…
In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…
We propose a class of two-sample statistics for testing the equality of proportions and the equality of survival functions. We build our proposal on a weighted combination of a score test for the difference in proportions and a Weighted…