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The method of optimizing entropy is used to (i) conduct Asymptotic Hypothesis Testing and (ii) determine the particle distribution for which Entropy is maximized. This paper focuses on two related applications of Information Theory:…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
We model equilibrium allocations in a distribution network as the solution of a linear program (LP) which minimizes the cost of unserved demands across nodes in the network. The constraints in the LP dictate that once a given node's supply…
We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step…
We consider the set of finite sequences of length n over a finite or countable alphabet C. We consider the function which associate each given sequence with the size of the maximum overlap with a (shifted) copy of itself. We compute the…
Designing networks to optimize robustness and other performance metrics is a well-established problem with applications ranging from electrical engineering to communication networks. Many such performance measures rely on the Laplacian…
Many functionals of interest in statistics and machine learning can be written as minimizers of expected loss functions. Such functionals are called $M$-estimands, and can be estimated by $M$-estimators -- minimizers of empirical average…
We focus on the optimal value for various information-theoretical tasks. There are several studies for the asymptotic expansion for these optimal values up to the order $\sqrt{n}$ or $\log n$. However, these expansions have errors of the…
We consider the distributionally robust optimization and show that computing the distributional worst-case is equivalent to computing the projection onto the canonical simplex with additional linear inequality. We consider several distance…
Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by…
Many sparse linear discriminant analysis (LDA) methods have been proposed to overcome the major problems of the classic LDA in high-dimensional settings. However, the asymptotic optimality results are limited to the case that there are only…
Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…
We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse…
We study convex empirical risk minimization for high-dimensional inference in binary models. Our first result sharply predicts the statistical performance of such estimators in the linear asymptotic regime under isotropic Gaussian features.…
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the…
In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…