Related papers: Expected $L_2-$discrepancy bound for a class of ne…
This paper introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponential decay of a novel Lyapunov function along with the…
We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random…
We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models. We show that the KL divergence is bounded below by a…
We investigate the high-probability estimation of discrete distributions from an \iid sample under $\chi^2$-divergence loss. Although the minimax risk in expectation is well understood, its high-probability counterpart remains largely…
This paper studies the convex hull of $d$-dimensional samples i.i.d. generated from spherically symmetric distributions. Specifically, we derive a complete integration formula for the expected facet number of the convex hull. This formula…
We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
Generative models have been successfully used for generating realistic signals. Because the likelihood function is typically intractable in most of these models, the common practice is to use "implicit" models that avoid likelihood…
We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
This paper develops a unified framework for partial identification and inference in stratified experiments with attrition, accommodating both equal and heterogeneous treatment shares across strata. For equal-share designs, we apply recent…
We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…
Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless…
We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we…
In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex…
We analyze the coordinate descent method with a new coordinate selection strategy, called volume sampling. This strategy prescribes selecting subsets of variables of certain size proportionally to the determinants of principal submatrices…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
We address the multiclass classification problem for stochastic diffusion paths, assuming that the classes are distinguished by their drift functions, while the diffusion coefficient remains common across all classes. In this setting, we…