Related papers: Learning discrete distributions with infinite supp…

This paper considers estimation and inference in semiparametric econometric models. Standard procedures estimate the model based on an independence restriction that induces a minimum distance between a joint cumulative distribution function…

We consider the Cauchy problem for the evolutive discrete p-Laplacian in infinite graphs, with initial data decaying at infinity. We prove optimal sup and gradient bounds for nonnegative solutions, when the initial data has finite mass, and…

This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…

We consider a residuals-based distributionally robust optimization (DRO) model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt both parametric and nonparametric regression models to learn…

This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is…

This paper is concerned with learning decision makers' preferences using data on observed choices from a finite set of risky alternatives. We propose a discrete choice model with unobserved heterogeneity in consideration sets and in…

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution $D$. The seller has "data"' about $D$ in the form of $m \ge 1$ i.i.d. samples, and the algorithmic challenge is to use these…

We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…

We consider the problem of estimating the support size of a discrete distribution whose minimum non-zero mass is at least $ \frac{1}{k}$. Under the independent sampling model, we show that the sample complexity, i.e., the minimal sample…

Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In addition, the intractable element of the infinite…

This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard…

Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we introduce some new computational tools that do…

For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed…

We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…

We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

We establish two theorems for assessing the accuracy in total variation of multivariate discrete normal approximation to the distribution of an integer valued random vector $W$. The first is for sums of random vectors whose dependence…

We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds…