Related papers: Optimal Closeness Testing of Discrete Distribution…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
In this paper, we present a method for factor analysis of discrete data. This is accomplished by fitting a dependent Poisson model with a factor structure. To be able to analyze ordinal data, we also consider a truncated Poisson…
Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete…
In this short note, we identify and address an error in the proof of Theorem 1.3 in Canonne et al. (2018), a recent breakthrough in conditional independence testing. After correcting the error, we show that the general sample complexity…
In this paper, we address the problem of testing goodness-of-fit for discrete distributions, where we focus on the geometric distribution. We define new likelihood-based goodness-of-fit tests using the beta-geometric distribution and the…
In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…
We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy. While the problems have a long history in statistics, finite…
We investigate the statistical task of closeness (or equivalence) testing for multidimensional distributions. Specifically, given sample access to two unknown distributions $\mathbf p, \mathbf q$ on $\mathbb R^d$, we want to distinguish…
By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein's method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying…
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
The paper is devoted to restricted Oppenheim expansion of real numbers ($ROE$),which includes as partial cases already known Engel, Silvester and L\"uroth expansions. We find conditions under which for almost all (with respect to Lebesgue…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized…