Related papers: Learning Discrete Distributions from Untrusted Bat…
In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…
In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete return distribution (denoted $\eta^\pi$) attained…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing,…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
We study the problem of learning exponential distributions under differential privacy. Given $n$ i.i.d.\ samples from $\mathrm{Exp}(\lambda)$, the goal is to privately estimate $\lambda$ so that the learned distribution is close in total…
We consider the problem of learning the exact skeleton of general discrete Bayesian networks from potentially corrupted data. Building on distributionally robust optimization and a regression approach, we propose to optimize the most…
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…
The classic problems of testing uniformity of and learning a discrete distribution, given access to independent samples from it, are examined under general $\ell_p$ metrics. The intuitions and results often contrast with the classic…
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
We establish optimal Statistical Query (SQ) lower bounds for robustly learning certain families of discrete high-dimensional distributions. In particular, we show that no efficient SQ algorithm with access to an $\epsilon$-corrupted binary…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
With the recently rapid development in deep learning, deep neural networks have been widely adopted in many real-life applications. However, deep neural networks are also known to have very little control over its uncertainty for unseen…
We consider learning in an adversarial environment, where an $\varepsilon$-fraction of samples from a distribution $P$ are arbitrarily modified (global corruptions) and the remaining perturbations have average magnitude bounded by $\rho$…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…