Related papers: $\ell_p$ Testing and Learning of Discrete Distribu…
In the first part of the paper we study absolute error of sampling discretization of the integral $L_p$-norm for function classes of continuous functions. We use basic approaches from chaining technique to provide general upper bounds for…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
Consider a regression problem where the learner is given a large collection of $d$-dimensional data points, but can only query a small subset of the real-valued labels. How many queries are needed to obtain a $1+\epsilon$ relative error…
We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…
Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…
In this paper we investigate the probability distribution of the sum $Y$ of $\ell$ independent identically distributed random variables taking values in $\mathbb{Z}_p$. Our main focus is the regime of small values of $\ell$, which is less…
We observe an infinite sequence of independent identically distributed random variables $X_1,X_2,\ldots$ drawn from an unknown distribution $p$ over $[n]$, and our goal is to estimate the entropy $H(p)=-\mathbb{E}[\log p(X)]$ within an…
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 $\varepsilon > 0$, $m_1$…
We consider the following basic learning task: given independent draws from an unknown distribution over a discrete support, output an approximation of the distribution that is as accurate as possible in $\ell_1$ distance (i.e. total…
Randomized smoothing, using just a simple isotropic Gaussian distribution, has been shown to produce good robustness guarantees against $\ell_2$-norm bounded adversaries. In this work, we show that extending the smoothing technique to…
Given samples from an unknown distribution $p$ and a description of a distribution $q$, are $p$ and $q$ close or far? This question of "identity testing" has received significant attention in the case of testing whether $p$ and $q$ are…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
Data subsampling is one of the most natural methods to approximate a massively large data set by a small representative proxy. In particular, sensitivity sampling received a lot of attention, which samples points proportional to an…
We study the question of identity testing for structured distributions. More precisely, given samples from a {\em structured} distribution $q$ over $[n]$ and an explicit distribution $p$ over $[n]$, we wish to distinguish whether $q=p$…
We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…
We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the $\ell_p$ ball of radius $\epsilon$ when $p>2$. Although random smoothing has been well understood for the $\ell_2$ case using…
Recently, there has been significant work studying distribution testing under the Conditional Sampling model. In this model, a query specifies a subset $S$ of the domain, and the output received is a sample drawn from the distribution…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
In many fairness and distribution robustness problems, one has access to labeled data from multiple source distributions yet the test data may come from an arbitrary member or a mixture of them. We study the problem of constructing a…
We study the problem of learning from unlabeled samples very general statistical mixture models on large finite sets. Specifically, the model to be learned, $\vartheta$, is a probability distribution over probability distributions $p$,…