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Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and in many cases also an upper bound. Estimating these bounds…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We introduce overdispersed black-box variational inference, a method to reduce the variance of the Monte Carlo estimator of the gradient in black-box variational inference. Instead of taking samples from the variational distribution, we use…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
We consider the problem of testing distribution identity. Given a sequence of independent samples from an unknown distribution on a domain of size n, the goal is to check if the unknown distribution approximately equals a known distribution…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example,…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by…
We study the prevalent problem when a test distribution differs from the training distribution. We consider a setting where our training set consists of a small number of sample domains, but where we have many samples in each domain. Our…
We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…
Machine-learning classifiers can be leveraged as a two-sample statistical test. Suppose each sample is assigned a different label and that a classifier can obtain a better-than-chance result discriminating them. In this case, we can infer…
We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…
It is crucial to detect when an instance lies downright too far from the training samples for the machine learning model to be trusted, a challenge known as out-of-distribution (OOD) detection. For neural networks, one approach to this task…
We introduce the problem of determining if the mode of the output distribution of a quantum circuit (given as a black-box) is larger than a given threshold, named HighDist, and a similar problem based on the absolute values of the…
Real-world visual data often exhibits a long-tailed distribution, where some ''head'' classes have a large number of samples, yet only a few samples are available for ''tail'' classes. Such imbalanced distribution causes a great challenge…
The capability of reliably detecting out-of-distribution samples is one of the key factors in deploying a good classifier, as the test distribution always does not match with the training distribution in most real-world applications. In…
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…