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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…

Chemical Physics · Physics 2023-03-24 Huan-Xiang Zhou

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…

Information Theory · Computer Science 2007-07-13 Joseph DeStefano , Erik Learned-Miller

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…

Information Theory · Computer Science 2018-12-07 Lin Zhou , Vincent Y. F. Tan , Mehul Motani

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…

Machine Learning · Statistics 2016-03-04 Francisco J. R. Ruiz , Michalis K. Titsias , David M. Blei

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…

Computational Complexity · Computer Science 2016-08-16 Vitaly Feldman , Elena Grigorescu , Lev Reyzin , Santosh Vempala , Ying Xiao

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…

Data Structures and Algorithms · Computer Science 2009-10-20 Krzysztof Onak

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…

Statistics Theory · Mathematics 2011-11-10 Daniel Berend , Aryeh Kontorovich

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…

Machine Learning · Computer Science 2025-07-04 Ilias Diakonikolas , Jingyi Gao , Daniel Kane , Sihan Liu , Christopher Ye

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,…

Statistics Theory · Mathematics 2019-07-09 Maryam Aliakbarpour , Ravi Kumar , Ronitt Rubinfeld

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…

Statistics Theory · Mathematics 2020-11-13 Christos Tzamos , Emmanouil-Vasileios Vlatakis-Gkaragkounis , Ilias Zadik

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…

Machine Learning · Computer Science 2023-12-04 Yishay Mansour , Mehryar Mohri , Afshin Rostamizadeh

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…

Machine Learning · Computer Science 2011-05-05 Dean Foster , Sham Kakade , Ruslan Salakhutdinov

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…

Data Structures and Algorithms · Computer Science 2024-11-25 Anindya De , Shivam Nadimpalli , Rocco A. Servedio

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…

Machine Learning · Computer Science 2022-12-20 Alejandro Álvarez-Ayllón , Manuel Palomo-Duarte , Juan-Manuel Dodero

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…

Statistics Theory · Mathematics 2024-01-05 Shyam Narayanan

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…

Quantum Physics · Physics 2022-02-23 Debajyoti Bera , Tharrmashastha Sapv

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…

Computer Vision and Pattern Recognition · Computer Science 2020-03-11 Junjie Zhang , Lingqiao Liu , Peng Wang , Chunhua Shen

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…

Machine Learning · Computer Science 2021-04-05 Dongha Lee , Sehun Yu , Hwanjo Yu

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…

Data Structures and Algorithms · Computer Science 2015-12-09 Jayadev Acharya , Constantinos Daskalakis , Gautam Kamath