English
Related papers

Related papers: Optimal Identity Testing with High Probability

200 papers

Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting where the algorithmic task is to accept functions $f : [n] \to \{0,1\}$ with a certain property P and reject…

Computational Complexity · Computer Science 2024-02-19 Hugo Aaronson , Tom Gur , Ninad Rajgopal , Ron D. Rothblum

This paper considers an ML inspired approach to hypothesis testing known as classifier/classification-accuracy testing ($\mathsf{CAT}$). In $\mathsf{CAT}$, one first trains a classifier by feeding it labeled synthetic samples generated by…

Statistics Theory · Mathematics 2025-11-25 Patrik Róbert Gerber , Yanjun Han , Yury Polyanskiy

We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…

Data Structures and Algorithms · Computer Science 2015-01-27 Thomas Steinke , Jonathan Ullman

We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $\ell_2$-norm. These problems have been extensively studied in distribution…

Data Structures and Algorithms · Computer Science 2016-11-14 Ilias Diakonikolas , Themis Gouleakis , John Peebles , Eric Price

A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…

Machine Learning · Computer Science 2016-12-15 Shaofeng Zou , Yingbin Liang , H. Vincent Poor , Xinghua Shi

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…

Data Structures and Algorithms · Computer Science 2021-12-24 Oliver Gebhard , Max Hahn-Klimroth , Olaf Parczyk , Manuel Penschuck , Maurice Rolvien , Jonathan Scarlett , Nelvin Tan

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 $\varepsilon > 0$, $m_1$…

Machine Learning · Computer Science 2015-04-20 Bhaswar B. Bhattacharya , Gregory Valiant

This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0,1\}^n$, given sample access to $P$. We show that the sample complexity of the problem is…

Machine Learning · Computer Science 2023-04-17 Vipul Arora , Arnab Bhattacharyya , Clément L. Canonne , Joy Qiping Yang

There has a major problem in the current theory of hypothesis testing in which no unified indicator to evaluate the goodness of various test methods since the cost function or utility function usually relies on the specific application…

Statistics Theory · Mathematics 2023-06-19 Dazhuan Xu , Nan Wang

Person re-identification (re-id), which aims to retrieve images of the same person in a given image from a database, is one of the most practical image recognition applications. In the real world, however, the environments that the images…

Computer Vision and Pattern Recognition · Computer Science 2025-12-03 Kazuki Adachi , Shohei Enomoto , Taku Sasaki , Shin'ya Yamaguchi

In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…

Information Theory · Computer Science 2025-01-07 Ching-Fang Li , I-Hsiang Wang

Given a finite set of unknown distributions or arms that can be sampled, we consider the problem of identifying the one with the maximum mean using a $\delta$-correct algorithm (an adaptive, sequential algorithm that restricts the…

Machine Learning · Computer Science 2023-11-27 Shubhada Agrawal , Sandeep Juneja , Peter Glynn

We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…

Information Theory · Computer Science 2022-02-15 Lin Zhou , Yun Wei , Alfred Hero

Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, they are often overconfident in their predictions, which leads to inaccurate and miscalibrated…

Machine Learning · Computer Science 2021-02-23 Jeffrey Willette , Juho Lee , Sung Ju Hwang

A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile…

Statistics Theory · Mathematics 2020-11-03 Yanjun Han , Kirankumar Shiragur

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…

Data Structures and Algorithms · Computer Science 2023-04-05 Renato Ferreira Pinto , Nathaniel Harms

Let $\theta_0,\theta_1 \in \mathbb{R}^d$ be the population risk minimizers associated to some loss $\ell:\mathbb{R}^d\times \mathcal{Z}\to\mathbb{R}$ and two distributions $\mathbb{P}_0,\mathbb{P}_1$ on $\mathcal{Z}$. The models…

Statistics Theory · Mathematics 2021-07-13 Dmitrii M. Ostrovskii , Mohamed Ndaoud , Adel Javanmard , Meisam Razaviyayn

Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…

Statistics Theory · Mathematics 2023-10-17 Trung Dang , Walter McKelvie , Paul Valiant , Hongao Wang

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…

Statistics Theory · Mathematics 2021-06-01 Liyan Xie , Rui Gao , Yao Xie

Methods of performing anomaly detection on high-dimensional data sets are needed, since algorithms which are trained on data are only expected to perform well on data that is similar to the training data. There are theoretical results on…

Machine Learning · Computer Science 2020-11-13 Forrest Laine , Claire Tomlin
‹ Prev 1 3 4 5 6 7 10 Next ›