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Simultaneous statistical inference has been a cornerstone in the statistics methodology literature because of its fundamental theory and paramount applications. The mainstream multiple testing literature has traditionally considered two…

Statistics Theory · Mathematics 2025-03-21 Monitirtha Dey , Subir Kumar Bhandari

Overparameterized models like deep neural networks have the intriguing ability to recover target functions with fewer sampled data points than parameters (see arXiv:2307.08921). To gain insights into this phenomenon, we concentrate on a…

Machine Learning · Computer Science 2024-05-24 Jiajie Zhao , Zhiwei Bai , Yaoyu Zhang

Deep models are designed to operate on huge volumes of high dimensional data such as images. In order to reduce the volume of data these models must process, we propose a set-based two-stage end-to-end neural subsampling model that is…

Machine Learning · Computer Science 2022-05-31 Bruno Andreis , Seanie Lee , A. Tuan Nguyen , Juho Lee , Eunho Yang , Sung Ju Hwang

A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…

Machine Learning · Computer Science 2024-07-01 Weizhi Li , Prad Kadambi , Pouria Saidi , Karthikeyan Natesan Ramamurthy , Gautam Dasarathy , Visar Berisha

Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce…

Statistics Theory · Mathematics 2017-06-06 Pragya Sur , Yuxin Chen , Emmanuel J. Candès

In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…

Statistics Theory · Mathematics 2024-10-08 Bilol Banerjee , Anil K. Ghosh

This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders…

Methodology · Statistics 2025-12-30 Falong Tan , Jie Liu , Heng Peng , Lixing Zhu

We propose a robust methodology to evaluate the performance and computational efficiency of non-parametric two-sample tests, specifically designed for high-dimensional generative models in scientific applications such as in particle…

Machine Learning · Statistics 2024-09-26 Samuele Grossi , Marco Letizia , Riccardo Torre

The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…

Statistics Theory · Mathematics 2014-12-30 Dayu Huang , Sean Meyn

Stochastic Programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely used class of stochastic programming models. Solving 2SPs exactly…

Optimization and Control · Mathematics 2022-10-14 Justin Dumouchelle , Rahul Patel , Elias B. Khalil , Merve Bodur

For randomized controlled trials to be conclusive, it is important to set the target sample size accurately at the design stage. Comparing two normal populations, the sample size calculation requires specification of the variance other than…

Methodology · Statistics 2026-02-04 Hirotada Maeda , Satoshi Hattori , Tim Friede

Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…

Statistics Theory · Mathematics 2025-03-19 Jialin Zhang , Zhiyi Zhang

We consider two-sample tests for high-dimensional data under two disjoint models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. We provide a general test statistic as a function of a positive-semidefinite matrix.…

Statistics Theory · Mathematics 2016-11-28 Makoto Aoshima , Kazuyoshi Yata

Research often necessitates of samples, yet obtaining large enough samples is not always possible. When it is, the researcher may use one of two methods for deciding upon the required sample size: rules-of-thumb, quick yet uncertain, and…

Methodology · Statistics 2016-04-08 Jose D. Perezgonzalez

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

Machine Learning · Statistics 2025-05-20 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo

We formulate and analyze a stochastic threshold group testing problem motivated by biological applications. Here a set of $n$ items contains a subset of $d \ll n$ defective items. Subsets (pools) of the $n$ items are tested -- the test…

Information Theory · Computer Science 2013-04-25 Chun Lam Chan , Sheng Cai , Mayank Bakshi , Sidharth Jaggi , Venkatesh Saligrama

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more…

Methodology · Statistics 2018-01-23 Z. Bai , D. Jiang , J. Yao , S. Zheng

We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…

Machine Learning · Statistics 2020-03-11 Matthias Kirchler , Shahryar Khorasani , Marius Kloft , Christoph Lippert

A select collection of pseudorandom number generators is applied to a Monte Carlo study of the two dimensional square site percolation model. A generator suitable for high precision calculations is identified from an application specific…

Disordered Systems and Neural Networks · Physics 2009-11-13 Michael J. Lee

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,…

Machine Learning · Computer Science 2024-12-03 Maryam Aliakbarpour , Piotr Indyk , Ronitt Rubinfeld , Sandeep Silwal