event

ISyE Statistic Seminar - Alon Kipnis

Title:

How to Test Uniformity in High Dimensions? Sharp Minimax Risk and Applications to Model Calibration

Abstract:

We study the problem of testing the goodness of fit of a sample to a uniform distribution over many categories. We consider a minimax setting in which the class of alternatives is obtained by the removal of an Lp ball around the uniform rate sequence. We deliver an expression describing the asymptotic minimax risk in terms of the number of categories, the size of the sample, and the radius of the Lp ball. 

Our result settles an open question related to works on identity testing in computer science and nonparametric hypothesis testing on distributions in mathematical statistics. It allows the comparison of the many estimators previously proposed for this problem at the constant level, rather than at the rate of convergence of the risk or the scaling order of the sample complexity. 
 
Both the chi-squared and the collision statistics lead to asymptotically minimax tests, although these tests are not asymptotically minimax in the Poissonized version of the problem associated with a random number of samples. We derive a test that is asymptotically minimax under either fixed or random sample size, hence it is better recommended for practitioners. 
 
The proof relies on the adaptations to Poisson data of methods developed for signal detection in white noise and on a new conditional central limit theorem by the de-poissonization step. 

Bio:

Alon Kipnis is a Senior Lecturer (Assistant Professor) at the Efi Arazi School of Computer Science, Reichman University, Israel. He received the Ph.D. in Electrical Engineering from Stanford University in 2017, and was a Koret Foundation Postdoctoral Fellow in Statistics at Stanford University from 2018 to 2021. His research interests include mathematical statistics, information theory, high-dimensional inference, and machine learning. Dr. Kipnis is the recipient of the 2023 Bergman Memorial Research Award of the U.S.–Israel Binational Science Foundation. 

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Summary

We study the problem of testing the goodness of fit of a sample to a uniform distribution over many categories. We consider a minimax setting in which the class of alternatives is obtained by the removal of an Lp ball around the uniform rate sequence. We deliver an expression describing the asymptotic minimax risk in terms of the number of categories, the size of the sample, and the radius of the Lp ball. 

Our result settles an open question related to works on identity testing in computer science and nonparametric hypothesis testing on distributions in mathematical statistics. It allows the comparison of the many estimators previously proposed for this problem at the constant level, rather than at the rate of convergence of the risk or the scaling order of the sample complexity. 
 
Both the chi-squared and the collision statistics lead to asymptotically minimax tests, although these tests are not asymptotically minimax in the Poissonized version of the problem associated with a random number of samples. We derive a test that is asymptotically minimax under either fixed or random sample size, hence it is better recommended for practitioners. 
 
The proof relies on the adaptations to Poisson data of methods developed for signal detection in white noise and on a new conditional central limit theorem by the de-poissonization step. 

 

Details

Tuesday
Mar 31 2026
11:00am - 12:00pm

Location: Groseclose 402

URL: https://www.isye.gatech.edu/about/school/facilities

In campus calendar: Yes

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  • Workflow status: Published
  • Created by: adrysdale7
  • Created: 03/03/2026
  • Modified By: adrysdale7
  • Modified: 03/03/2026

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