On Universality and Training in Binary Hypothesis Testing

04/03/2020
by   Michael Bell, et al.
0

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For testing in the simple normal location problem (that is, testing for the mean of multivariate Gaussians), we overcome the difficulty as follows. In this problem there exists a natural hardness order between parameters as for different parameters the error-probailities curves (when the parameter is known) are either identical, or one dominates the other. We can thus define minimax performance as the worst-case among parameters which are below some hardness level. Fortunately, there exists a universal minimax test, in the sense that it is minimax for all hardness levels simultaneously. Under this criterion we also find the optimal test for composite hypothesis testing with training data. This criterion extends to the wide class of local asymptotic normal models, in an asymptotic sense where the approximation of the error probabilities is additive. Since we have the asymptotically optimal tests for composite hypothesis testing with and without training data, we quantify the loss of universality and gain of training data for these models.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/04/2021

Generalized Likelihood Ratio Test for Adversarially Robust Hypothesis Testing

Machine learning models are known to be susceptible to adversarial attac...
research
03/09/2022

A continuous multiple hypothesis testing framework for optimal exoplanet detection

The detection of exoplanets is hindered by the presence of complex astro...
research
06/29/2023

Universal Reverse Information Projections and Optimal E-statistics

Information projections have found many important applications in probab...
research
11/16/2020

Adversarially Robust Classification based on GLRT

Machine learning models are vulnerable to adversarial attacks that can o...
research
02/27/2018

Generalized Binary Search For Split-Neighborly Problems

In sequential hypothesis testing, Generalized Binary Search (GBS) greedi...
research
12/08/2017

Nonparametric Composite Hypothesis Testing in an Asymptotic Regime

We investigate the nonparametric, composite hypothesis testing problem f...
research
08/21/2019

Efficient and powerful equivalency test on combined mean and variance with application to diagnostic device comparison studies

In medical device comparison studies, equivalency test is commonly used ...

Please sign up or login with your details

Forgot password? Click here to reset