DeepAI AI Chat
Log In Sign Up

Geometry of the Minimum Volume Confidence Sets

by   Heguang Lin, et al.
University of Wisconsin-Madison

Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. This paper studies the geometry of the minimum-volume confidence sets for the multinomial parameter. When used in place of more standard confidence sets and intervals based on bounds and asymptotic approximation, learning algorithms can exhibit improved sample complexity. Prior work showed the minimum-volume confidence sets are the level-sets of a discontinuous function defined by an exact p-value. While the confidence sets are optimal in that they have minimum average volume, computation of membership of a single point in the set is challenging for problems of modest size. Since the confidence sets are level-sets of discontinuous functions, little is apparent about their geometry. This paper studies the geometry of the minimum volume confidence sets by enumerating and covering the continuous regions of the exact p-value function. This addresses a fundamental question in A/B testing: given two multinomial outcomes, how can one determine if their corresponding minimum volume confidence sets are disjoint? We answer this question in a restricted setting.


page 1

page 2

page 3

page 4


Optimal hypergeometric confidence sets are (almost) always intervals

We present an efficient method of calculating exact confidence intervals...

Optimal Confidence Regions for the Multinomial Parameter

Construction of tight confidence regions and intervals is central to sta...

Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry

This paper studies and critically discusses the construction of nonparam...

Robust Exploration with Tight Bayesian Plausibility Sets

Optimism about the poorly understood states and actions is the main driv...

A Note on High-Dimensional Confidence Regions

Recent advances in statistics introduced versions of the central limit t...

Asymptotic Confidence Regions for Density Ridges

We develop large sample theory including nonparametric confidence region...

Constructing Exact Confidence Regions on Parameter Manifolds of Non-Linear Models

Using the mathematical framework of information geometry, we introduce a...