Detection and Feature Selection in Sparse Mixture Models

TL;DR

This paper investigates detection and feature selection in high-dimensional Gaussian mixture models, deriving theoretical bounds and evaluating procedures like eigenvalue-based tests and moment-based tests under sparsity assumptions.

Contribution

It provides new information bounds and compares the performance of various detection procedures in sparse high-dimensional Gaussian mixtures.

Findings

Eigenvalue-based tests perform well under certain sparsity conditions

Moment-based tests like skewness and kurtosis are effective with improved null control

Theoretical bounds guide the choice of detection methods in high-dimensional settings

Abstract

We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance of various procedures, including the top sparse eigenvalue of the sample covariance matrix and other projection tests based on moments, such as the skewness and kurtosis tests of Malkovich and Afifi (1973), and other variants which we were better able to control under the null.