An approximate Bayes factor based high dimensional MANOVA using Random Projections

TL;DR

This paper introduces a novel high-dimensional MANOVA test using Bayes factors and random projections, effectively handling complex feature dependencies without assuming sparsity or diagonal covariance structures.

Contribution

It develops a new Bayesian testing procedure based on random projections for high-dimensional mean comparisons, avoiding covariance matrix inversion and dependency assumptions.

Findings

The proposed tests perform well in simulations across various dependency structures.

Application to scRNA-seq data demonstrates practical utility.

Ensemble of Bayes factors improves robustness of the test.

Abstract

High-dimensional mean vector testing problem for two or more groups remain a very active research area. In these setting, traditional tests are not applicable because they involve the inversion of rank deficient group covariance matrix. In current approaches, this problem is addressed by simply looking at a test assuming a sparse or diagonal covariance matrix potentially ignoring complex dependency between features. In this paper, we develop a Bayes factor (BF) based testing procedure for comparing two or more population means in (very) high dimensional settings. Two versions of the Bayes factor based test statistics are considered which are based on a Random projection (RP) approach. RPs are appealing since they make not assumption about the form of the dependency across features in the data. The final test statistic is based on an ensemble of Bayes factors corresponding to multiple replications of randomly projected data. Both proposed test statistics are compared through a battery of simulation settings. Finally they are applied to the analysis of a publicly available genomic single cell RNA-seq (scRNA-seq) dataset.