Computational Inference for Directions in Canonical Correlation Analysis

TL;DR

This paper introduces a bootstrap-based computational method for inference on canonical directions in CCA, enhancing interpretability and validated through simulations and brain imaging data analysis.

Contribution

The paper presents combootcca, a novel bootstrap method for inference on CCA directions, addressing a gap in interpretability of canonical variates.

Findings

Combootcca accurately estimates canonical directions in simulations.

The method outperforms existing competitors in statistical validation.

Application reveals meaningful brain connectivity patterns linked to behavior.

Abstract

Canonical Correlation Analysis (CCA) is a method for analyzing pairs of random vectors; it learns a sequence of paired linear transformations such that the resultant canonical variates are maximally correlated within pairs while uncorrelated across pairs. CCA outputs both canonical correlations as well as the canonical directions which define the transformations. While inference for canonical correlations is well developed, conducting inference for canonical directions is more challenging and not well-studied, but is key to interpretability. We propose a computational bootstrap method (combootcca) for inference on CCA directions. We conduct thorough simulation studies that range from simple and well-controlled to complex but realistic and validate the statistical properties of combootcca while comparing it to several competitors. We also apply the combootcca method to a brain imaging dataset and discover linked patterns in brain connectivity and behavioral scores.