Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions

TL;DR

This paper develops spectral algorithms for high-dimensional correlated two-view models, achieving optimal detection and recovery thresholds without prior parameter knowledge, validated across three canonical models.

Contribution

It introduces a unified spectral framework based on a TAP heuristic, providing explicit algorithms that match theoretical limits in multiple models.

Findings

Spectral algorithms achieve detection and recovery down to theoretical thresholds.

Algorithms operate without prior knowledge of model parameters.

Framework applies to canonical correlation analysis, spiked Wigner, and Wishart models.

Abstract

We study high-dimensional inference in correlated two-view models, focusing on spectral methods for strong detection and weak recovery. We introduce a general framework, motivated by a TAP type heuristic from statistical physics, that provides a unified treatment of three canonical models: high-dimensional canonical correlation analysis, and the correlated spiked Wigner and Wishart models. Our main contribution is to construct explicit spectral algorithms in all three settings, that achieve strong detection and weak recovery down to the corresponding thresholds, where we prove matching information-theoretic lower bounds. Furthermore, our spectral procedures operate without knowledge of the model parameters, relying solely on the observed data. This demonstrates the optimality of spectral methods in these models and the broad statistical applicability of the framework.