Optimal thresholds and algorithms for a model of multi-modal learning in high dimensions

This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance and recovery thresholds in a model where the objective is t...

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Bibliographic Details
Published in:	Journal of statistical mechanics Vol. 2025; no. 9
Main Authors:	Keup, Christian, Zdeborová, Lenka
Format:	Journal Article
Language:	English
Published:	IOP Publishing 01.09.2025
Subjects:	analysis of algorithms classical phase transitions learning theory machine learning message-passing algorithms statistical inference
ISSN:	1742-5468
Online Access:	Get full text
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Summary:	This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance and recovery thresholds in a model where the objective is to recover the latent structures from two noisy data matrices with correlated spikes. The paper derives the approximate message passing (AMP) algorithm for this model and characterizes its performance in the high-dimensional limit via the associated state evolution. The analysis holds for a broad range of priors and noise channels, which can differ across modalities. The linearization of AMP is compared numerically to the widely used partial least squares (PLS) and canonical correlation analysis methods, which are both observed to suffer from a sub-optimal recovery threshold.
Bibliography:	JSTAT_008P_1224
ISSN:	1742-5468
DOI:	10.1088/1742-5468/ae0428