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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Vydáno v:Journal of statistical mechanics Ročník 2025; číslo 9
Hlavní autoři: Keup, Christian, Zdeborová, Lenka
Médium: Journal Article
Jazyk:angličtina
Vydáno: IOP Publishing 01.09.2025
Témata:
analysis of algorithms
classical phase transitions
learning theory
machine learning
message-passing algorithms
statistical inference
ISSN:1742-5468
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Shrnutí: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.
Bibliografie:JSTAT_008P_1224
ISSN:1742-5468
DOI:10.1088/1742-5468/ae0428