Optimal thresholds and algorithms for a model of multi-modal learning in high dimensions
Abstract: 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 weak 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 (CCA) methods, which are both observed to suffer from a sub-optimal recovery threshold.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=VYvYYRKTBO
Changes Since Last Submission: changed from two column to single column formatting
Assigned Action Editor: ~Antoine_Patrick_Isabelle_Eric_Ledent1
Submission Number: 3372
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