Optimal thresholds and algorithms for a model of multi-modal learning in high dimensions
This work addresses the challenge of efficiently recovering latent structures in multi-modal data for fields like machine learning and statistics, providing foundational analytical insights and algorithms, though it is incremental as it builds on existing AMP frameworks.
The paper tackles the problem of multi-modal inference in high-dimensional settings by analytically quantifying the performance gain over single-modal analysis, deriving Bayes-optimal performance and recovery thresholds for recovering latent structures from two noisy data matrices with correlated spikes. It presents an approximate message passing (AMP) algorithm that achieves these thresholds, showing that partial least squares (PLS) and canonical correlation analysis (CCA) methods suffer from sub-optimal recovery thresholds.
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 (CCA) methods, which are both observed to suffer from a sub-optimal recovery threshold.