Speakers

Lars Kai Hansen

Professor, Technical University of Denmark (Denmark)

Missing-Data-Induced Phase Transition in Spectral PLS for Multimodal Learning

Partial Least Squares (PLS) learns shared structure from paired data via the top singular vectors of the empirical cross-covariance (PLS-SVD), but multimodal datasets often have missing entries in both views. We study PLS-SVD under independent entry-wise missing-completely-at-random masking in a simple high-dimensional model. We find theoretically and empirically that PLS-SVD exhibits a sharp BBP-type phase transition: below a critical signal-to-noise threshold the leading singular vectors are asymptotically uninformative, while above it they achieve nontrivial alignment with the "planted" shared directions. The theoretical analysis provides closed-form asymptotic overlap formulas.