The authors improve probabilistic partial least squares (PPLS)—a likelihood-based method for two-view learning (e.g., linking gene expression and clinical outcomes) that produces interpretable latent factors and calibrated uncertainty. Existing fitting methods couple noise and signal in awkward ways and struggle with orthogonality constraints; this paper separates noise estimation from signal estimation, replaces penalty-based constraint handling with exact optimization on the Stiefel manifold (the space of orthonormal matrices), and provides closed-form standard errors. The result is better-calibrated uncertainty and improved prediction, especially in high-noise settings.
Main takeaways:
- PPLS is a probabilistic model for two-view learning (e.g., multi-omics data) that jointly estimates latent factors and their uncertainty.
- Previous methods entangled noise and signal estimation and used awkward penalty methods for orthogonality constraints.
- This paper pre-estimates noise in a separate subspace, then optimizes the likelihood exactly on the Stiefel manifold (the space of orthonormal matrices).
- The noise-subspace estimator achieves a signal-strength-independent finite-sample rate and matches a minimax lower bound; the old full-spectrum estimator is provably inconsistent.
- Experiments on TCGA-BRCA and PBMC CITE-seq show near-nominal coverage without recalibration, Ridge-level accuracy at rank 3, and better stability than competing methods.