MOFTy: Multimodal Gaussian Process Factor Analysis with Numerical Information Field Theory

Abstract

Multimodal Gaussian process factor analysis provides a flexible framework for dimensionality reduction in temporally or spatially resolved omics data. Existing approaches, however, typically rely on pre-specified Gaussian process kernel families and do not explicitly separate each latent factor into a component capturing gradual, smooth variation and a complementary component capturing fine-scale, non-smooth variation. Here, we present MOFTy, a Bayesian multimodal factor analysis framework based on numerical information field theory (NIFTy) that replaces fixed kernel families with the flexible correlated field model in NIFTy and enables explicit additive component separation within each latent factor with quantified uncertainty. NIFTy has been successfully applied to high-resolution Bayesian imaging in astrophysics and facilitates scalable, curvature-aware variational inference for efficient posterior approximations. We validate MOFTy on simulated data; applications to published multi-omics data demonstrate that MOFTy disentangles latent spatial structures by separating smooth gradients from localized fine-scale heterogeneity in human glioblastoma and recovers cross-modal patterns in a mouse gastrulation dataset.