Reproduce “Identifiable Feature Learning for Spatial Data with Nonlinear ICA” on OpenResearch

About this paper

Hermanni Hälvä, Jonathan So, Richard E. Turner, Aapo Hyvärinen

The authors introduce tp-NICA, a nonlinear method for spatial independent component analysis. It models latent maps as Student’s t-processes and learns a nonlinear mixing function. In simulations, it recovers two latent maps from four noisy observations with mean absolute correlation coefficient 0.95. On a six-date satellite task, its features improve date-prediction accuracy over raw images; this does not test crop classification.

Key insights

• T-processes, due to their non-Gaussianity, enable broader identifiability for nonlinear Independent Component Analysis compared to Gaussian Processes, which require distinct covariance kernels for identifiability.
• Identifiable nonlinear ICA can be successfully extended to higher-dimensional latent dependencies, like spatial and spatio-temporal data, through the principled use of structured t-Process priors and specific variational inference techniques.
• The learned spatio-temporal features extracted by tp-NICA are demonstrably meaningful, improving performance on real-world downstream classification tasks.

Summary by alphaXiv.