Slow Feature Analysis as Variational Inference Objective

TL;DR

This paper introduces a probabilistic variational inference perspective on Slow Feature Analysis, relaxing linearity constraints and framing slowness as a regularizer within a reconstruction loss framework.

Contribution

It provides a novel probabilistic interpretation of SFA via variational inference, extending beyond linear models and offering new insights into the method's constraints.

Findings

Recasts SFA as a variational inference problem.

Shows slowness as a regularizer for reconstruction.

Discusses potential new research directions.

Abstract

This work presents a novel probabilistic interpretation of Slow Feature Analysis (SFA) through the lens of variational inference. Unlike prior formulations that recover linear SFA from Gaussian state-space models with linear emissions, this approach relaxes the key constraint of linearity. While it does not lead to full equivalence to non-linear SFA, it recasts the classical slowness objective in a variational framework. Specifically, it allows the slowness objective to be interpreted as a regularizer to a reconstruction loss. Furthermore, we provide arguments, why -- from the perspective of slowness optimization -- the reconstruction loss takes on the role of the constraints that ensure informativeness in SFA. We conclude with a discussion of potential new research directions.