Active-Subspace Particle Filtering for Efficient Inference in High-Dimensional State-Space Models

Particle filtering methods provide a powerful framework for state estimation in nonlinear and non-Gaussian systems. However, their performance deteriorates in high-dimensional settings due to the difficulty of proposing particles that align with the posterior distribution. In many models, the likelihood depends primarily on a low-dimensional projection of the latent state. We introduce the active-subspace particle filter (AS-PF) that exploits this structure to improve sample efficiency. At each time step, the AS-PF estimates a likelihood-informed subspace using particle-based score statistics and constructs structured proposals that concentrate particle mass along the informative directions. The method employs an optimal importance function (which minimizes the weight variance) in the active subspace and propagates the inactive components under the prior. This approach reduces the effects of dimensionality and enhances robustness in complex state-space models. Experimental results on synthesized data demonstrate that AS-PF consistently outperforms standard particle filters, particularly when the observation model has a low-dimensional structure.