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Regime Learning for Differentiable Particle Filters

John-Joseph Brady, Yuhui Luo, Wenwu Wang, Victor Elvira, Yunpeng Li

TL;DR

This work addresses state-space models that can switch between a finite set of regimes by learning both the regimes and the switching dynamics with neural networks. It introduces the regime-learning particle filter (RLPF), which embeds a compact latent memory and an LSTM-like forget-gate mechanism to parameterise the switching, and trains the model with a combined ELBO and MSE objective via a marginal filter strategy. Empirically, the RLPF with the proposed training objective achieves state-of-the-art or competitive performance against strong baselines on regime-switching tasks, outperforming pure supervised or purely probabilistic approaches in terms of accuracy and uncertainty quantification. The approach advances practical regime-aware inference for switching-dynamic systems and lays groundwork for more sophisticated differentiable filtering in complex, real-world scenarios.

Abstract

Differentiable particle filters are an emerging class of models that combine sequential Monte Carlo techniques with the flexibility of neural networks to perform state space inference. This paper concerns the case where the system may switch between a finite set of state-space models, i.e. regimes. No prior approaches effectively learn both the individual regimes and the switching process simultaneously. In this paper, we propose the neural network based regime learning differentiable particle filter (RLPF) to address this problem. We further design a training procedure for the RLPF and other related algorithms. We demonstrate competitive performance compared to the previous state-of-the-art algorithms on a pair of numerical experiments.

Regime Learning for Differentiable Particle Filters

TL;DR

This work addresses state-space models that can switch between a finite set of regimes by learning both the regimes and the switching dynamics with neural networks. It introduces the regime-learning particle filter (RLPF), which embeds a compact latent memory and an LSTM-like forget-gate mechanism to parameterise the switching, and trains the model with a combined ELBO and MSE objective via a marginal filter strategy. Empirically, the RLPF with the proposed training objective achieves state-of-the-art or competitive performance against strong baselines on regime-switching tasks, outperforming pure supervised or purely probabilistic approaches in terms of accuracy and uncertainty quantification. The approach advances practical regime-aware inference for switching-dynamic systems and lays groundwork for more sophisticated differentiable filtering in complex, real-world scenarios.

Abstract

Differentiable particle filters are an emerging class of models that combine sequential Monte Carlo techniques with the flexibility of neural networks to perform state space inference. This paper concerns the case where the system may switch between a finite set of state-space models, i.e. regimes. No prior approaches effectively learn both the individual regimes and the switching process simultaneously. In this paper, we propose the neural network based regime learning differentiable particle filter (RLPF) to address this problem. We further design a training procedure for the RLPF and other related algorithms. We demonstrate competitive performance compared to the previous state-of-the-art algorithms on a pair of numerical experiments.
Paper Structure (16 sections, 12 equations, 3 figures, 2 tables, 2 algorithms)

This paper contains 16 sections, 12 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Preliminaries
  4. Regime switching particle filtering
  5. Differentiable particle filtering
  6. The regime-learning particle filter
  7. Redefining the model
  8. Parameterising the switching dynamic
  9. Training the RLPF
  10. Experiments
  11. Dynamic and observation models
  12. Switching dynamic
  13. Baseline Models
  14. Experiment settings
  15. Results
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Bayesian network representation of the general regime switching model.
  • Figure 2: Bayesian network representation of the proposed modified regime switching model.
  • Figure 3: Graphical representation of our proposed switching dynamic. Blue nodes are input/outputs, purple nodes are fully connected network layers with the specified activation, and yellow nodes are non-learned functions. The switching probability mass, $K^{\theta}\left({k_{t+1}|\mathbf{r}_{t}}\right)$, is the value at the $k_{t+1}^{\text{th}}$ index of the model output $K^{\theta}$.