Learning state and proposal dynamics in state-space models using differentiable particle filters and neural networks

2024-11-23

Signal Processing

AI Summary

For sequential inference in highly nonlinear state-space models, this paper proposes StateMixNN: an end-to-end learning framework built upon differentiable particle filtering. The method introduces a dual neural network architecture—where one network parameterizes the proposal distribution and the other the state transition distribution—both unified as differentiable Gaussian mixture models (GMMs). This constitutes the first approach to jointly parameterize both distributions and optimize the log-likelihood end-to-end via gradient-based learning. Unlike conventional particle filters or black-box deep state estimators, StateMixNN preserves distributional interpretability while substantially enhancing expressiveness for strong nonlinearities. Empirical evaluation on multiple challenging nonlinear benchmark tasks demonstrates that StateMixNN achieves superior latent state recovery accuracy compared to current state-of-the-art methods.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that uses a pair of neural networks to learn the proposal distribution and transition distribution of a particle filter. Both distributions are approximated using multivariate Gaussian mixtures. The component means and covariances of these mixtures are learnt as outputs of learned functions. Our method is trained targeting the log-likelihood, thereby requiring only the observation series, and combines the interpretability of state-space models with the flexibility and approximation power of artificial neural networks. The proposed method significantly improves recovery of the hidden state in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.

Problem

• Learning proposal and transition distributions in particle filters
• Improving hidden state recovery in non-linear state-space models
• Combining interpretability of SSMs with neural network flexibility

Innovation

• Uses neural networks for proposal and transition distributions
• Approximates distributions with multivariate Gaussian mixtures
• Trains using log-likelihood targeting observation series