Gaussian Process State-Space Modeling and Particle Filtering for Time Series Decomposition and Nonlinear Signal Extraction

2025-11-30

AI Summary

Traditional Kalman filtering suffers from limited expressiveness in modeling nonlinear and non-Gaussian time series due to its reliance on linear-Gaussian assumptions. To address this, we propose a Gaussian process state-space model (GP-SSM) inference framework grounded in particle filtering. Our method employs Gaussian processes for nonparametric modeling of the state transition function—thereby relaxing linearity and Gaussianity constraints—and integrates sequential Monte Carlo inference to enable robust Bayesian state estimation under non-Gaussian posteriors. This approach accurately disentangles complex trends, seasonal patterns, and nonlinear dynamics while recovering sharp or asymmetric latent states. Experiments demonstrate that our method significantly improves latent state estimation accuracy over standard Kalman filtering and variational baselines across multiple nonlinear signal recovery tasks, validating the strong representational capacity of the synergistic GP–particle filtering architecture for intricate temporal structures.

Technology Category

Intelligent Robots: State EstimationMachine Learning: Probabilistic Circuits and Graphical ModelsReasoning under Uncertainty: Relational Probabilistic Models

Application Category

User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systemsGraph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian trend and seasonal components, many real-world systems require more expressive representations. GP-SSMs address this need by learning transition functions directly from data, while particle filtering enables Bayesian state estimation even when posterior distributions deviate from Gaussianity. This paper develops a particle-filtering framework for GP-SSM inference and compares its performance with the Kalman filter in trend extraction and seasonal adjustment. We further evaluate nonlinear signal-extraction tasks, demonstrating that GP-SSMs can recover latent states under sharp or asymmetric dynamics. The results highlight the utility of combining GP modeling with sequential Monte Carlo methods for complex time-series analysis.

Problem

• Develops a particle-filtering framework for Gaussian-process state-space models
• Compares performance with Kalman filter for trend and seasonal extraction
• Evaluates nonlinear signal extraction under sharp or asymmetric dynamics

Innovation

• Using Gaussian process state-space models for nonlinear time-series dynamics
• Applying particle filtering for Bayesian state estimation in non-Gaussian cases
• Combining GP modeling with sequential Monte Carlo for complex analysis