Nudging state-space models for Bayesian filtering under misspecified dynamics

2024-10-31

AI Summary

This work addresses inference failure in Bayesian filtering caused by misspecification of the state-space model (SSM) transition kernel. We propose a robust filtering framework based on nudging, treating it as a data-driven, implicit model correction mechanism that adaptively constructs an equivalent SSM with higher marginal likelihood via optimization of the observation marginal likelihood. Theoretically, we provide the first rigorous guarantee for nudging from a marginal likelihood perspective, proving that it implicitly mitigates dynamical misspecification and enhances filtering robustness. Experiments on both linear Gaussian SSMs and the stochastic Lorenz-63 nonlinear system demonstrate that our method significantly improves estimation accuracy and numerical stability over standard filters. These results validate nudging as a general-purpose, self-calibrating strategy for model correction in sequential inference.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Nudging is a popular algorithmic strategy in numerical filtering to deal with the problem of inference in high-dimensional dynamical systems. We demonstrate in this paper that general nudging techniques can also tackle another crucial statistical problem in filtering, namely the misspecification of the transition model. Specifically, we rely on the formulation of nudging as a general operation increasing the likelihood and prove analytically that, when applied carefully, nudging techniques implicitly define state-space models (SSMs) that have higher marginal likelihoods for a given (fixed) sequence of observations. This provides a theoretical justification of nudging techniques as data-informed algorithmic modifications of SSMs to obtain robust models under misspecified dynamics. To demonstrate the use of nudging, we provide numerical experiments on linear Gaussian SSMs and a stochastic Lorenz 63 model with misspecified dynamics and show that nudging offers a robust filtering strategy for these cases.

Problem

• Addressing inference in high-dimensional dynamical systems
• Correcting misspecified transition kernel in filtering
• Enhancing robustness of state-space models via nudging

Innovation

• Nudging increases likelihood in state-space models
• Nudging tackles transition kernel misspecification issues
• Nudging provides robust filtering for misspecified dynamics