Robust Filtering and Learning in State-Space Models: Skewness and Heavy Tails Via Asymmetric Laplace Distribution

2025-07-29

AI Summary

To address the limited robustness of state-space models under non-Gaussian (skewed, heavy-tailed) noise, this paper proposes a novel modeling framework based on the asymmetric Laplace distribution (ALD). By explicitly incorporating ALD for both observation and process noise, the framework captures skewness and heavy-tailedness in dynamic data. We develop a single-loop variational Bayesian algorithm that jointly performs filtering, smoothing, and parameter learning—eliminating multi-stage iterations and manual hyperparameter tuning. The method is highly adaptive, computationally efficient, and achieves superior performance over conventional Gaussian-assumption models across diverse anomalous noise scenarios. Moreover, it incurs lower memory and runtime overhead. This work establishes an interpretable, lightweight, and deployable paradigm for robust analysis of dynamic systems.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

State-space models are pivotal for dynamic system analysis but often struggle with outlier data that deviates from Gaussian distributions, frequently exhibiting skewness and heavy tails. This paper introduces a robust extension utilizing the asymmetric Laplace distribution, specifically tailored to capture these complex characteristics. We propose an efficient variational Bayes algorithm and a novel single-loop parameter estimation strategy, significantly enhancing the efficiency of the filtering, smoothing, and parameter estimation processes. Our comprehensive experiments demonstrate that our methods provide consistently robust performance across various noise settings without the need for manual hyperparameter adjustments. In stark contrast, existing models generally rely on specific noise conditions and necessitate extensive manual tuning. Moreover, our approach uses far fewer computational resources, thereby validating the model's effectiveness and underscoring its potential for practical applications in fields such as robust control and financial modeling.

Problem

• Handles outlier data with skewness and heavy tails
• Improves filtering and parameter estimation efficiency
• Reduces computational resources and manual tuning

Innovation

• Uses asymmetric Laplace distribution for robustness
• Implements efficient variational Bayes algorithm
• Novel single-loop parameter estimation strategy