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

TL;DR

This paper presents a robust state-space modeling approach using the asymmetric Laplace distribution, improving filtering and learning in the presence of skewed and heavy-tailed noise, with efficient algorithms and broad applicability.

Contribution

It introduces a novel robust extension for state-space models employing the asymmetric Laplace distribution, along with an efficient variational Bayes algorithm and a single-loop parameter estimation method.

Findings

Consistently robust performance across various noise conditions

Requires less manual hyperparameter tuning

Uses fewer computational resources

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.