Robust Filtering and Learning in State-Space Models: Skewness and Heavy Tails Via Asymmetric Laplace Distribution
This work addresses robust filtering and learning for dynamic systems in fields like control and finance, offering a practical solution with reduced tuning needs, though it appears incremental as it builds on existing distribution-based methods.
The paper tackled the problem of state-space models struggling with outlier data exhibiting skewness and heavy tails by introducing a robust extension using the asymmetric Laplace distribution, resulting in consistently robust performance across various noise settings without manual hyperparameter adjustments and using far fewer computational resources.
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.