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

arXiv: https://arxiv.org/abs/2507.22343 · HTML: https://mlsanity.com/paper/2507.22343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 63 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization](https://mlsanity.com/paper/1805.06963/) (2018)
- [A Variational Bayesian Approach for Image Restoration. Application to Image Deblurring with Poisson-Gaussian Noise](https://mlsanity.com/paper/1610.07519/) (2016)
- [Robust Inference for State-Space Models with Skewed Measurement Noise](https://mlsanity.com/paper/1503.06606/) (2015)
- [Skew-t Filter and Smoother with Improved Covariance Matrix Approximation](https://mlsanity.com/paper/1608.07435/) (2016)

## Abstract (arXiv)

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.