用非对称拉普拉斯分布提升状态空间模型对偏斜重尾噪声的鲁棒性
Robust Filtering and Learning in State-Space Models: Skewness and Heavy Tails Via Asymmetric Laplace Distribution
- 以非对称拉普拉斯分布建模偏斜和重尾噪声，替代传统高斯假设
- 提出单循环参数估计法，过滤与学习效率显著提升，无需手动调参
- 计算资源消耗少，适用于金融建模、鲁棒控制等实际场景
状态空间模型在动态系统分析中至关重要，但常因偏离高斯分布的异常值而表现不佳，尤其在存在偏斜和重尾噪声时。本文引入非对称拉普拉斯分布，专门捕捉这些复杂特性，提出一种高效的变分贝叶斯算法及新颖的单循环参数估计策略，显著提升了滤波、平滑与参数估计的效率。实验表明，该方法在多种噪声条件下均表现稳健，无需人工调参；而现有方法通常依赖特定噪声假设且需大量调参。此外，本方法计算开销更小，验证了其有效性与在鲁棒控制、金融建模等领域的应用潜力。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。