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

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.

Robust and Constrained Estimation of State-Space Models: A Majorization-Minimization Approach

In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in existing approaches: susceptibility to measurement noise outliers and difficulties in incorporating constraints into state estimation. By formulating constrained state estimation as an optimization problem and employing the Majorization-Minimization (MM) approach, our framework provides a unified solution that enhances the robustness of the Kalman filter. Experimental results demonstrate high accuracy and computational efficiency achieved by our proposed approach, establishing it as a promising solution for robust and constrained state estimation in real-world applications.

A Fast Successive QP Algorithm for General Mean-Variance Portfolio Optimization

The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express a preference among these efficient portfolios, investors have put forward many mean-variance portfolio (MVP) formulations which date back to the classical Markowitz portfolio. However, most existing algorithms are highly specialized to particular formulations and cannot be generalized for broader applications. Therefore, a fast and unified algorithm would be extremely beneficial. In this paper, we first introduce a general MVP problem formulation that can fit most existing cases by exploring their commonalities. Then, we propose a widely applicable and provably convergent successive quadratic programming algorithm (SCQP) for the general formulation. The proposed algorithm can be implemented based on only the QP solvers and thus is computationally efficient. In addition, a fast implementation is considered to accelerate the algorithm. The numerical results show that our proposed algorithm significantly outperforms the state-of-the-art ones in terms of convergence speed and scalability.