2022/04/27 by Niladri Das, Jed A. Duersch, Das, Niladri +3
Computer Science · #Applications (stat.AP) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Electrical engineering #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2204.13089
openalex publication_date 2022/04/27 · openalex created_date 2022/04/30 · openalex updated_date 2026/07/28
In this paper, we address the problem of convergence of sequential variational inference filter (VIF) through the application of a robust variational objective and Hinf-norm based correction for a linear Gaussian system. As the dimension of state or parameter space grows, performing the full Kalman update with the dense covariance matrix for a large scale system requires increased storage and computational complexity, making it impractical. The VIF approach, based on mean-field Gaussian variational inference, reduces this burden through the variational approximation to the covariance usually in the form of a diagonal covariance approximation. The challenge is to retain convergence and correct for biases introduced by the sequential VIF steps. We desire a framework that improves feasibility while still maintaining reasonable proximity to the optimal Kalman filter as data is assimilated. To accomplish this goal, a Hinf-norm based optimization perturbs the VIF covariance matrix to improve robustness. This yields a novel VIF- Hinf recursion that employs consecutive variational inference and Hinf based optimization steps. We explore the development of this method and investigate a numerical example to illustrate the effectiveness of the proposed filter.