Variational Kalman Filtering with Hinf-Based Correction for Robust Bayesian Learning in High Dimensions

• URL: http://arxiv.org/abs/2204.13089v1
• Date: Wed, 27 Apr 2022 17:38:13 GMT
• Title: Variational Kalman Filtering with Hinf-Based Correction for Robust Bayesian Learning in High Dimensions
• Authors: Niladri Das, Jed A. Duersch, and Thomas A. Catanach
• Abstract summary: 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. A novel VIF- Hinf recursion that employs consecutive variational inference and Hinf based optimization steps is proposed.
• Score: 2.294014185517203
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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