Learning Linear Dynamical Systems with Sparse System Matrices
Keywords: linear dynamical systems, state estimation, system identification, expectation–maximization algorithm
Abstract: Due to the tractable analysis and control, linear dynamical systems (LDSs) provide a fundamental mathematical tool for time-series data modeling in various disciplines. Particularly, many LDSs have sparse system matrices because interactions among variables are limited or only a few significant relationships exist. However, available learning algorithms for LDSs lack the ability to learn system matrices with the sparsity constraint. To address this issue, we impose sparsity-promoting priors on system matrices and explore the expectation–maximization (EM) algorithm to give a maximum a posteriori (MAP) estimate of both hidden states and system matrices from noisy observations. In addition, we find that many learning algorithms based on the gradient descent method use an inappropriate derivative rule, because they neglect the inherent symmetry of noise covariance matrices. Here, we consider the derivative rule of structured matrices during the optimization process to guarantee their symmetry. Experimental results on simulation and real-world problems illustrate that the proposed algorithm significantly improves learning accuracy over classical ones.
Supplementary Material: zip
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 10892
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