2022/06/01 by Mathis Chagneux, Élisabeth Gassiat, Chagneux, Mathis +5
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2206.00319
openalex publication_date 2022/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish for the first time that, under mixing assumptions, the variational approximation of expectations of additive state functionals induces an error which grows at most linearly in the number of observations. This guarantee is consistent with the known upper bounds for the approximation of smoothing distributions using standard Monte Carlo methods. Moreover, we propose an amortized inference framework where a neural network shared over all times steps outputs the parameters of the variational kernels. We also study empirically parametrizations which allow analytical marginalization of the variational distributions, and therefore lead to efficient smoothing algorithms. Significant improvements are made over state-of-the art variational solutions, especially when the generative model depends on a strongly nonlinear and noninjective mixing function.