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Amortized backward variational inference in nonlinear state-space models | | Mathis Chagneux
; Élisabeth Gassiat
; Pierre Gloaguen
; Sylvain Le Corff
; | | Date: |
1 Jun 2022 | | Abstract: | 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. | | Source: | arXiv, 2206.00319 | | Services: | Forum | Review | PDF | Favorites | |
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