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Pré-Publication, Document De Travail Année : 2021

Viking: Variational Bayesian Variance Tracking

Résumé

We consider the problem of time series forecasting in an adaptive setting. We focus on the inference of state-space models under unknown and potentially time-varying noise variances. We introduce an augmented model in which the variances are represented as auxiliary gaussian latent variables in a tracking mode. As variances are nonnegative, a transformation is chosen and applied to these latent variables. The inference relies on the online variational Bayesian methodology, which consists in minimizing a Kullback-Leibler divergence at each time step. We observe that the minimum of the Kullback-Leibler divergence is an extension of the Kalman filter taking into account the variance uncertainty. We design a novel algorithm, named Viking, using these optimal recursive updates. For auxiliary latent variables, we use second-order bounds whose optimum admit closed-form solutions. Experiments on synthetic data show that Viking behaves well and is robust to misspecification.
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Dates et versions

hal-03199401 , version 1 (15-04-2021)
hal-03199401 , version 2 (08-11-2021)

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Joseph de Vilmarest, Olivier Wintenberger. Viking: Variational Bayesian Variance Tracking. 2021. ⟨hal-03199401v2⟩
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