  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.
