Viking: variational Bayesian variance tracking

We consider the problem of robust and adaptive time series forecasting in an uncertain environment. We focus on the inference in state-space models under unknown time-varying noise variances and potential misspecification (violation of the state-space data generation assumption). We introduce an augmented model in which the variances are represented by auxiliary Gaussian latent variables in a tracking mode. The inference relies on the online variational Bayesian methodology, which minimizes a Kullback–Leibler divergence at each time step. We observe that optimizing the Kullback–Leibler divergence leads to an extension of the Kalman filter. We design a novel algorithm named Viking, using second-order bounds for the auxiliary latent variables, whose minima admit closed-form solutions. The main step of Viking does not coincide with the standard Kalman filter when the variances of the state-space model are uncertain. Experiments on synthetic and real data show that Viking behaves well and is robust to misspecification.