Viking: Variational Bayesian Variance Tracking
This work addresses adaptive forecasting for scenarios with uncertain noise variances, though it appears incremental as it builds on existing variational Bayesian and Kalman filter frameworks.
The paper tackles time series forecasting with unknown, time-varying noise variances by introducing an augmented state-space model with auxiliary Gaussian latent variables for variance tracking, resulting in a novel algorithm called Viking that demonstrates robustness to model misspecification in synthetic experiments.
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.