Viking: Variational Bayesian Variance Tracking

TL;DR

Viking introduces an online variational Bayesian method for adaptive time series forecasting that effectively tracks unknown, time-varying noise variances within state-space models, extending Kalman filtering.

Contribution

The paper proposes a novel algorithm, Viking, which models variances as latent variables and uses variational Bayesian inference for adaptive variance tracking in time series forecasting.

Findings

Viking performs well on synthetic data.

Viking is robust to model misspecification.

The method extends Kalman filtering to account for variance uncertainty.

Abstract

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.