# Viking: Variational Bayesian Variance Tracking

arXiv: https://arxiv.org/abs/2104.10777 · HTML: https://mlsanity.com/paper/2104.10777/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 16 Apr 2021.

## Builds on (most cited first, 2 of 2)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Stochastic gradient variational Bayes for gamma approximating distributions](https://mlsanity.com/paper/1509.01631/) (2015)

## Built on by (most cited first, 4 of 4)

- [Low-rank extended Kalman filtering for online learning of neural networks from streaming data](https://mlsanity.com/paper/2305.19535/) (2023)
- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)
- [Adaptive time series forecasting with markovian variance switching](https://mlsanity.com/paper/2402.14684/) (2024)
- [Hedging Memory Horizons for Non-Stationary Prediction via Online Aggregation](https://mlsanity.com/paper/2605.06541/) (2026)

## Abstract (arXiv)

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.