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.
翻译:我们考虑在适应环境下的时间序列预测问题。 我们侧重于在未知和潜在时间变化的噪音差异下对州- 空间模型的推论。 我们引入了一种强化模型, 差异在跟踪模式中作为辅助的保西潜伏变量。 由于差异不是消极的, 我们选择了一种变异, 并应用到这些潜在变量。 推论依赖于在线的变异贝叶西亚方法, 其中包括在每一个步骤中最大限度地减少库尔后背- 利伯尔差异。 我们观察到, Kullman 过滤器的最小差异是考虑到差异不确定性的延伸。 我们设计了一个名为维京的新型算法, 使用这些最佳的递归性更新。 对于辅助潜在变量, 我们使用第二顺序的界限, 其最佳的允许封闭式解决方案。 合成数据实验显示, Viking 运行良好, 且 强于错误的定位 。