The Hierarchical Adaptive Forgetting Variational Filter
This work addresses the challenge of real-time distribution change detection for machine learning and statistics, though it appears incremental as it builds on existing variational and hierarchical Bayesian methods.
The paper tackles the problem of detecting distribution shifts and outliers in streaming data by introducing a hierarchical Bayesian algorithm that learns time-specific approximate posterior distributions for exponential family models, with applications in reinforcement learning, adaptive Bayesian autoregressive models, and stochastic gradient descent optimization.
A common problem in Machine Learning and statistics consists in detecting whether the current sample in a stream of data belongs to the same distribution as previous ones, is an isolated outlier or inaugurates a new distribution of data. We present a hierarchical Bayesian algorithm that aims at learning a time-specific approximate posterior distribution of the parameters describing the distribution of the data observed. We derive the update equations of the variational parameters of the approximate posterior at each time step for models from the exponential family, and show that these updates find interesting correspondents in Reinforcement Learning (RL). In this perspective, our model can be seen as a hierarchical RL algorithm that learns a posterior distribution according to a certain stability confidence that is, in turn, learned according to its own stability confidence. Finally, we show some applications of our generic model, first in a RL context, next with an adaptive Bayesian Autoregressive model, and finally in the context of Stochastic Gradient Descent optimization.