A Generalization Bound for Online Variational Inference
This provides theoretical justification for using approximate Bayesian methods in online learning, which is incremental as it extends existing Bayesian guarantees to practical approximations.
The paper tackles the problem of whether variational inference algorithms preserve the generalization guarantees of Bayesian inference in online learning, showing that some online, tempered VI algorithms do indeed maintain these bounds, with theoretical results supported by empirical evidence.
Bayesian inference provides an attractive online-learning framework to analyze sequential data, and offers generalization guarantees which hold even with model mismatch and adversaries. Unfortunately, exact Bayesian inference is rarely feasible in practice and approximation methods are usually employed, but do such methods preserve the generalization properties of Bayesian inference ? In this paper, we show that this is indeed the case for some variational inference (VI) algorithms. We consider a few existing online, tempered VI algorithms, as well as a new algorithm, and derive their generalization bounds. Our theoretical result relies on the convexity of the variational objective, but we argue that the result should hold more generally and present empirical evidence in support of this. Our work in this paper presents theoretical justifications in favor of online algorithms relying on approximate Bayesian methods.