Bayesian Learning for Dynamic Inference

TL;DR

This paper formulates Bayesian learning for dynamic inference, addressing sequential estimation where future states depend on current estimates, and unifies various machine learning problems under this framework.

Contribution

It introduces optimal Bayesian learning rules for dynamic inference, both offline and online, and shows how many machine learning problems are special cases of this meta problem.

Findings

Derived optimal Bayesian learning rules for dynamic inference.

Unified multiple machine learning paradigms under a single Bayesian framework.

Provided insights into the broad applicability of dynamic Bayesian learning.

Abstract

The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity. In some sequential estimation problems however, the future values of the quantity to be estimated depend on the estimate of its current value. This type of estimation problems has been formulated as the dynamic inference problem. In this work, we formulate the Bayesian learning problem for dynamic inference, where the unknown quantity-generation model is assumed to be randomly drawn according to a random model parameter. We derive the optimal Bayesian learning rules, both offline and online, to minimize the inference loss. Moreover, learning for dynamic inference can serve as a meta problem, such that all familiar machine learning problems, including supervised learning, imitation learning and reinforcement learning, can be cast as its special cases or variants. Gaining a good understanding of this unifying meta problem thus sheds light on a broad spectrum of machine learning problems as well.