From prediction to inference: Bayesian uncertainty quantification for recursive predictive algorithms

We are used to go from inference to prediction.  In a predictive approach,  one would directly reason on the predictive rule.  Yet,  many predictive algorithms lack formal uncertainty quantification. This talk presents a methodology for providing Bayesian uncertainty quantification for a class of recursive predictive algorithms that includes, for example, popular online gradient descent with streaming data.
We read these algorithms as Bayesian predictive learning rules, which allows us reveal their  implicit modeling assumptions and provide uncertainty quantification through a new asymptotic expression of the posterior distribution. The key for these results lies in the Bayesian predictive approach, where inferential model are deduced from the predictive rule.