  Bayesian modelling allows for the quantification of predictive uncertainty
which is crucial in safety-critical applications. Yet for many machine learning
(ML) algorithms, it is difficult to construct or implement their Bayesian
counterpart. In this work we present a promising approach to address this
challenge, based on the hypothesis that commonly used ML algorithms are
efficient across a wide variety of tasks and may thus be near Bayes-optimal
w.r.t. an unknown task distribution. We prove that it is possible to recover
the Bayesian posterior defined by the task distribution, which is unknown but
optimal in this setting, by building a martingale posterior using the
algorithm. We further propose a practical uncertainty quantification method
that apply to general ML algorithms. Experiments based on a variety of non-NN
and NN algorithms demonstrate the efficacy of our method.
