On Uncertainty Quantification for Near-Bayes Optimal Algorithms
This work addresses the problem of uncertainty quantification for safety-critical applications in machine learning, offering a novel approach that applies broadly but is incremental in building on existing Bayesian and algorithmic efficiency concepts.
The paper tackles the challenge of quantifying predictive uncertainty for machine learning algorithms that lack a Bayesian counterpart by hypothesizing that efficient algorithms are near Bayes-optimal relative to an unknown task distribution, and it proves that the Bayesian posterior can be recovered via a martingale posterior, with experiments showing the method's efficacy across various algorithms.
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.