Meta-Learning PAC-Bayes Priors in Model Averaging

TL;DR

This paper introduces two data-driven algorithms for learning priors in model averaging to better handle model uncertainty, supported by theoretical guarantees and practical success in simulations and real data.

Contribution

It proposes novel meta-learning and subsampling algorithms for PAC-Bayes prior estimation in model averaging, with theoretical risk bounds and empirical validation.

Findings

Algorithms perform well in simulations.

Effective with poor-quality data.

Theoretical risk bounds established.

Abstract

Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a single final model via a model selection procedure to account for this model's uncertainty to improve the reliability and accuracy of inferences. Here one main challenge is to learn the prior over the model set. To tackle this problem, we propose two data-based algorithms to get proper priors for model averaging. One is for meta-learner, the analysts should use historical similar tasks to extract the information about the prior. The other one is for base-learner, a subsampling method is used to deal with the data step by step. Theoretically, an upper bound of risk for our algorithm is presented to guarantee the performance of the worst situation. In practice, both methods perform well in simulations and real data studies, especially with poor-quality data.