2021/06/01 by Jose, Sharu Theresa, Park, Sangwoo, Simeone, Osvaldo · 2 citations
#FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Machine Learning (cs.LG) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2106.00252
The overall predictive uncertainty of a trained predictor can be decomposed into separate contributions due to epistemic and aleatoric uncertainty. Under a Bayesian formulation, assuming a well-specified model, the two contributions can be exactly expressed (for the log-loss) or bounded (for more general losses) in terms of information-theoretic quantities (Xu and Raginsky, 2020). This paper addresses the study of epistemic uncertainty within an information-theoretic framework in the broader setting of Bayesian meta-learning. A general hierarchical Bayesian model is assumed in which hyperparameters determine the per-task priors of the model parameters. Exact characterizations (for the log-loss) and bounds (for more general losses) are derived for the epistemic uncertainty -quantified by the minimum excess meta-risk (MEMR)- of optimal meta-learning rules. This characterization is leveraged to bring insights into the dependence of the epistemic uncertainty on the number of tasks and on the amount of per-task training data. Experiments are presented that use the proposed information-theoretic bounds, evaluated via neural mutual information estimators, to compare the performance of conventional learning and meta-learning as the number of meta-learning tasks increases.