Information-Theoretic Analysis of Epistemic Uncertainty in Bayesian Meta-learning

Sharu Theresa Jose, Sangwoo Park, Osvaldo Simeone
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:9758-9775, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-theresa-jose22a, title = { Information-Theoretic Analysis of Epistemic Uncertainty in Bayesian Meta-learning }, author = {Theresa Jose, Sharu and Park, Sangwoo and Simeone, Osvaldo}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {9758--9775}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/theresa-jose22a/theresa-jose22a.pdf}, url = {https://proceedings.mlr.press/v151/theresa-jose22a.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Information-Theoretic Analysis of Epistemic Uncertainty in Bayesian Meta-learning %A Sharu Theresa Jose %A Sangwoo Park %A Osvaldo Simeone %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-theresa-jose22a %I PMLR %P 9758--9775 %U https://proceedings.mlr.press/v151/theresa-jose22a.html %V 151 %X 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.
APA
Theresa Jose, S., Park, S. & Simeone, O.. (2022). Information-Theoretic Analysis of Epistemic Uncertainty in Bayesian Meta-learning . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:9758-9775 Available from https://proceedings.mlr.press/v151/theresa-jose22a.html.

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