@inproceedings{discovery10032247, title = {Bayesian Approaches to Distribution Regression}, publisher = {Proceedings of Machine Learning Research}, year = {2018}, booktitle = {Proceedings International Conference on Artificial Intelligence and Statistics - 2018}, series = {International Conference on Artificial Intelligence and Statistics}, note = {This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.}, volume = {84}, editor = {Neil Lawrence and Mark Reid}, address = {Playa Blanca, Lanzarote, Canary Islands}, author = {Law, HCL and Sutherland, DJ and Sejdinovic, D and Flaxman, S}, abstract = {Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the groups. This effectively assumes that small and large groups are estimated equally well, and should have equal weight in the final regression. We account for this uncertainty with a Bayesian distribution regression formalism, improving the robustness and performance of the model when group sizes vary. We frame our models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. We demonstrate our approach on illustrative toy datasets, as well as on a challenging problem of predicting age from images.}, url = {http://proceedings.mlr.press/v84/law18a/law18a.pdf} }