# Bayesian Approaches to Distribution Regression

arXiv: https://arxiv.org/abs/1705.04293 · HTML: https://mlsanity.com/paper/1705.04293/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2017.

## Built on by (most cited first, 9 of 9)

- [Signature Methods in Machine Learning](https://mlsanity.com/paper/2206.14674/) (2022)
- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [BayesIMP: Uncertainty Quantification for Causal Data Fusion](https://mlsanity.com/paper/2106.03477/) (2021)
- [Learning to Embed Distributions via Maximum Kernel Entropy](https://mlsanity.com/paper/2408.00549/) (2024)
- [A fast and effective kernel two-sample test for large-scale data](https://mlsanity.com/paper/2110.03118/) (2021)
- [Bayesian Additive Distribution Regression](https://mlsanity.com/paper/2603.06462/) (2026)
- [GGMPs: Generalized Gaussian Mixture Processes](https://mlsanity.com/paper/2603.10442/) (2026)
- [LearnedWMP: Workload Memory Prediction Using Distribution of Query Templates](https://mlsanity.com/paper/2401.12103/) (2024)
- [Scalable Signature-Based Distribution Regression via Reference Sets](https://mlsanity.com/paper/2410.09196/) (2024)

## Abstract (arXiv)

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.