# Distribution-Free Distribution Regression

arXiv: https://arxiv.org/abs/1302.0082 · HTML: https://mlsanity.com/paper/1302.0082/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2013.

## Built on by (most cited first, 21 of 21)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution Regression with Sliced Wasserstein Kernels](https://mlsanity.com/paper/2202.03926/) (2022)
- [Label-Free Model Evaluation with Semi-Structured Dataset Representations](https://mlsanity.com/paper/2112.00694/) (2021)
- [Robust Kernel-based Distribution Regression](https://mlsanity.com/paper/2104.10637/) (2021)
- [Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernels](https://mlsanity.com/paper/2402.03838/) (2024)
- [Gaussian Processes on Distributions based on Regularized Optimal Transport](https://mlsanity.com/paper/2210.06574/) (2022)
- [Statistical learning on measures: an application to persistence diagrams](https://mlsanity.com/paper/2303.08456/) (2023)
- [Learning Theory of Distribution Regression with Neural Networks](https://mlsanity.com/paper/2307.03487/) (2023)
- [Learning to Embed Distributions via Maximum Kernel Entropy](https://mlsanity.com/paper/2408.00549/) (2024)
- [Performance of Distribution Regression with Doubling Measure under the seek of Closest Point](https://mlsanity.com/paper/2203.00155/) (2022)
- [Generalized Identifiability Bounds for Mixture Models with Grouped Samples](https://mlsanity.com/paper/2207.11164/) (2022)
- [Coefficient-based Regularized Distribution Regression](https://mlsanity.com/paper/2208.12427/) (2022)
- [Improved learning theory for kernel distribution regression with two-stage sampling](https://mlsanity.com/paper/2308.14335/) (2023)
- [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)
- [Guidance Not Obstruction: A Conjugate Consistent Enhanced Strategy for Domain Generalization](https://mlsanity.com/paper/2412.10089/) (2024)
- [Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regression](https://mlsanity.com/paper/2606.00512/) (2026)
- [A Unified Framework for In-Context Learning with Causal and Masked Language Models](https://mlsanity.com/paper/2607.04081/) (2026)
- [Sparse Priors for Efficient Distribution Learning](https://mlsanity.com/paper/2609.20883/) (2026)

## Abstract (arXiv)

`Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + mu where f is an unknown regression function and mu is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P. In this paper we develop theory and methods for distribution-free versions of distribution regression. This means that we do not make distributional assumptions about the error term mu and covariate P. We prove that when the effective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.