mlsanityData to 7 Oct 2026

Distribution-Free Distribution Regression

arXiv 1302.0082 ↗First posted 1 Feb 2013stat.ML cs.LG math.STcited by 21

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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.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Feb 2013.

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Citing papers per year: 2021: 3; 2022: 5; 2023: 3; 2024: 5; 2025: 0; 2026: 5.

21 papers.

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  1. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 777
  2. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  3. 2021Label-Free Model Evaluation with Semi-Structured Dataset Representationscited by 10
  4. 2021Robust Kernel-based Distribution Regressioncited by 7
  5. 2024Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernelscited by 7
  6. 2022Gaussian Processes on Distributions based on Regularized Optimal Transportcited by 6
  7. 2023Learning Theory of Distribution Regression with Neural Networkscited by 3
  8. 2024Learning to Embed Distributions via Maximum Kernel Entropycited by 3
  9. 2022Performance of Distribution Regression with Doubling Measure under the seek of Closest Pointcited by 2
  10. 2022Generalized Identifiability Bounds for Mixture Models with Grouped Samplescited by 2
  11. 2022Coefficient-based Regularized Distribution Regressioncited by 2
  12. 2023Statistical learning on measures: an application to persistence diagramscited by 2
9 more
  1. 2023Improved learning theory for kernel distribution regression with two-stage samplingcited by 1
  2. 2026GGMPs: Generalized Gaussian Mixture Processescited by 1
  3. 2024LearnedWMP: Workload Memory Prediction Using Distribution of Query Templatescited by 0
  4. 2024Scalable Signature-Based Distribution Regression via Reference Setscited by 0
  5. 2024Guidance Not Obstruction: A Conjugate Consistent Enhanced Strategy for Domain Generalizationcited by 0
  6. 2026Bayesian Additive Distribution Regressioncited by 0
  7. 2026Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regressioncited by 0
  8. 2026A Unified Framework for In-Context Learning with Causal and Masked Language Modelscited by 0
  9. 2026Sparse Priors for Efficient Distribution Learningcited by 0