Distribution regression

Poczos et al. (2013):

‘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 \(P .\)


Bachoc, F., F. Gamboa, J. Loubes, and N. Venet. 2018. A Gaussian Process Regression Model for Distribution Inputs.” IEEE Transactions on Information Theory 64 (10): 6620–37.
Bachoc, Francois, Alexandra Suvorikova, David Ginsbourger, Jean-Michel Loubes, and Vladimir Spokoiny. 2019. Gaussian Processes with Multidimensional Distribution Inputs via Optimal Transport and Hilbertian Embedding.” arXiv:1805.00753 [Stat], April.
Ohsawa, Shohei. 2021. Unbiased Self-Play.” arXiv:2106.03007 [Cs, Econ, Stat], June.
Poczos, Barnabas, Aarti Singh, Alessandro Rinaldo, and Larry Wasserman. 2013. Distribution-Free Distribution Regression.” In Artificial Intelligence and Statistics, 507–15. PMLR.

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