# 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 $$P .$$

## References

Bachoc, F., F. Gamboa, J. Loubes, and N. Venet. 2018. IEEE Transactions on Information Theory 64 (10): 6620–37.
Bachoc, Francois, Alexandra Suvorikova, David Ginsbourger, Jean-Michel Loubes, and Vladimir Spokoiny. 2019. arXiv:1805.00753 [Stat], April.
Ohsawa, Shohei. 2021. arXiv:2106.03007 [Cs, Econ, Stat], June.
Poczos, Barnabas, Aarti Singh, Alessandro Rinaldo, and Larry Wasserman. 2013. In Artificial Intelligence and Statistics, 507–15. PMLR.

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