# Distribution regression

December 1, 2020 — December 1, 2020

functional analysis

metrics

optimization

statistics

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 \(P .\)

## 1 References

Bachoc, F., Gamboa, Loubes, et al. 2018. “A Gaussian Process Regression Model for Distribution Inputs.”

*IEEE Transactions on Information Theory*.
Bachoc, Francois, Suvorikova, Ginsbourger, et al. 2019. “Gaussian Processes with Multidimensional Distribution Inputs via Optimal Transport and Hilbertian Embedding.”

*arXiv:1805.00753 [Stat]*.
Ohsawa. 2021. “Unbiased Self-Play.”

*arXiv:2106.03007 [Cs, Econ, Stat]*.
Poczos, Singh, Rinaldo, et al. 2013. “Distribution-Free Distribution Regression.” In

*Artificial Intelligence and Statistics*.