Distribution regression

December 1, 2020 — December 1, 2020

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Figure 1

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.