Optimal Rates for Regularized Conditional Mean Embedding Learning. (arXiv:2208.01711v2 [stat.ML] UPDATED)

We address the consistency of a kernel ridge regression estimate of the
conditional mean embedding (CME), which is an embedding of the conditional
distribution of $Y$ given $X$ into a target reproducing kernel Hilbert space
$\mathcal{H}_Y$. The CME allows us to take conditional expectations of target
RKHS functions, and has been employed in nonparametric causal and Bayesian
inference. We address the misspecified setting, where the target CME is in the
space of Hilbert-Schmidt operators acting from an input interpolation space …

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