Minimax Estimation of Kernel Mean Embeddings

@article{Tolstikhin2017MinimaxEO,
  title={Minimax Estimation of Kernel Mean Embeddings},
  author={I. Tolstikhin and Bharath K. Sriperumbudur and Krikamol Muandet},
  journal={J. Mach. Learn. Res.},
  year={2017},
  volume={18},
  pages={86:1-86:47}
}
  • I. Tolstikhin, Bharath K. Sriperumbudur, Krikamol Muandet
  • Published 2017
  • Mathematics, Computer Science
  • J. Mach. Learn. Res.
  • In this paper, we study the minimax estimation of the Bochner integral $$\mu_k(P):=\int_{\mathcal{X}} k(\cdot,x)\,dP(x),$$ also called as the kernel mean embedding, based on random samples drawn i.i.d.~from $P$, where $k:\mathcal{X}\times\mathcal{X}\rightarrow\mathbb{R}$ is a positive definite kernel. Various estimators (including the empirical estimator), $\hat{\theta}_n$ of $\mu_k(P)$ are studied in the literature wherein all of them satisfy $\bigl\| \hat{\theta}_n-\mu_k(P)\bigr\|_{\mathcal{H… CONTINUE READING
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