Minimax Manifold Estimation
نویسندگان
چکیده
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R given a noisy sample from the manifold. Under certain conditions, we show that the optimal rate of convergence is n−2/(2+d). Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.
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ورودعنوان ژورنال:
- Journal of Machine Learning Research
دوره 13 شماره
صفحات -
تاریخ انتشار 2012