Minimax Manifold Estimation

作者：Genovese Christopher R^*; Perone Pacifico Marco; Verdinelli Isabella; Wasserman Larry

来源：Journal of Machine Learning Research, 2012, 13: 1263-1291.

• manifold learning
• minimax estimation

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R-D 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.

• 出版日期2012-5