@inproceedings{500f46d1485740bfaa6e8a1310e6f505,

title = "Minimax-optimal semi-supervised regression on unknown manifolds",

abstract = "We consider semi-supervised regression when the predictor variables are drawn from an unknown manifold. A simple two step approach to this problem is to: (i) estimate the manifold geodesic distance between any pair of points using both the labeled and unlabeled instances; and (ii) apply a k nearest neighbor regressor based on these distance estimates. We prove that given sufficiently many unlabeled points, this simple method of geodesic kNN regression achieves the optimal finite-sample minimax bound on the mean squared error, as if the manifold were known. Furthermore, we show how this approach can be efficiently implemented, requiring only O(k N log N) operations to estimate the regression function at all N labeled and unlabeled points. We illustrate this approach on two datasets with a manifold structure: indoor localization using WiFi fingerprints and facial pose estimation. In both cases, geodesic kNN is more accurate and much faster than the popular Laplacian eigenvector regressor.",

author = "Amit Moscovich and Ariel Jaffe and Nadler Boaz",

year = "2017",

month = aug,

day = "1",

language = "الإنجليزيّة",

series = "Proceedings of Machine Learning Research",

publisher = "PMLR",

pages = "933--942",

editor = "Aarti Singh and Jerry Zhu",

booktitle = "Proceedings of the 20th International Conference on Artificial Intelligence and Statistics",

note = "20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017 ; Conference date: 20-04-2017 Through 22-04-2017",

}