Math @ Duke

Publications [#243779] of Mauro Maggioni
Papers Published
 Maggioni, M, Geometric estimation of probability measures in highdimensions,
Conference Record of the Asilomar Conference on Signals, Systems and Computers
(January, 2013),
pp. 13631367, ISSN 10586393 [doi]
(last updated on 2017/12/18)
Abstract: We are interested in constructing adaptive probability models for highdimensional data that is wellapproximated by lowdimensional geometric structures. We discuss a family of estimators for probability distributions based on dataadaptive multiscale geometric approximations. They are particularly effective when the probability distribution concentrates near lowdimensional sets, having sample and computational complexity depending mildly (linearly in cases of interest) in the ambient dimension, as well as in the intrinsic dimension of the data, suitably defined. Moreover the construction of these estimators may be performed, under suitable assumptions, by fast algorithms, with cost O((c d ; d 2 )Dnlog n) where n is the number of samples, D the ambient dimension, d is the intrinsic dimension of the data, and c a small constant. © 2013 IEEE.


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