Minimax Rates for Estimating the Dimension of a Manifold

Curvature measures

Herbert Federer · 1959

Earlier work this paper cites.

Adaptive Control Processes - A Guided Tour

Richard E. Bellman · 1961

Earlier work this paper cites.

Riemannian Geometry

Manfredo Perdigão do Carmo · 1992

Earlier work this paper cites.

2. concentration of measure and the classical theorems

J. Michael Steele · 1997

Earlier work this paper cites.

Assouad, fano, and le cam

Bin Yu · 1997

Earlier work this paper cites.

Metric Spaces of Non-Positive Curvature

Martin R. Bridson and André Häfliger · 1999

Earlier work this paper cites.

Empirical geometry of multivariate data: a deconvolution approach

V. I. Koltchinskii · 2000

Earlier work this paper cites.

Introduction to Topological Manifolds

John Marshall Lee · 2000

Earlier work this paper cites.

Intrinsic dimension estimation using packing numbers, 2003

Balázs Kégl · 2003

Earlier work this paper cites.

Introduction to Smooth Manifolds

John Marshall Lee · 2003

Cited alongside, same era.

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Elizaveta Levina, Peter J Bickel, Elizaveta Levina, and Peter J. Bickel · 2004

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Matthias Hein and Jean-Yves Audibert · 2005

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Maxim Raginsky and Svetlana Lazebnik · 2005

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Peter Petersen · 2006

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Kevin. Buchin · 2008

Cited alongside, same era.

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Anna V. Little, Yoon-Mo Jung, and Mauro Maggioni · 2009

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Kumar Sricharan, Raviv Raich, and Alfred O. Hero III · 2010

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Yunqian Ma and Yun Fu · 2011

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Alessandro Rozza, Gabriele Lombardi, Claudio Ceruti, Elena Casiraghi, and Paola Campadelli · 2012

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