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On the Sample Complexity of Subspace Learning
Alessandro Rudi · Guillermo D Canas · Lorenzo Rosasco

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor

A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from samples. In this paper we introduce a general formulation of this problem and derive novel learning error estimates. Our results rely on natural assumptions on the spectral properties of the covariance operator associated to the data distribution, and hold for a wide class of metrics between subspaces. As special cases, we discuss sharp error estimates for the reconstruction properties of PCA and spectral support estimation. Key to our analysis is an operator theoretic approach that has broad applicability to spectral learning methods.

Author Information

Alessandro Rudi (Istituto Italiano di Tecnologia)
Guillermo D Canas (Massachusetts Institute of Technology)
Lorenzo Rosasco (University of Genova- MIT - IIT)

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