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Misha Belkin, Ohio State University

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Learning a Hidden Basis through Imperfect Measurements
22 October 2015 from 4:00 PM to 5:00 PM
201 Thomas Building
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Misha BelkinA number of problems from the classical spectral theorem for  symmetric matrices to such topics of recent interest as the Independent Component  Analysis, Gaussian mixture learning and some  recent applications of tensor methods for statistical inference and spectral clustering can be recast in terms of learning a hidden orthogonal basis from (potentially noisy) observations.

In this talk I will introduce the problem and propose a "gradient iteration" algorithm for provable basis recovery.  I will describe some of its theoretical properties including fast (super-linear) convergence and a perturbation analysis
which can be viewed as a non-linear generalization of classical perturbation results for matrices. Unlike most of the existing related work our approach based not on matrix or tensorial properties but on certain underlying "hidden convexity".

I will discuss applications of these ideas to spectral graph clustering and to the Independent Component Analysis.

Joint work with L. Rademacher and J. Voss.

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