[Ml-stat-talks] Fwd: Wilks Statistics Seminar: Mikhail Belkin, Today, March 7th @ 12:30pm, Sherrerd Hall 101
Barbara Engelhardt
bee at princeton.edu
Mon Mar 7 08:26:08 EST 2016
Talk of interest today.
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*** Wilks Statistics Seminar ***
DATE: Today, March 7, 2016 **** Note different day*
TIME: 12:30pm
LOCATION: Sherrerd Hall 101
SPEAKER: Mikhail Belkin, Ohio State University
TITLE: Basis Learning and Applications to Spectral Clustering
ABSTRACT: A number of important problems in machine learning and inference
can be interpreted as recovering a certain basis. These include symmetric
matrix eigendecomposition, orthogonal tensor decompositions, Independent
Component Analysis (ICA), spectral clustering (which will be discussed in
the talk) and Gaussian mixture learning. Each of these problems reduces to
an instance of our general model, which we call a “Basis Encoding Function”
(BEF). We show that learning a basis within this model can then be provably
and efficiently achieved using a first order iteration algorithm (gradient
iteration). Our algorithm goes beyond tensor methods while generalizing a
number of existing algorithms—e.g., the power method for symmetric
matrices, the tensor power iteration for orthogonal decomposable tensors,
and cumulant-based FastICA—all within a broader function-based dynamical
systems framework. The framework also unifies the unusual phenomenon
observed in these domains that they can be solved using efficient
non-convex optimization. Specifically, we describe a class of BEFs such
that their local maxima on the unit sphere are in one-to-one correspondence
with the basis elements. This description relies on a certain “hidden
convexity” property of these functions. We provide a complete theoretical
analysis of the gradient iteration even when the BEF is perturbed. We show
convergence and complexity bounds polynomial in dimension and other
relevant parameters, such as perturbation size. Our perturbation results
can be considered as a nonlinear version of the classical Davis-Kahan
theorem for perturbations of eigenvectors of symmetric matrices.
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