[YPNG] YPNG, Friday 14 October 2016

Sekhar Tatikonda sekhar.tatikonda at yale.edu
Mon Oct 10 07:59:38 EDT 2016

Hi Everybody,

Tengyu Ma, from Princeton, will talk in the YPNG seminar this week:

Title: Matrix Completion has No Spurious Local Minimum

Abstract:  Matrix completion is a basic machine learning problem that has
wide applications, especially in collaborative filtering and recommender
systems. Simple non-convex optimization algorithms are popular and
effective in practice. Despite recent progress in proving various
non-convex algorithms converge from a good initial point, it remains
unclear why random or arbitrary initialization suffices in practice.

We prove that the commonly used non-convex objective function for matrix
completion has no spurious local minima --- all local minima must also be
global. Therefore, many popular optimization algorithms such as
(stochastic) gradient descent can provably solve positive semidefinite
matrix completion with arbitrary initialization in polynomial time. The
result can be generalized to the setting when the observed entries contain
noise. We believe that our main proof strategy can be useful for
understanding geometric properties of other statistical problems involving
partial or noisy observations.

See you Friday at 11am in the Stat's classroom.

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