Fast low-rank estimation by projected gradient descent: Statistical and algorithmic guarantees

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• Martin Wainwright (UC Berkeley)
• Friday 20 November 2015, 16:00-17:00
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge..

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Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA , matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the low-rank matrix, and to run projected gradient descent on the nonconvex problem in the lower dimensional factorized space. We provide a general set of conditions under which projected gradient descent, when given a suitable initialization, converges geometrically to a statistically optimal solution. Our results are applicable even when the initial solution is outside any region of local convexity, and even when the problem is globally concave.

This talk is part of the Statistics series.

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