A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions

We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, we consider the sparse inverse covariance matrix estimation in graph learning problems. Via a careful dual formulation and a novel analytic step-size selection procedure, our approach for graph learning avoids Cholesky decompositions and matrix inversions in its iteration making it attractive for parallel and distributed implementations.


Published in:
Proceedings of the 30th International Conference on Machine Learning
Presented at:
30th International Conference on Machine Learning, Atlanta, GA, USA, June 16-19, 2013
Year:
2013
Laboratories:




 Record created 2013-01-08, last modified 2018-03-17

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