Nearest neighbor based greedy coordinate descent

Friday, October 12, 2012

Increasingly, optimization problems in machine learning, especially those arising from high-dimensional statistical estimation tasks, involve a large number of variables. As regards the statistical estimation tasks themselves, methods developed over the past decade have been shown to have *statistical or sample complexity* that depends only weakly on the number of parameters, when there is some structure to the problem, such as sparsity. A central question is whether similar advances can be made in their *computational complexity* as well. In this talk, we propose strategies that indicate that such advances can indeed be made. In particular, we investigate the greedy coordinate descent algorithm, and note that performing the greedy step efficiently weakens the costly dependence on the problem size provided the solution is sparse. We then propose a suite of methods that perform these greedy steps efficiently by a reduction to nearest neighbor search. One specialization of our algorithm combines greedy coordinate descent with locality sensitive hashing, using which we are not only able to significantly speed up the vanilla greedy method, but also outperform cyclic descent when the problem size becomes large. 


 Pradeep Ravikumar received his BTech in Computer Science and Engineering from the Indian Institute of Technology, Bombay, and his PhD in Machine Learning from the School of Computer Science at Carnegie Mellon University. He was then a postdoctoral scholar at the Department of Statistics at the University of California, Berkeley. He is now an Assistant Professor in the Department of Computer Science, at the University of Texas at Austin. He is also affiliated with the Division of Statistics and Scientific Computation, and the Institute for Computational Engineering and Sciences at UT Austin. His thesis has received honorable mentions in the ACM SIGKDD Dissertation award and the CMU School of Computer Science Distinguished Dissertation award. He has also a recipient of the NSF CAREER Award.