Provable Nonconvex Optimization for Machine Learning Problems
In this work, we explore theoretical properties of simple nonconvex optimization methods for problems that feature prominently in several important areas such as recommendation systems, compressive sensing, computer vision etc.
Talks:

Iterative Hard Thresholding for Sparse/Lowrank Linear Regression. INRIA, France, 2015. [pdf version]

Iterative Hard Thresholding for Robust Regression. ITW, 2015. [pdf version]

Provable Alternating Minimization methods for Machine Learning related Problems. IISC Bangalore, January 2014.
Papers:
 P. Jain, C. Jin, S. Kakade, P. Netrapalli. Computing Matrix Squareroot via Non Convex Local Search. In preparation.
 P. Jain, A. Tewari. Alternating Minimization for Regression Problems with Vectorvalued Outputs. To appear, NIPS 2015.
 K. Bhatia, P. Jain, P Kar. Robust Regression via Hard Thresholding. To appear, NIPS 2015.
 P. Jain, P. Netrapalli. Fast Exact Matrix Completion with Finite Samples. Proc. Annual Conference on Learning Theory (COLT), 2015.
 P. Netrapalli, U N Niranjan, A. Anandkumar, S. Sanghavi, P. Jain. Nonconvex Robust PCA. Proc. the Advances in Neural Information Processing Systems (NIPS), 2014.
 P. Jain, S. Oh, Provable Tensor Factorization with Missing Data. . Proc. the Advances in Neural Information Processing Systems (NIPS), 2014.
 A. Agarwal, A. Anandkumar, P. Jain, P. Netrapalli, R. Tandon, Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization. Arxiv Preprint, 2013.
 P. Jain, I. S. Dhillon, Provable Inductive Matrix Completion. Arxiv Preprint, 2013.
 P. Netrapalli, P. Jain, S. Sanghavi, Phase Retrieval using Alternating Minimization. NIPS 2013.
 P. Jain, P. Netrapalli, S. Sanghavi, Lowrank Matrix Completion using Alternating Minimization. STOC 2013.
 P. Jain, A. Tewari, I. S. Dhillon. Orthogonal Matching Pursuit with Replacement. In Proceedings, NIPS 2011. (arxiv preprint)
 P. Jain, R. Meka, I. S. Dhillon. Guaranteed Rank Minimization via Singular Value Projection. NIPS 2010. (supplementary material) source code
 R. Meka, P. Jain, I. S. Dhillon. Matrix Completion from PowerLaw Distributed Samples. Proc. the Advances in Neural Information Processing Systems (NIPS), 2009.
 R. Meka, P. Jain, C. Caramanis, I. S. Dhillon. Rank Minimization via Online Learning. Proc. the International Conference on Machine Learning, 2008.