Nonnegative Matrix Factorization
Lee, D., and S. Seung. “ Learning the Parts of Objects by Nonnegative Matrix Factorization .” Nature 401 (1999): 788–91.
Vavasis, S. “ On the Complexity of Nonnegative Matrix Factorization .” SIAM Journal on Optimization (2009).
Arora, S., R. Ge, et al. “ Computing a Nonnegative Matrix Factorization—Provably .” Symposium on Theory of Computing (2012).
Arora, S., R. Ge, et al. “ Learning Topic Models—Going Beyond SVD .” Foundations of Computer Science (2012).
Arora, S., R. Ge, et al. “ A Practical Algorithm for Topic Modeling with Provable Guarantees .” International Conference on Machine Learning (2013).
Hillar, C., and L. Lim. “ Most Tensor Problems are NP-hard .” Journal of the ACM (2013).
Mossel, E., and S. Roch. “ Learning Nonsingular Phylogenies and Hidden Markov Models .” The Annals of Applied Probability 16, no. 2 (2006): 583–614.
Anandkumar, A., D. Foster, et al. “ A Spectral Algorithm for Latent Dirichlet Allocation .” Neural Information Processing System (2012).
Anandkumar, A., R. Ge, et al. “ A Tensor Spectral Approach to Learning Mixed Membership Community Models .” Conference on Learning Theory (2013).
Goyal, N., S. Vempala, et al. “ Fourier PCA and Robust Tensor Decomposition .” Symposium on Theory of Computing (2014).
Olshausen, B., and D. Field. “ Emergence of Simple-cell Receptive Field Properties by Learning a Sparse Code for Natural Images .” Nature 381, (1996): 607–09.
Spielman, D., H. Wang, et al. “ Exact Recovery of Sparsely-used Dictionaries .” Conference on Learning Theory (2012).
Arora, S., R. Ge, et al. “ Simple, Efficient, and Neural Algorithms for Sparse Coding .” Manuscript (2015).
Barak, B., J. Kelner, et al. “ Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method .” Manuscript (2014).
Geman, S., and D. Geman. “ Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images .” Pattern Analysis and Machine Intelligence (1984). (See discussion )
Learning Mixture Models
Dempster, A., N. Laird, et al. “ Maximum Likelihood from Incomplete Data via the EM Algorithm .” Journal of Royal Statistical Society 39, no. 1 (1977): 1–38.
Dasgupta, S. “ Learning Mixtures of Gaussians .” Foundations of Computer Science (1999): 634–44.
Arora, S., and R. Kannan. “ Learning Mixtures of Separated Nonspherical Gaussians .” The Annals of Applied Probability 15, no. 1A (2005): 69–92.
Kalai, A., A. Moitra, et al. “Efficiently Learning Mixtures of Two Gaussians.” (PDF) Symposium on Theory of Computing (2010).
Moitra, A., and G. Valiant. “ Settling the Polynomial Learnability of Mixtures of Gaussians .” Foundations of Computer Science (2010).
Belkin, M., and K. Sinha. “ Polynomial Learning of Distribution Families .” Foundations of Computer Science (2010).
Linear Inverse Problems
Candes, E., and B. Recht. “ Exact Matrix Completion via Convex Optimization .” Foundations of Computational Mathematics 9, no. 6 (2009): 717–72.
Chandrasekaran, V., P. Parrilo, et al. “ The Convex Geometry of Linear Inverse Problems .” Foundations of Computational Mathematics 12, no. 6 (2012): 805–49.
Jain, P., P. Netrapalli, et al. “ Low-rank Matrix Completion using Alternating Minimization .” Symposium on Theory of Computing (2012).
Hardt, M. “ Understanding Alternating Minimization for Matrix Completion .” Foundations of Computational Mathematics (2014).
Barak, B., and A. Moitra. “ Tensor Prediction, Rademacher Complexity and Random 3-XOR .” Manuscript (2015).
Chandrasekaran, V., and M. Jordan. “ Computational and Statistical Tradeoffs via Convex Relaxation .” Proceedings of the National Academy of Sciences of the United States of America 110, no. 13 (2013): E1181–90. (See discussion )