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).

Balcan, M., A. Blum, et al. “ Clustering under Approximation Stability .” Journal of the ACM 60, no. 2 (2013). (See discussion )

Tensor Decompositions

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).

Feige, U., and J. Kilian. “ Heuristics for Semirandom Graph Problems .” Journal of Computing and System Sciences 63, no. 4 (2001): 639–71. (See discussion )

Sparse Coding

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).

Bhaskara, A., M. Charikar, et al. “ Smoothed Analysis of Tensor Decompositions .” Symposium on Theory of Computing (2014). (See discussion )

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).

Berthet, Q., and P. Rigollet. “ Computational Lower Bounds for Sparse PCA .” Conference on Learning Theory (2013). (See discussion )

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 )

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