## 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
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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. “
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.” *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
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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. “
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.” *Manuscript* (2015).

Barak, B., J. Kelner, et al. “
Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method
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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. “
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.” *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
)