A detailed analysis of a robust tensor power method is provided, establishing an analogue of Wedin's perturbation theorem for the singular vectors of matrices, and implies a robust and computationally tractable estimation approach for several popular latent variable models.Expand

This paper identifies strict saddle property for non-convex problem that allows for efficient optimization of orthogonal tensor decomposition, and shows that stochastic gradient descent converges to a local minimum in a polynomial number of iterations.Expand

Generative Adversarial Networks (GANs) have become one of the dominant methods for fitting generative models to complicated real-life data, and even found unusual uses such as designing good… Expand

This paper presents an algorithm for topic model inference that is both provable and practical and produces results comparable to the best MCMC implementations while running orders of magnitude faster.Expand

These results provide some theoretical justification for widespread empirical success in compressing deep nets and show generalization bounds that're orders of magnitude better in practice.Expand

This paper shows that a perturbed form of gradient descent converges to a second-order stationary point in a number iterations which depends only poly-logarithmically on dimension, which shows that perturbed gradient descent can escape saddle points almost for free.Expand

This work bridges the gap showing that (model free) policy gradient methods globally converge to the optimal solution and are efficient (polynomially so in relevant problem dependent quantities) with regards to their sample and computational complexities.Expand

This work gives an algorithm that runs in time polynomial in n, m and r under the separablity condition identified by Donoho and Stodden in 2003, and is the firstPolynomial-time algorithm that provably works under a non-trivial condition on the input matrix.Expand

This paper formally justifies Nonnegative Matrix Factorization (NMF) as a main tool in this context, which is an analog of SVD where all vectors are nonnegative, and gives the first polynomial-time algorithm for learning topic models without the above two limitations.Expand

It is proved that the commonly used non-convex objective function for positive semidefinite matrix completion has no spurious local minima --- all local minata must also be global.Expand