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This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their low-order observable moments (typically, of second-and third-order). Specifically,… (More)

- Sanjeev Arora, Rong Ge, Yonatan Halpern, David M. Mimno, Ankur Moitra, David Sontag +2 others
- ICML
- 2013

Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model learning have been based on a maximum likelihood objective. Efficient algorithms exist that attempt to approximate this objective, but they have no provable guarantees. Recently, algorithms have been… (More)

The Nonnegative Matrix Factorization (NMF) problem has a rich history spanning quantum mechanics, probability theory, data analysis, polyhedral combinatorics, communication complexity, demography, chemometrics, etc. In the past decade NMF has become enormously popular in machine learning, where the factorization is computed using a variety of local search… (More)

Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational works both in machine learning [15] and in theory [27] have suggested a probabilistic model for documents, whereby… (More)

—Energy efficiency is a major concern in modern high-performance computing system design. In the past few years, there has been mounting evidence that power usage limits system scale and computing density, and thus, ultimately system performance. However, despite the impact of power and energy on the computer systems community, few studies provide insight… (More)

Performance and power are critical design constraints in today's high-end computing systems. Reducing power consumption without impacting system performance is a challenge for the HPC community. We present a run-time system (CPU MISER) and an integrated performance model for performance-directed, power-aware cluster computing. CPU MISER supports… (More)

In sparse recovery we are given a matrix A ∈ R n×m (" the dictionary ") and a vector of the form AX where X is sparse, and the goal is to recover X. This is a central notion in signal processing, statistics and machine learning. But in applications such as sparse coding, edge detection, compression and super resolution, the dictionary A is unknown and has… (More)

We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our gen-erative model is an n node multilayer network that has degree at most n γ for some γ < 1 and each edge has a random edge weight in [−1, 1]. Our algorithm learns almost all networks in this class with polynomial… (More)

- Rong Ge, Furong Huang, Chi Jin, Yang Yuan
- COLT
- 2015

We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper we identify strict saddle property for non-convex problem that allows for efficient optimization. Using… (More)