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- Anima Anandkumar, Rong Ge, Daniel J. Hsu, Sham M. Kakade, Matus Telgarsky
- Journal of Machine Learning Research
- 2014

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)

- Anima Anandkumar, Daniel J. Hsu, Sham M. Kakade
- COLT
- 2012

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics (e.g., the EM algorithm) which are prone to failure, and existing consistent methods are unfavorable due to their high… (More)

- Myung Jin Choi, Vincent Y. F. Tan, Anima Anandkumar, Alan S. Willsky
- Journal of Machine Learning Research
- 2011

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not… (More)

- Anima Anandkumar, Dean P. Foster, Daniel J. Hsu, Sham M. Kakade, Yi-Kai Liu
- Algorithmica
- 2012

Topic modeling is a generalization of clustering that posits that observations (words in a document) are generated by multiple latent factors (topics), as opposed to just one. The increased representational power comes at the cost of a more challenging unsupervised learning problem for estimating the topic-word distributions when only words are observed,… (More)

- Anima Anandkumar, Nithin Michael, Ao Tang, Ananthram Swami
- IEEE Journal on Selected Areas in Communications
- 2011

—The problem of distributed learning and channel access is considered in a cognitive network with multiple secondary users. The availability statistics of the channels are initially unknown to the secondary users and are estimated using sensing decisions. There is no explicit information exchange or prior agreement among the secondary users. We propose… (More)

- Anima Anandkumar, Dean P. Foster, Daniel J. Hsu, Sham M. Kakade, Yi-Kai Liu
- ArXiv
- 2012

- Anima Anandkumar, Vincent Y. F. Tan, Furong Huang, Alan S. Willsky
- Journal of Machine Learning Research
- 2012

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional covariances. Under a set of transparent conditions, we establish structural consistency (or sparsistency) for the proposed… (More)

- Anima Anandkumar, Nithin Michael, Ao Tang
- INFOCOM
- 2010

—The problem of cooperative allocation among multiple secondary users to maximize cognitive system throughput is considered. The channel availability statistics are initially unknown to the secondary users and are learnt via sensing samples. Two distributed learning and allocation schemes which maximize the cognitive system throughput or equivalently… (More)

- Alekh Agarwal, Anima Anandkumar, Prateek Jain, Praneeth Netrapalli
- SIAM Journal on Optimization
- 2016

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps,… (More)

- Anima Anandkumar, Lang Tong, Ananthram Swami
- IEEE Trans. Information Theory
- 2009

The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, a closed-form expression for the log-likelihood ratio is derived, in terms of the coefficients of its covariance matrix and the edges of the dependency graph. Assuming random placement of nodes over a large region… (More)