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Anima Anandkumar

Wednesday 21st August 2013

Time: 4pm

 

Basement Seminar Room

Alexandra House, 17 Queen Square, London, WC1N 3AR

 

Provable Learning of Latent Variable Models: A Tensor-based Approach

 

It is widely recognized that incorporating latent or hidden variables
is a crucial ingredient of modeling. In general, guaranteed
(unsupervised) learning of latent variable models is  challenging, and
expectation maximization (EM) or sampling-based approaches are
employed in practice.   I will present an alternative tensor-based
approach which can provide guaranteed learning for a range of latent
variable models such as topic models, Gaussian mixtures, hidden Markov
models and network community models.

The tensor-based approach involves decomposition of low-order observed
moment tensors (typically third or fourth order) to obtain estimates
of the model parameters. Under a natural non-degeneracy assumption,
the moment tensor can be reduced to an orthogonal symmetric form,
whose decomposition can then be computed via the tensor power method.
Recovery under noisy input of the moment tensors is analyzed and we
establish robust recovery guarantees, along the lines of Wedin's
theorem for matrix perturbation. We establish that our method has
polynomial computational and sample complexities (of a low order), and
is efficient for high-dimensional estimation of latent variable
models. I will briefly describe some recent experimental results from
the deployment of the tensor method on GPUs.

Relevant Paper:
"Tensor Decompositions for Learning Latent Variable Models," by A.
Anandkumar, R. Ge, D. Hsu, S.M. Kakade and M. Telgarsky. on ArXiv,
Oct. 2012.

Bio: Anima Anandkumar is  a faculty at the EECS Dept. at U.C.Irvine.
Her research interests are in the area of large-scale machine learning
and high-dimensional statistics  with a focus on learning
probabilistic graphical models and latent variable models.  She is the
recipient of the Microsoft Faculty Fellowship,  ARO Young Investigator
Award, NSF CAREER Award, IBM Fran Allen PhD fellowship, and paper
awards from the ACM Sigmetrics and IEEE Signal Processing Societies.
She has been a visiting faculty  at the Microsoft Research New England
and  a postdoctoral researcher at the Stochastic Systems Group at MIT.
She received her B.Tech in Electrical Engineering from IIT Madras  and
her PhD from Cornell University.