The tensor graphical lasso (Teralasso)

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• Alfred Hero (University of Michigan)
• Tuesday 31 October 2017, 14:00-14:50
• Seminar Room 1, Newton Institute.

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VMVW02 - Generative models, parameter learning and sparsity

Co-authors: Kristjian Greenewald (Harvard University), Shuheng Zhou (University of Michigan), Alfred Hero (University of Michigan)

We propose a new ultrasparse graphical model for representing multiway data based on a Kronecker sum representation of the process inverse covariance matrix. This statistical model decomposes the inverse covariance into a linear Kronecker sum representation with sparse Kronecker factors.

Under the assumption that the multiway observations are matrix-normal the l1 sparsity regularized log-likelihood function is convex and admits significantly faster statistical rates of convergence than other sparse matrix normal algorithms such as graphical lasso or Kronecker graphical lasso.

We specify a scalable composite gradient descent method for minimizing the objective function and analyze both the statistical and the computational convergence ratesm, showing that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to the global minimizer. We will illustrate the method on several real multiway datasets, showing that we can recover sparse graphical structures in high dimensional data.

Related Links

• https://arxiv.org/abs/1705.03983 – Paper

This talk is part of the Isaac Newton Institute Seminar Series series.

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