An algorithm for online tensor prediction

John Pothier; Josh Girson; Shuchin Aeron

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arXiv · 1507.07974

An algorithm for online tensor prediction

John Pothier·Josh Girson·Shuchin Aeron

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Abstract

We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor decompositions proposed in [1]. In this framework it is possible to treat 3-D tensors as linear operators and appropriately generalize notions of rank and positive definiteness to tensors in a natural way. Using these notions we propose a generalization of the matrix exponentiated gradient descent algorithm [2] to a tensor exponentiated gradient descent algorithm using an extension of the notion of von-Neumann divergence to tensors. Then following a similar construction as in [3], we exploit this algorithm to propose an online algorithm for learning and prediction of tensors with provable regret guarantees. Simulations results are presented on semi-synthetic data sets of ratings evolving in time under local influence over a social network. The result indicate superior performance compared to other (online) convex tensor completion methods.

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stat.ML cs.IT cs.LG math.IT

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BibTeX RIS

John Pothier, Josh Girson, Shuchin Aeron. 2015-07-28. An algorithm for online tensor prediction. https://arxiv.org/abs/1507.07974

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