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More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees

Osman Asif Malik

Hall E #614

Keywords: [ PM: Monte Carlo and Sampling Methods ] [ MISC: Supervised Learning ] [ OPT: Sampling and Optimization ] [ MISC: Everything Else ] [ MISC: Scalable Algorithms ]


Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.

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