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

More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees