Tensor Sandwich: Tensor Completion for Low CP-Rank Tensors via Adaptive Random Sampling

Cullen Haselby, Santhosh Karnik, Mark Iwen

Abstract: We propose an adaptive and provably accurate tensor completion approach based on combining matrix completion techniques for a small number of slices with a modified noise robust version of Jennrich’s algorithm. In the simplest case, this leads to a sampling strategy that more densely samples two outer slices (the bread), and then more sparsely samples additional inner slices (the bbq-braised tofu) for the final completion. Under mild assumptions on the factor matrices, this algorithm with high probability completes an $n \times n \times n$ tensor with CP-rank $r$ and uses at most $\mathcal{O}(nr\log^2 r)$ adaptively chosen samples. Empirical experiments further verify that the proposed approach works well in practice, including as a low-rank approximation method in the presence of additive noise.

Submission Type: Full Paper