Noisy Tensor Completion via the Sum-of-Squares Hierarchy

  title={Noisy Tensor Completion via the Sum-of-Squares Hierarchy},
  author={Boaz Barak and Ankur Moitra},
In the noisy tensor completion problem we observe m entries (whose location is chosen uniformly at random) from an unknown n1 × n2 × n3 tensor T . We assume that T is entry-wise close to being rank r. Our goal is to fill in its missing entries using as few observations as possible. Let n = max(n1, n2, n3). We show that if m = nr then there is a polynomial time algorithm based on the sixth level of the sum-of-squares hierarchy for completing it. Our estimate agrees with almost all of T ’s… CONTINUE READING
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