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Near-optimal fitting of ellipsoids to random points
6031-6036, 2013] conjecture that the ellipsoid fitting problem transitions from feasible to infeasible as the number of points $n$ increases, with a sharp threshold at $n \sim d^2/4$.
Exact nuclear norm, completion and decomposition for random overcomplete tensors via degree-4 SOS
In this paper we show that simple semidefinite programs inspired by degree $4$ SOS can exactly solve the tensor nuclear norm, tensor decomposition, and tensor completion problems on tensors with random asymmetric components.
Exact tensor completion with sum-of-squares
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion.
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