# Tensor principal component analysis via sum-of-square proofs

computational learning theory, Volume abs/1507.03269, 2015, Pages 956-1006.

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Abstract:

We study a statistical model for the tensor principal component analysis problem introduced by Montanari and Richard: Given a order-$3$ tensor $T$ of the form $T = \tau \cdot v_0^{\otimes 3} + A$, where $\tau \geq 0$ is a signal-to-noise ratio, $v_0$ is a unit vector, and $A$ is a random noise tensor, the goal is to recover the planted ...More

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