Sum of Squares
A hierarchical relaxation method based on semidefinite programming that provides a unified framework for polynomial-time algorithms and can generate corresponding computational lower bounds.
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Tensor PCA exhibits an information-computation gap: when the signal-to-noise ratio is above the algorithmic threshold, global algorithms such as spectral methods and sum-of-squares can successfully recover in polynomial time; below that threshold, lower bounds for these algorithms and for certain restricted computational models show that they must fail.
In tensor PCA, spectral methods succeed when the signal-to-noise ratio is above the algorithmic threshold, SoS also succeeds at the same threshold, and SoS lower bounds show that below this threshold any SoS algorithm fails.
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Tensor PCA exhibits an information-computation gap: when the signal-to-noise ratio is above the algorithmic threshold, global algorithms such as spectral methods and sum-of-squares can successfully recover in polynomial time; below that threshold, lower bounds for these algorithms and for certain restricted computational models show that they must fail.
50%UnverifiedIn tensor PCA, spectral methods succeed when the signal-to-noise ratio is above the algorithmic threshold, SoS also succeeds at the same threshold, and SoS lower bounds show that below this threshold any SoS algorithm fails.
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