Information-Computation Gap
The gap between the information-theoretically optimal threshold and the threshold achievable by polynomial-time algorithms in statistical estimation problems. It appears widely in high-dimensional statistics.
Timeline (last 90 days)
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.
The information-computation gap widely exists in high-dimensional statistical problems, such as sparse principal component analysis, the planted clique problem, and community detection, and is one of the most central open problems in the field of statistical computation.
All Facts (2)
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%UnverifiedThe information-computation gap widely exists in high-dimensional statistical problems, such as sparse principal component analysis, the planted clique problem, and community detection, and is one of the most central open problems in the field of statistical computation.
50%