New techniques establish sharp lower bounds ruling out low-degree polynomial estimation at the BBP and Kesten-Stigum thresholds for planted submatrix, dense subgraph, spiked Wigner, and stochastic block models.
Tensor Cumulants for Statistical Inference on Invariant Distributions
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The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.
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Sharp Phase Transitions in Estimation with Low-Degree Polynomials
New techniques establish sharp lower bounds ruling out low-degree polynomial estimation at the BBP and Kesten-Stigum thresholds for planted submatrix, dense subgraph, spiked Wigner, and stochastic block models.
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Properties of tensorial free cumulants
The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.