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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Establishes sharp low-degree estimation thresholds in planted hypergraphs and tensor PCA, resolving open hardness questions and yielding polynomial-time algorithms above thresholds.
The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.
citing papers explorer
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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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Low-degree estimation thresholds in planted hypergraphs and tensor PCA
Establishes sharp low-degree estimation thresholds in planted hypergraphs and tensor PCA, resolving open hardness questions and yielding polynomial-time algorithms above thresholds.
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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.