The minimax rate for estimating d-th order moment tensors is sqrt(p/n) wedge 1, while low-degree evidence shows detection of vanishing cumulants is hard for n much less than p to the d/2, creating a reverse detection-estimation gap.
Sta- tistical query algorithms and low-degree tests are almost equivalent
2 Pith papers cite this work. Polarity classification is still indexing.
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Sum-of-Squares and statistical query algorithms cannot efficiently refute or detect multiple disjoint planted cliques or bicliques below the sqrt(n) total-size threshold.
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Detection Is Harder Than Estimation in Certain Regimes: Inference for Moment and Cumulant Tensors
The minimax rate for estimating d-th order moment tensors is sqrt(p/n) wedge 1, while low-degree evidence shows detection of vanishing cumulants is hard for n much less than p to the d/2, creating a reverse detection-estimation gap.
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Multiple Planted Structures Below $\sqrt{n}$: An SoS Integrality Gap and an SQ Lower Bound
Sum-of-Squares and statistical query algorithms cannot efficiently refute or detect multiple disjoint planted cliques or bicliques below the sqrt(n) total-size threshold.