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Title: Detection-Recovery and Detection-Refutation Gaps via Reductions from Planted Clique
Planted Dense Subgraph (PDS) problem is a prototypical problem with a computational-statistical gap. It also exhibits an intriguing additional phenomenon: different tasks, such as detection or re- covery, appear to have different computational limits. A detection-recovery gap for PDS was sub- stantiated in the form of a precise conjecture given by Chen and Xu (2014) (based on the parameter values for which a convexified MLE succeeds), and then shown to hold for low-degree polynomial algorithms by Schramm and Wein (2022) and for MCMC algorithms for Ben Arous et al. (2020). In this paper we demonstrate that a slight variation of the Planted Clique Hypothesis with secret leakage (introduced in Brennan and Bresler (2020)), implies a detection-recovery gap for PDS. In the same vein, we also obtain a sharp lower bound for refutation, yielding a detection-refutation gap. Our methods build on the framework of Brennan and Bresler (2020) to construct average-case reductions mapping secret leakage Planted Clique to appropriate target problems.  more » « less
Award ID(s):
1940205
PAR ID:
10570051
Author(s) / Creator(s):
;
Publisher / Repository:
Proceedings of Thirty Sixth Conference on Learning Theory
Date Published:
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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