A sharp information-theoretic threshold for approximate recovery of a planted sparse submatrix is derived, and an overlap gap property is proved that blocks local MCMC algorithms in a conjecturally hard phase.
High-dimensional analysis of semidefinite relaxations for sparse prin- cipal components
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The Overlap Gap Property in Principal Submatrix Recovery
A sharp information-theoretic threshold for approximate recovery of a planted sparse submatrix is derived, and an overlap gap property is proved that blocks local MCMC algorithms in a conjecturally hard phase.