Student Probability Seminar

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The All-or-Nothing Phenomenon

Speaker: Ilias Zadik, CIMS

Location: Online

Date: Wednesday, April 21, 2021, 9 a.m.

Synopsis:

In this short talk, I will present to you a new sharp phase transition, coined as the all-or-nothing (AoN) phenomenon. The AoN phenomenon concerns the fact that in certain sparse inference models the asymptotic minimum mean squared error exhibits a sharp phase transition at some critical threshold; below the threshold, it is “trivial” (i.e. not beating the random guess), and above it, it is zero. This is in sharp contrast with multiple well-studied dense inference models such as Wigner PCA or the stochastic block model where the transition is either known or proven to be continuous. In this talk, we will primarily focus on the AoN phenomenon in the context of sparse tensor PCA. This is joint work with Jonathan Niles-Weed.