Title: Pseudo Maximum Likelihood Estimation Theory For High Dimension Rank one inference tasks
Abstract: We study the problem of recovering rank one information from a random matrix whose entries are generated conditionally on the signal in the large N limit. We develop the theory of several classical estimators for such models and obtain a variational characterization for their performance. By proving a universality result, we show that four information parameters determine the performance of these estimators. The universality result allows us to determine a form of equivalence for estimation problems. Consequently, we obtain a complete description of the performance of the least-squares estimator for any rank one inference problem.
This is joint work with Aukosh Jagannath and Justin Ko.