Date of Award
Spring 2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Statistics and Data Science
First Advisor
Fan, Zhou
Abstract
Approximate Message Passing algorithms are a versatile family of iterative algorithms that have found applications in various statistical problems. This thesis highlights some of the recent advancements that generalize the applicability of AMP. First, we analyze the universality of AMP algorithms, showing that their state evolutions hold over a broader range of random matrices, including those with heavy-tailed entries and heterogeneous entry-wise variances. Second, we explore extensions of AMP algorithms of multi-variate iterates with spectral initialization for rotationally invariant matrices, to handle data matrices with correlated noise entries. Lastly, we investigate practical AMP procedures for inference under the Bayesian framework for the prototypical ``structured PCA'' problem and demonstrate the effectiveness of the EB-PCA algorithm in achieving optimal estimation accuracy.
Recommended Citation
Zhong, Xinyi, "Approximate Message Passing algorithms for general random matrices" (2023). Yale Graduate School of Arts and Sciences Dissertations. 1046.
https://elischolar.library.yale.edu/gsas_dissertations/1046
