作者：Mukherjee, Rajarshi; Mukherjee, Sumit; Yuan, Ming
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence. The profound impact of dependence is best illustrated under the Curie-Weiss model where we observe the effect of a thermodynamic phase transition. ...
作者：Perry, Amelia; Wein, Alexander S.; Bandeira, Afonso S.; Moitra, Ankur
作者单位：Massachusetts Institute of Technology (MIT); New York University; New York University; Massachusetts Institute of Technology (MIT)
摘要：A central problem of random matrix theory is to understand the eigen-values of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or spike) is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Peche showed that the spiked Wishart ensemble exhibits a sharp phase transition asymptotically: when the spike strength is above a critical thr...
