A seminar by Dr Fan Yang from the University of Pennsylvania
Title: Selecting the number of components in high-dimensional CCA
Abstract: Given two random vectors, canonical correlation analysis (CCA) has been one of the most classical and powerful methods to study the correlations between them since the seminal work by Hotelling. We study the canonical correlation coefficients (CCCs) between a pair of large random vectors through their sample counterparts, i.e., the sample CCCs, in a high-dimensional setting where the dimensions of the two random vectors are comparable to the sample size. In this talk, I will discuss three different methods to estimate and test the rank of correlations between two random vectors through sample CCCs: a deterministic threshold, the Onatski’s statistic, and the parallel analysis method. We will justify theoretically and compare these three methods for a signal-plus-noise model. Our analysis is based on our recent works on high-dimensional CCA, which established rigorously the BBP transition of the sample CCCs using random matrix theory tools. Based on joint work with Zongming Ma, Edgar Dobriban and David Hong.
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