Optimally Weighted PCA for High-dimensional Heteroscedastic Data

Today I had the opportunity to speak about very recent results by my student David Hong (joint work also with Jeff Fessler) in analyzing asymptotic recovery guarantees for weighted PCA for high-dimensional heteroscedastic data. In the paper we recently posted online, we have asymptotic analysis (as both the number of samples and dimension of the problem grow to infinity, but converge to a fixed constant) of the recovery for weighted PCA components, amplitudes, and scores. Those recovery expressions allow us to find weights that give optimal recovery, and the weights turn out to be a very simple expression involving only the noise variance and the PCA amplitudes. To learn more, watch my talk here, and let us know if you have any questions!