On estimation of sparse eigenvectors in high dimensions

In this talk we'll discuss estimation of the population eigenvectors from a high dimensional sample covariance matrix, under a low-rank spiked model whose eigenvectors are assumed to be sparse. We present several models of sparsity, corresponding minimax rates and a procedure that attains these rates. We'll also discuss some differences between $L_0$ and $L_q$ sparsity for $q > 0$, as well as some limitations of recently suggested SDP procedures.