PCA from noisy, linearly reduced data: the diagonal case

Edgar Dobriban, William Leeb, Amit Singer

Suppose we observe data of the form $Y_i=D_i(S_i+{\epsilon }_i)\in {\mathbb{R}}^p$ or $Y_i=D_i{S}_i+{\epsilon }_i\in {\mathbb{R}}^p$, $i=1,\dots ,n$, where $D_i \in \mathbb{R…