UPS delivers optimal phase diagram in high-dimensional variable selection

Pengsheng Ji, Jiashun Jin

Consider a linear model $Y=X\beta +z$, $z\sim N(0,I_n)$. Here, $X=X_{n,p}$, where both $p$ and $n$ are large, but $p>n$. We model the rows of $X$ as i.i.d. samples from $N(0,\frac{1}{n}…