|
Abstract:
|
Sorted L-One Penalized Estimator (SLOPE, Bogdan at al., 2015, Annals of Applied Statistics) is a relatively new method for estimating coefficients in the high dimensional Generalized Linear Models. Compared to the well know LASSO, SLOPE reduces the dimension both by letting some of the coefficients to be equal to zero as well as by allowing some of them to be equal to each other. In this talk we will present new theoretical results concerning asymptotic control of the False Discovery Rate by SLOPE as well as novel results on its clustering properties. Specifically, we will define the SLOPE models by specifying the groups of variables with equal regression coefficients and present the conditions under which SLOPE can properly identify or separate such groups. We will also show that the clustering properties of SLOPE lead to the superior predictive properties and present a novel speedy SLOPE algorithm, which allows for computationally efficient selection of the tuning parameters by cross-validation.Finally, we will discuss application of SLOPE for identifying colored gaussian graphical models, where colors mark edges with the same values of elements in the precision matrix.
|
