|
Abstract:
|
We introduce a new method named Distance-based Independence Screening for Canonical Analysis (DISCA) to reduce dimensions of two random vectors with arbitrary dimensions. DISCA is based on the distance-based independence measure, also known as the distance covariance, proposed by Sz{\'e}kely and Rizzo in 2007. Unlike the existing canonical analysis methods, DISCA does not need the assumption that the dimensions of the reduced subspaces of the two random vectors are equal. Besides, it can be applied to any types of distributions, continuous or discrete, light- or heavy-tailed. Since our method is formulated as a difference-of-convex (DC) optimization problem, which can be solved efficiently by adopting the alternating direction method of multipliers (ADMM), thus avoiding the potentially numerically-intensive bootstrap method to determine the dimension of the reduced subspaces. In both the simulation studies and the real data cases, DISCA can not only handle the cases that other methods cannot do but also perform comparably or better than other dimension reduction methods. We are preparing an R package to include all the codes. This is a joint work with Chuanping Yu.
|
