EM algorithm for generalized Ridge regression with spatial covariates

TL;DR

This paper introduces an EM algorithm for estimating generalized Ridge regression parameters with spatial covariance structures, enhancing modeling in high-dimensional spatial data applications.

Contribution

It proposes a novel EM algorithm tailored for generalized Ridge regression with spatial covariance matrices, including diagonal, Matérn, and CAR structures.

Findings

The method accurately estimates covariance parameters in simulations.

Application to ocean wave height prediction demonstrates practical utility.

Abstract

The generalized Ridge penalty is a powerful tool for dealing with overfitting and for high-dimensional regressions. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given covariance matrix. The covariance matrix controls the structure of the coefficients, which depends on the particular application. For example, it is appropriate to assume that the coefficients have a spatial structure in spatial applications. This study proposes an expectation-maximization algorithm for estimating generalized Ridge parameters whose covariance structure depends on specific parameters. We focus on three cases: diagonal (when the covariance matrix is diagonal with constant elements), Mat\'ern, and conditional autoregressive covariances. A simulation study is conducted to evaluate the performance of the proposed method, and then the method is applied to predict ocean wave heights using wind conditions.