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arXiv · 2208.04754

EM algorithm for generalized Ridge regression with spatial covariates

Said Obakrim·Pierre Ailliot·Valérie Monbet·Nicolas Raillard
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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.

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Said Obakrim, Pierre Ailliot, Valérie Monbet, Nicolas Raillard. 2022-08-09. EM algorithm for generalized Ridge regression with spatial covariates. https://arxiv.org/abs/2208.04754

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