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Abstract:
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Penalized regression is a common approach for feature selection. To enhance model prediction and interpretation, some methods exist to integrate prior data during the modeling process rather than post-hoc analysis for regression and binary classification. To this end, we developed an approach that implements prior-informed penalized regression for multi-classification problems. Specifically, regression coefficients are regularized by feature-specific penalty parameters which are modeled as a log-linear function of prior covariates. Penalty vectors are estimated by empirical Bayes method instead of cross-validation and a partial quadratic approximation is implemented for an analytical solution reducing the computational complexity for multi-class outcomes. The resulting marginal likelihood is optimized by a designed iterative reweighted-L2 algorithm. Through simulation studies and an applied example, we demonstrate our method's improved prediction accuracy, feature selection, and effect estimation compared with regular penalized models. We discuss the relationship to relevant vector machine and present extensions for grouped and ungrouped penalty vectors across multiple classes.
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