# Tuning Matters: Comparing Lambda Optimization Approaches for Ridge Regression in Genomic Prediction

## TL;DR

This study compares new methods for tuning the regularization parameter in ridge regression, showing improved accuracy and speed for genomic prediction.

## Contribution

A novel λ-selection strategy is proposed and shown to outperform traditional methods in genomic prediction.

## Key findings

- The new λ-selection method consistently outperforms conventional approaches in prediction accuracy and computational speed.
- A hybrid strategy combining the new method with another recent approach delivers the best performance in some cases.
- Modern tuning approaches significantly improve ridge regression model performance in high-dimensional settings.

## Abstract

Background/Objectives: Ridge regression (RR) is a widely used statistical learning method for predicting continuous response variables, particularly in high-dimensional contexts where the number of predictors (p) far exceeds the number of observations (n). RR is known for its simplicity, as it depends on a single regularization hyperparameter (λ), and for its strong predictive performance, especially in genomic prediction applications. However, selecting the optimal value of λ remains a key challenge, with standard techniques such as cross-validation often being computationally intensive and potentially suboptimal in terms of predictive accuracy. Methods: To address this issue, recent studies have proposed alternative methods for tuning λ, aiming to enhance both predictive power and computational efficiency. In this study, we perform a comprehensive benchmarking analysis of two novel λ-selection strategies and compare them with traditional approaches. The evaluation was conducted across 14 real-world genomic selection datasets, covering diverse scenarios representative of practical breeding programs. Results: Our results demonstrate that the method proposed consistently outperforms conventional approaches in both prediction accuracy and computational speed. Additionally, we found that combining this method with another recent approach yields a hybrid strategy that, in some cases, delivers the best overall performance. These findings underscore the importance of carefully selecting the regularization parameter in ridge regression models and suggest that modern, data-driven tuning approaches can substantially improve model performance. Conclusions: This study contributes valuable insights into optimizing hyperparameter selection for high-dimensional prediction problems, with direct implications for genomic selection and other applications in the life sciences.