Approaches to Regularized Regression - A Comparison between Gradient Boosting and the Lasso.

Area of Science:

• Biomedical research
• Statistical modeling
• High-dimensional data analysis

Background:

• Penalization and regularization techniques are crucial for statistical modeling with high-dimensional data.
• Algorithms with automatic variable selection, such as the least absolute shrinkage operator (lasso) and statistical boosting, are gaining prominence.

Purpose of the Study:

• This study compares lasso and gradient boosting, two common techniques for variable selection in linear regression.
• The comparison is conducted from both methodological and practical viewpoints.

Main Methods:

• The study describes lasso and gradient boosting, identifying conditions where their results converge in low-dimensional settings.
• Extensive simulations evaluate performance in scenarios with more predictors than observations, varying noise-to-signal ratios and coefficient numbers.
• The impact of different tuning methods on the outcomes is also examined.

Main Results:

• Both lasso and boosting perform penalization and variable selection for high-dimensional data, often yielding highly similar models.
• Lasso offers a faster computation time.
• Gradient boosting's modular design facilitates extensions to other regression models.

Conclusions:

• Despite differing optimization and regularization strategies, lasso and gradient boosting impose comparable constraints on estimation.
• Both methods demonstrate similar practical performance in prediction accuracy and variable selection for high-dimensional datasets.