A neutral comparison of algorithms to minimize L₀ penalties for high-dimensional variable selection

Area of Science:

• Statistics
• Computational Biology
• Genetics

Background:

• L0 penalty methods offer theoretical advantages for sparse model selection in high-dimensional data.
• Existing methods like modified Bayesian Information Criterion (mBIC, mBIC2) control error rates but face computational challenges due to NP-hard L0 minimization.
• Convex alternatives like LASSO are popular due to computational ease, but L0 methods are seeing algorithmic advancements.

Purpose of the Study:

• To compare the performance of recent algorithms designed to minimize L0-based selection criteria.
• To evaluate statistical properties and computational runtime of different L0 minimization algorithms.
• To demonstrate the practical application of these algorithms in expression quantitative trait loci (eQTL) mapping.

Main Methods:

• Simulation studies across diverse scenarios, inspired by genetic association studies.
• Comparison of selection criteria values obtained from various L0 minimization algorithms.
• Analysis of statistical characteristics of selected models and algorithm runtimes.

Main Results:

• Simulation results provide a comprehensive comparison of L0 minimization algorithm performance.
• Statistical properties and computational efficiency of algorithms are evaluated.
• The study illustrates the practical utility of these algorithms on a real eQTL mapping dataset.

Conclusions:

• Recent algorithmic developments have made L0 penalty minimization more computationally feasible.
• The study provides valuable insights for selecting appropriate algorithms for sparse model selection in high-dimensional settings.
• These advanced methods show promise for applications in genetic association studies and eQTL mapping.