Bayesian Approximate Kernel Regression with Variable Selection.

Area of Science:

• Statistics and Machine Learning
• Computational Biology
• Statistical Genetics

Background:

• Nonlinear kernel regression models offer higher accuracy than linear models but lack clear effect size measures for variable selection.
• Existing methods for genomic selection and association mapping rely on kernel regression and linear models, respectively, limiting their combined applicability.

Purpose of the Study:

• To develop a novel framework for Bayesian kernel regression that provides an effect size analog for each explanatory variable.
• To enable efficient variable selection in nonlinear models, addressing a key challenge in kernel regression.
• To create a unified method competitive in both genomic selection and association mapping.

Main Methods:

• Utilized function analytic properties of shift-invariant reproducing kernel Hilbert spaces (RKHS), specifically approximation via random Fourier bases.
• Developed a computationally efficient class of Bayesian approximate kernel regression (BAKR) models.
• Defined a projection onto explanatory variables as an analog of effect sizes.

Main Results:

• Proposed BAKR models for nonlinear regression and binary classification, allowing computation of effect size analogs.
• Demonstrated BAKR's utility in statistical genetics, specifically for genomic selection (phenotypic prediction) and association mapping (variant inference).
• Showcased BAKR as a competitive method in both genomic selection and association mapping settings.

Conclusions:

• The proposed framework offers a robust solution for variable selection in Bayesian kernel regression models.
• BAKR provides a unified and efficient approach for complex problems in statistical genetics.
• This novel method enhances the capabilities of nonlinear models by providing interpretable effect size analogs.