Sparse partial least squares regression for simultaneous dimension reduction and variable selection.

Area of Science:

• Genomics
• Statistical modeling
• Bioinformatics

Background:

• Partial least squares regression (PLSR) is a statistical method used for analyzing data with multicollinearity.
• PLSR has gained traction in high-dimensional genomic data analysis.
• Traditional PLSR's asymptotic consistency is questioned under the 'large p, small n' paradigm common in genomics.

Purpose of the Study:

• To investigate the limitations of standard PLSR in high-dimensional genomic data.
• To develop an improved PLSR method for enhanced predictive performance and variable selection.
• To address the challenges of multicollinearity and the 'large p, small n' problem in genomic data analysis.

Main Methods:

• Demonstrated that known asymptotic consistency of PLSR does not hold for univariate and multivariate responses under the 'large p, small n' conditions.
• Proposed a sparse partial least squares (sPLS) formulation.
• Developed an efficient implementation of sPLS regression.

Main Results:

• Established that standard PLSR estimators are not consistently reliable for high-dimensional genomic data.
• The proposed sPLS formulation achieves both good predictive performance and effective variable selection.
• Simulation experiments showed sPLS outperforms existing variable selection and dimension reduction methods.

Conclusions:

• Sparse partial least squares regression is a viable and effective method for analyzing high-dimensional genomic data.
• sPLS offers a robust approach for joint analysis of gene expression and genomewide binding data.
• The findings have significant implications for statistical genomics and bioinformatics research.