Feature screening for metric space-valued responses based on Fréchet regression with its applications

Area of Science:

• Statistics
• Bioinformatics
• Neuroimaging

Background:

• Handling complex response variables (distributional, matrix-valued) is crucial in high-dimensional data analysis.
• Identifying relevant predictors for these complex responses is a significant challenge, particularly in fields like neuroimaging.

Purpose of the Study:

• To propose a novel sure independence screening (SIS) procedure for general metric space-valued responses.
• To address the challenge of selecting relevant single nucleotide polymorphisms (SNPs) for complex neuroimaging data in Alzheimer's disease research.

Main Methods:

• Developed Fréchet-SIS, a procedure based on global Fréchet regression for metric space-valued responses.
• Utilized marginal general residual sum of squares as a predictor importance measure, requiring only distances between data objects.
• Theoretically established the sure screening property of Fréchet-SIS under mild regularity conditions.

Main Results:

• Fréchet-SIS demonstrates excellent finite-sample performance in Monte Carlo simulations.
• Successfully identified important genes correlating with brain activity in an Alzheimer's disease neuroimaging study.
• Validated the method's applicability with an additional economic case study.

Conclusions:

• Fréchet-SIS provides a robust and theoretically sound method for variable selection with complex response data.
• The procedure is effective in identifying biologically relevant genetic markers in neuroimaging studies.
• The approach has broad applicability across various scientific domains requiring analysis of high-dimensional data with complex responses.