A Consistent Feature Screening Approach for Tensor Responses with Applications to Genome-Wide Facial Shape Association

2026-07-24

AI Summary

This study addresses the challenge of associating ultra-high-dimensional genetic data with high-dimensional tensor-valued responses, such as human facial shape. It proposes TrimTenRidge, a trimmed tensor ridge regression method that circumvents the need for sparsity assumptions by thresholding tensor coefficients to perform variable selection. The approach simultaneously accommodates ultra-high-dimensional predictors and structured tensor responses, enabling precise localization of facial regions influenced by significant genetic loci. Theoretical analysis establishes its estimation consistency, and simulation studies demonstrate superior performance. Applied to real facial shape data of dimension 2342 × 7160 × 3, the method successfully identifies multiple novel genetic loci while corroborating established findings, showcasing both interpretability and practical utility.

Abstract

As data collecting technologies advance, data structures are getting more and more complex, from single vectors to multi-dimensional tensors. This article is motivated by a variable selection problem to detect important genes from an ultrahigh dimensional pool that are associated with human facial shape variations. We propose a data-driven trimmed feature screening method based on a tensor ridge regression model (TrimTenRidge) through setting thresholds on the tensor coefficients to perform a feature screening procedure. Unlike existing approaches, the TrimTenRidge does not require any sparse structures. In addition, it not only detects important predictors but also locates specific regions/components of the tensor response that are associated with each of the selected predictors. We prove the theoretical selection consistency and also assess its empirical performance through various simulation settings. The approach copes with ultra-high dimensional predictors and tensor responses simultaneously and contributes to the literature from theoretical, methodological, and five applicational aspects. We further apply the TrimTenRidge approach to genome-wide human facial shape data, from which the entire facial shapes form a $2,342\times 7,160\times 3$ tensor, and we successfully detect several novel genetic loci and also confirm some existing findings that are associated to facial shape.

Problem

• tensor response
• ultra-high dimensional
• feature screening
• genetic association
• facial shape

Innovation

• tensor regression
• feature screening
• ultra-high-dimensional data
• selection consistency
• genomic association