High-dimensional partial linear model with trend filtering

TL;DR

This paper introduces a high-dimensional partial linear model with trend filtering to effectively analyze complex, nonlinear relationships in biological data, demonstrated through dietary and metabolic health studies.

Contribution

It presents a novel high-dimensional partial linear regression framework that combines interpretability and flexibility using trend filtering, achieving minimax optimal rates.

Findings

Successfully applied to IDATA Study data to identify UPF intake biomarkers.

Captures both linear and nonlinear effects in high-dimensional biological data.

Demonstrates improved modeling of complex biological relationships.

Abstract

Understanding the links between diet, metabolic changes, and health outcomes is a key focus in nutritional science and broader biological research. Analyzing relationships, such as those between ultra-processed food (UPF) intake and metabolites, offers insights into potential biomarkers for diet-related diseases and public health applications. However, these analyses are challenging due to high-dimensional data structures and complex, often nonlinear associations between covariates and health outcomes. Traditional linear models and conventional nonparametric methods often lack the flexibility to accurately capture such complexities in biological data. To address these challenges, we propose a high-dimensional partial linear regression model that captures both linear and nonlinear effects, combining the interpretability of linear models with the adaptability of nonparametric approaches. Our model leverages trend filtering to handle local smoothness variations effectively and achieves minimax optimal rates, making it suitable for complex biological datasets. We apply this model to data from the Interactive Diet and Activity Tracking in AARP (IDATA) Study, demonstrating its utility in identifying biomarkers associated with UPF intake and illustrating its potential for broader applications in dietary, metabolic, and health-related research.