Multivariate Scalar on Multidimensional Distribution Regression With Application to Modeling the Association Between...

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Traditional regression methods often analyze univariate outcomes or unidimensional predictors, failing to capture complex dependencies.
• Existing approaches neglect the correlation structure of multivariate responses and the interdependence of distributional predictors.

Purpose of the Study:

• To develop a novel multivariate distributional analysis framework for improved regression modeling.
• To address limitations of traditional methods by incorporating multivariate density functions and multitask learning.
• To provide accurate uncertainty quantification for predictions.

Main Methods:

• A computationally efficient semiparametric estimation method for modeling latent joint density effects on multivariate responses.
• A new conformal prediction algorithm for uncertainty quantification based on subject characteristics and distributional predictors.
• Validation through comprehensive numerical simulations and application to real-world data.

Main Results:

• The proposed method demonstrates superior performance compared to traditional approaches in numerical simulations.
• The framework effectively models the association between physical activity distributional representations and cognitive scores.
• Multidimensional distributional information from triaxial accelerometer data significantly enhances prediction accuracy.

Conclusions:

• The developed multivariate distributional analysis framework offers a significant advancement over traditional methods.
• Incorporating multidimensional distributional information is crucial for accurately modeling complex relationships.
• The method provides valuable insights into the conditional distribution of responses, enhancing predictive modeling in health and nutrition studies.