Robust, Adaptive Functional Regression in Functional Mixed Model Framework.

Area of Science:

• Statistics
• Computational Biology
• Data Science

Background:

• Functional data analysis presents challenges due to high dimensionality and complexity.
• Existing functional regression methods lack robustness to outlying curves and curve regions.

Purpose of the Study:

• Introduce a novel Bayesian method, robust functional mixed models (R-FMM), for robust functional regression.
• Accommodate multiple predictors and random effects within a flexible framework.

Main Methods:

• Developed a hierarchical scale mixture model for fixed effects, random effects, and residual errors.
• Employed wavelet transforms for sparsity and adaptive shrinkage properties of wavelet coefficients.
• Implemented a fully Bayesian approach with general, automatic code for efficient analysis of large datasets.

Main Results:

• R-FMM provides robust nonparametric estimators that down-weight outliers, flagging global and local outliers.
• Achieved adaptive estimation that removes spurious features while retaining true functional features.
• Demonstrated efficient handling of large datasets with posterior samples for Bayesian inference.

Conclusions:

• R-FMM offers a robust and adaptive solution for functional regression, outperforming existing methods in handling outliers.
• The method is flexible and can be extended to higher-dimensional data and alternative transformations.
• The developed code is efficient and user-friendly for practical application in scientific studies.