Inverse problem approach to regularized regression models with application to predicting recovery after stroke

Area of Science:

• Biomedical and clinical research
• Statistical modeling
• Machine learning

Background:

• Regression modeling is crucial in biomedical research.
• It can be framed as an inverse problem, linking predictors to outcomes.
• Challenges like collinearity and high dimensionality necessitate regularization.

Purpose of the Study:

• To propose an optimal regularizer for regression problems using Huber's robust statistics.
• To address challenges in linear regression, such as non-unique solutions due to collinearity.
• To enhance variable selection and coefficient estimation in regression analysis.

Main Methods:

• Formulating regression as an inverse problem to estimate parameters.
• Applying Huber's robust statistics framework to develop an optimal regularizer.
• Comparing the proposed method against penalized regression techniques (ridge, lasso, adaptive-lasso, elastic-net).

Main Results:

• The proposed robust regularizer demonstrates effectiveness under challenging conditions like high covariance matrix conditioning and error amplitude.
• Performance was evaluated on both simulated and real-world data (South London Stroke Register).
• The method shows promise for improving regression model fitting and learning.

Conclusions:

• The inverse problem framework combined with robust statistics offers novel insights into regression and learning.
• The proposed approach can be extended to mixed regression models.
• This methodology opens new avenues for research in statistical model fitting and machine learning.