Novel mixed integer optimization sparse regression approach in chemometrics.

Area of Science:

• Chemometrics
• Mathematical Modeling
• Regression Analysis

Background:

• Sparse mathematical modeling is crucial in chemometrics for interpretability and prediction.
• Existing sparse techniques often use L1 penalization, while Mixed Integer Optimization (MIO) uses direct constraints for sparsity.

Purpose of the Study:

• Develop an intuitive and flexible robust sparse regression framework using MIO.
• Enhance model accuracy, sparsity, and robustness compared to existing methods like LASSO and sparse PLS (sPLS).

Main Methods:

• Implemented a robust sparse regression framework utilizing Mixed Integer Optimization (MIO).
• Achieved sparsity through direct model constraints and robustness via penalization.
• Compared MIO performance against LASSO, sPLS, and PLS using a LIBS dataset of mineral ores.

Main Results:

• The MIO framework demonstrated superior accuracy, sparsity, and robustness over LASSO and sPLS.
• MIO achieved an average R-squared (R²) of at least 10.6% higher than other methods.
• MIO models used significantly fewer variables (average 4.3) compared to LASSO (16.1) and sPLS (805.8).
• MIO maintained strong performance (average R² of 0.69) even with added noise, where other models showed negative R² values.

Conclusions:

• The proposed MIO framework offers a versatile and effective approach for robust sparse regression in chemometrics.
• MIO enhances model interpretability, leading to potentially better model development.
• The MIO framework shows promise for various chemometric applications beyond the studied mineral ore analysis.