A Robust Regression Framework with Laplace Kernel-Induced Loss.

Area of Science:

• Machine Learning
• Statistical Modeling
• Spectroscopy

Background:

• Robust regression is crucial for handling noisy data.
• Nonconvex loss functions can offer improved performance but are challenging to optimize.
• Traditional Support Vector Regression (SVR) methods have limitations with complex datasets.

Purpose of the Study:

• To propose a robust regression framework utilizing a nonconvex Laplace kernel-induced loss (LK-loss).
• To develop an efficient optimization method for the proposed LK-loss regression.
• To evaluate the framework's performance on real-world spectral data and benchmark datasets.

Main Methods:

• Developed two regression formulations based on the LK-loss, approximating the zero-norm.
• Formulated optimization problems as difference of convex functions (DC) programming.
• Applied continuous optimization and DC algorithms (DCAs) for linear convergence.

Main Results:

• The proposed LK-loss regression framework demonstrated improved generalization compared to SVR, especially in high-frequency spectral regions.
• Experiments on licorice seed hardness using near-infrared spectral data showed superior performance.
• Benchmark dataset evaluations indicated better results than traditional regression methods across most datasets.

Conclusions:

• The proposed robust regression framework with LK-loss offers a powerful alternative to traditional methods, particularly for noisy and complex data.
• The developed DC programming approach provides an effective optimization strategy for nonconvex loss functions.
• This method shows significant potential for applications in chemometrics and other fields requiring accurate data analysis.