Robust support vector regression in the primal.

Area of Science:

• Machine Learning
• Statistical Learning Theory

Background:

• Classical Support Vector Regression (SVR) models utilize convex loss functions.
• Non-convex loss functions offer potential advantages in generalization and robustness over convex counterparts.

Purpose of the Study:

• To propose a novel non-convex loss function for SVR.
• To develop a robust SVR method that improves generalization and handles outliers.

Main Methods:

• A non-convex loss function was proposed for SVR.
• The concave-convex procedure was employed to convert the non-convex optimization problem into a convex one.
• A Newton-type optimization algorithm was developed to solve the robust SVR in the primal space.

Main Results:

• The proposed method retains the sparseness property of SVR.
• The approach effectively suppresses outliers in training data.
• Experiments on synthetic and real-world datasets confirmed superior generalization performance.

Conclusions:

• The proposed non-convex loss function and optimization method provide a robust and effective SVR model.
• This approach enhances generalization performance and outlier suppression capabilities in SVR.