Robust support vector regression for uncertain input and output data.

Area of Science:

• Machine Learning
• Statistical Modeling
• Optimization

Background:

• Support Vector Regression (SVR) is a powerful tool for regression analysis.
• Handling data uncertainty in SVR is crucial for real-world applications.
• Existing robust SVR methods may not adequately address both input and output uncertainties.

Purpose of the Study:

• To develop a robust support vector regression (RSVR) method capable of handling uncertain input and output data.
• To establish both linear and nonlinear RSVR formulations for regression problems with data uncertainties.
• To demonstrate the superiority of the proposed RSVR method over existing approaches.

Main Methods:

• Investigated data uncertainties within a stochastic framework, deriving two linear robust formulations.
• Considered linear formulations robust to ellipsoidal uncertainties from a geometric viewpoint.
• Established kernelized RSVR formulations for nonlinear regression, converting all formulations to second-order cone programming problems solvable by interior point methods.

Main Results:

• Developed novel linear and nonlinear RSVR formulations to manage data uncertainty.
• Successfully converted these formulations into efficiently solvable second-order cone programming problems.
• Simulations confirmed the proposed RSVR method's superior performance compared to existing RSVR techniques when faced with input and output data uncertainties.

Conclusions:

• The proposed robust support vector regression (RSVR) method effectively handles uncertain input and output data.
• The formulation as second-order cone programming problems allows for efficient computation.
• This advanced RSVR approach offers improved performance in scenarios with data uncertainty.