Greedy Criterion in Orthogonal Greedy Learning.

Area of Science:

• Machine Learning
• Signal Processing
• Optimization

Background:

• Orthogonal Greedy Learning (OGL) is a stepwise algorithm for constructing estimators.
• The standard OGL utilizes Steepest Gradient Descent (SGD) to select dictionary atoms.
• The computational efficiency and convergence of OGL are areas of active research.

Purpose of the Study:

• To explore alternative greedy criteria beyond Steepest Gradient Descent (SGD) for Orthogonal Greedy Learning (OGL).
• To introduce a novel epsilon-greedy threshold criterion for OGL.
• To analyze the theoretical performance and practical efficiency of the new OGL variant.

Main Methods:

• Introduced a new greedy criterion: the epsilon-greedy threshold.
• Derived a straightforward termination rule based on the new criterion.
• Conducted theoretical analysis to evaluate learning rates and generalization performance.
• Performed numerical experiments to compare the new scheme with standard OGL.

Main Results:

• The proposed epsilon-greedy threshold criterion achieves an (almost) optimal learning rate comparable to existing OGL methods.
• The new learning scheme demonstrates competitive generalization performance.
• Numerical experiments indicate significantly reduced computational requirements compared to standard OGL.

Conclusions:

• The epsilon-greedy threshold offers an effective alternative greedy criterion for Orthogonal Greedy Learning (OGL).
• This new scheme provides a favorable trade-off between performance and computational cost.
• The findings suggest potential for more efficient model building in various applications of OGL.