Greedy Criterion in Orthogonal Greedy Learning
This work provides an incremental improvement for machine learning practitioners by offering a more efficient greedy learning scheme with theoretical guarantees.
The paper tackles the problem of selecting atoms in orthogonal greedy learning by introducing a new greedy criterion called the δ-greedy threshold, which achieves almost optimal learning rates and reduces computational requirements compared to existing methods.
Orthogonal greedy learning (OGL) is a stepwise learning scheme that starts with selecting a new atom from a specified dictionary via the steepest gradient descent (SGD) and then builds the estimator through orthogonal projection. In this paper, we find that SGD is not the unique greedy criterion and introduce a new greedy criterion, called "$δ$-greedy threshold" for learning. Based on the new greedy criterion, we derive an adaptive termination rule for OGL. Our theoretical study shows that the new learning scheme can achieve the existing (almost) optimal learning rate of OGL. Plenty of numerical experiments are provided to support that the new scheme can achieve almost optimal generalization performance, while requiring less computation than OGL.