Learning capability of the truncated greedy algorithm

Pure greedy algorithm (PGA), orthogonal greedy algorithm (OGA) and relaxed greedy algorithm (RGA) are three widely used greedy type algorithms in both nonlinear approximation and supervised learning. In this paper, we apply another variant of greedy-type algorithm, called the truncated greedy algorithm (TGA) in the realm of supervised learning and study its learning performance. We rigorously prove that TGA is better than PGA in the sense that TGA possesses the faster learning rate than PGA. Furthermore, in some special cases, we also prove that TGA outperforms OGA and RGA. All these theoretical assertions are verified by both toy simulations and real data experiments.