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We consider the approximation capability of orthogonal super greedyalgorithms (OSGA) and its applications in supervised learning. OSGA isconcerned with selecting more than one atoms in each iteration step, which, ofcourse, greatly reduces the computational burden when compared with theconventional orthogonal greedy algorithm (OGA). We prove that even for functionclasses that are not the convex hull of the dictionary, OSGA does not degradethe approximation capability of OGA provided the dictionary is incoherent.Based on this, we deduce a tight generalization error bound for OSGA learning.Our results show that in the realm of supervised learning, OSGA provides apossibility to further reduce the computational burden of OGA in the premise ofmaintaining its prominent generalization capability.

Learning and approximation capability of orthogonal super greedy algorithm