The Key Theorem of Learning Theory Based on Random Sets Samples

Statistical learning theory based on random samples is regarded as the best theory for dealing with small-sample learning problems at present. And it has become an interesting research after neural networks in machine learning. But it can hardly be handle by the learning problems based on random sets samples. In this paper, combined with the theory of random sets, the definition of the subtraction between the set and the real number is presented, and then some correlative theorems are proven. According to these, some of main concepts of statistical learning theory based on random sets samples are introduced, and at last, the key theorem of learning theory based on random sets samples is given and proven.