STATISTICAL APPROACH TO THE PROBLEM OF LEARNING PATTERN RECOGNITION

The paper shows that the problem of learning to recognize patterns is susceptible of statistical formulation and may be viewed as a particular case of the general problem of statistical solutions. Learning in this case may be accomplished by two methods, one of which is applicable when it is possible to measure directly the risk function characterizing the performance of the machine being taught (learning by reinforcement). The second method, called learning by patterns, is used when the risk function cannot be measured. Exact solution of this problem consists in finding the a posteriori distribution of unknown parameters and subsequent averaging of distributions containing these parameters, with the above-mentioned distribution serving as a weight. An evaluation is made of the minimum learning time, showing that in the absence of any substantial limitations superimposed on the probability distribution or on the determinant rules, the learning process must involve nearly all input signals. In the case of multidimensional input signals, learning time in the absence of limitations proves to be inadmissibly long. Edited machine trans. of Raspoznavanie Obrazov i Konstruyrovanie Chitayushchikh Avtomatov (USSR) n1 p3-14 1966, by Robert D. Hill.