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This book is devoted to the theory of inductive inference, a model of which is statistical inference (inference for the simplest statistical models). The main problem in inductive inference lies in philosophy, in finding the principles of inference t rather than in the mathematical analysis of the formulated principles. However, to find the principles of inference that reflect the phenomenon of human inference, one cannot utilize two thousand years of philosophical heritage. Recall that when in the beginning of the 1960s the problem of modeling learning processes on computers arose, the only inspiration for constructing learning machines was a physiological analogy (the Perceptron), but not general philosophical principles. For this reason, it is important to analyze in great detail a simple math- ematical problem of induction and try to discover the general principles of inference from this analysis. Such a simple mathematical problem is the pattern recognition problem.

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