One-hot approach to identification of integrated rating mechanisms

The problem of identifying the integrated rating mechanisms for a given set of training examples is considered. An approach to the solution based on one-hot encoding is proposed. Basic concepts and definitions are formalized, such as: an integrated rating mechanism with a binary tree and convolution matrices, an integrated rating mechanism with a binary tree for discrete scales, a training example, a training set (consistent, complete, uniform scaled), a monotone training set. Identification tasks are formulated in the form of tasks for the implementation of the training set by the integrated rating mechanism and approximation. The proposed one-hot representation of the complex estimation mechanism using the quadratic form is illustrated with several examples. The rules for coding the integrated rating mechanisms are presented. It is shown that the problem of approximation and the problem of implementation as its particular case can be reduced to the problem of maximizing a certain polynomial obtained for a given binary tree and a set of examples using one-hot encoding. Assertions about the properties of these polynomials for an arbitrary integrated rating mechanism are formulated and proved. Examples of solving the problem of identification of an integrated rating mechanism are given, which implements an example through solving a system of equations based on one-hot encoding. In conclusion, the results of a numerical experiment on the approximation of all Boolean functions of three variables by the integrated rating mechanism are presented.