On the principle of minimizing the average empiric risk to solutions of regression problems

In this paper, we propose an extension of the principle of empirical risk minimization to solve the problem of regression. It is based on the use of averaging aggregate functions to calculate the empirical risk instead of the arithmetic mean. Such intermediate risk assessment can be constructed using averaging aggregate functions, which are the solution of the problem of minimizing the penalty function for the deviation from its mean value. Such an approach to represent the average aggregate functions allows, on the one hand, to define a much broader middle class functions. In this paper we propose a new gradient scheme for solving the problem of minimizing the average risk. It is an analog circuit used in the SAG algorithm in the case when the risk is calculated using the arithmetic mean. An illustrative example of the construction of robust procedures for assessment of parameters in a linear regression based on the use of the averaging function average approximating the median is demonstrated.