The principle of empirical risk minimization: mining for data stable patterns

Abstract

In this paper, we propose an extension for empirical risk minimization to solve the problem of regression. We applied averaging aggregation functions instead of the arithmetic mean to calculate the empirical risk. Such an intermediate risk assessment can be constructed using aggregate functions. These functions promote the solution to the problem for the penalty function minimization resulted from a deviation of its mean value. Such an approach to represent the aggregate average functions allows, on the one hand, to identify a much wider class of functions with mean-values. 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 with the arithmetic mean. Herein we present an illustrative example of the robust parameter estimation design in a linear regression based on the average function that approximates the median.