A method for constructing non-elementary Cobb – Douglas production functions

The actual scientific problem in machine learning is the development of new interpretable mathematical models, as well methods and programs for their construction. Many well-known regression models have good interpretative properties, example, linear power (Cobb – Douglas production functions). Previously, author developed non-elementary regressions, constructing which was reduced to mixed integer 0–1 programming problem.Based on this paper, first time, Cobb-Douglas functions are proposed, include not only explanatory variables degrees, but also all possible pair combinations, transformed using binary operations min max. proposed linearized, makes it apply construction formulated same way regressions. As a result its solution, optimal structure model automatically determined. advantage such formulation that solution can be obtained faster than enumeration procedures, signs estimates constructed guaranteed consistent with meaningful meaning factors. At control requirements constraints variables. In particular, used select structures traditional elementary Cobb functions.The modeling gross regional product Tomsk region solved. following were chosen variables: average per capita cash income population, investments fixed capital, costs innovative activities organizations, annual number employees, cost assets, internal research development. LPSolve package solver problem. solving problem, function chosen, contains six three regressors. coefficient determination turned out 0.997. All coefficients significant according Student's t-test, satisfy An interpretation given.