Uncertainty estimation in machine learning

Most machine learning methods are based on statistical learning theory, often using procedural simplification to achieve acceptable computational speed. The purpose of the study. To form a general approach to uncertainty estimation in machine learning models. In econometrics, in any model the uncertainty is necessarily put in the form of standard deviation (sigma) for coefficients and based on it the sigma for predictions is constructed. The problem is that in machine learning we cannot analytically calculate uncertainty through sigma. Therefore, we propose to use numerical methods instead of analytical methods. Materials and methods. For a detailed consideration of uncertainty estimation, we choose classical methods of regression analysis, which pay much attention to the uncertainty of model coefficients and - more importantly - the accuracy of the predictions obtained from such a model. Results. We propose a technique for estimating uncertainty, demonstrated by a model example in order to show that it is consistent with traditional classical methods in terms of results. In future practice, we propose to use cross validation. Conclusion. When using machine models of complex processes, including forecasts based on such models, the problem of evaluating uncertainty and risks arising from the inevitable uncertainty becomes more and more relevant when making managerial decisions. This problem can be solved on the basis of nonparametric methods, although it will require much more computing power than that used to train a machine model. The proposed approach can be generalized to other machine learning methods, for example, to the problem of classification and clustering.