Statistical Significance of Predicting the Production Process Results by Means of an Artificial Neural Network

Abstract

As a result of the research of production process organization for the roof construction of residential multi-storey buildings, an artificial neural network (ANN) was designed, the purpose of which is to predict the labor productivity based on organizational factors. One of the main tasks on the way to this purpose is the training of ANN on precedents of the sample extracted from the research object. In view of the deficiency of training data, the main problem is to determine the conditions for the statistical significance of the predictions of the model trained on limited sample. This article is devoted to solving this problem within the research of production organization. The paper uses the provisions of the statistical learning theory, the notion of the Vapnik-Chervonenkis dimension for describing the sample complexity, and also the approaches of probably approximately correct learning (PAC-learning). The technologies of statistical bootstrapping and bagging are described, which allow expanding the training sample. ANN training is conducted using a computer experiment on the programming language Python. The bounds of the theoretical sample complexity, which is necessary for obtaining of ANN results within a given confidence interval with a confidence level of 0,95, were estimated. The sample was transformed by an order comparable to the theoretical lower bound. ANN was trained and the mean square error (MSE) in the test sample was defined, which amounted to . The theoretical bounds of the sample complexity to ensure a given statistical significance are determined in the article. After the ANN training on the sample, the order of which corresponds to theoretical lower bound, a prediction error was obtained on the test sample within the given confidence interval.