The results of research are presented, the purpose of which was to develop a method for predicting the outflow of clients of a commercial bank based on the use of machine learning models (including deep artificial neural networks) for processing client data, as well as the creation of software tools that implement this method. The object of the study is a commercial bank, and the subject of the study is its activities in the B2C segment, which includes commercial interaction between businesses and individuals. The relevance of the chosen area of research is determined by the increased activity of banks in the field of introducing digital services to reduce non-operating costs associated, in particular, with retaining clients, since the costs of attracting new ones are much higher than maintaining existing clients. The scientific novelty of the research results is the developed method for predicting the outflow of commercial bank clients, as well as the algorithm underlying the software that implements the proposed method. The proposed ensemble forecasting model is based on three classification algorithms: k-means, random forest and multilayer perceptron. To aggregate the outputs of individual models, it is proposed to use a learning tree of fuzzy inference systems of the Mamdani type. Training of the ensemble model is carried out in two stages: first, the listed three classifiers are trained, and then, based on the data obtained from their outputs, a tree of fuzzy inference systems is trained. The ensemble model in the proposed method implements a static version of the forecast, the results of which are used in a dynamic forecast performed in two versions – based on the recurrent least squares method and based on a convolutional neural network. Model experiments carried out on a synthetic dataset taken from the Kaggle website showed that the ensemble model has a higher quality of binary classification than each model individually.

Outliers in statistical data, which are the result of erroneously collected information, are often an obstacle to the successful application of machine learning methods in many subject areas. The presence of outliers in training data sets reduces the accuracy of machine learning models, and in some cases, makes the application of these methods impossible. Currently existing outlier detection methods are unreliable. They are fundamentally unable to detect some types of outliers, while observations that are not outliers are often classified as outliers by these methods. Recently emerging neural network methods for outlier detection are free from this drawback, but they are not universal, since the ability of neural networks to detect outliers depends both on the architecture of the neural network itself and on the problem being solved. The purpose of this study is to develop an algorithm for creating and using neural networks that can correctly detect outliers regardless of the problem being solved. This goal is achieved by using the property of some specially created neural networks to demonstrate the largest training errors on those observations that are outliers. The use of this property, as well as the implementation of a series of computational experiments and the generalization of their results using a mathematical formula, which is a modification of the consequence of the Arnold – Kolmogorov – Hecht-Nielsen theorem, made it possible to achieve the stated goal. The use of the developed algorithm turned out to be especially effective in solving the problems of forecasting and controlling interdependent thermophysical and chemical-energy-technological processes of processing ore raw materials, occurring at existing serial metallurgical enterprises, where the presence of outliers in statistical data is almost inevitable, and without their identification and exclusion, the construction of neural network systems that are acceptable in accuracy models are generally impossible.

Solving the problems of effective business management is associated with a variety of current goals facing the same and, by implication, requires the construction of appropriate models of efficient business. The article presents two problems of doing business which, apart from their common target being an improvement of business efficiency, have different current goals. The creation or development of any business involves the construction of a specific business plan for it, including a list of those areas of business development, the implementation of which will increase its efficiency. The first problem considered in the article is related to the phased implementation of all areas of efficiency improvement in order to ultimately obtain the greatest efficiency of their realization. The second one solves the problem of increasing efficiency by partially implementing efficiency improvement directions from the initial list, taking into account certain limitations, for example, in conditions of limited company resources. For the construction of models which would meet the problems set, an efficiency criterion is substantiated and proposed in the article, and Algorithms 1 and 2 are developed which made it possible to build the efficient business models which take into account the difference in its current goals. The authors have developed a multi-stage Algorithm 1 for the generation of individual sets of areas for improvement of efficiency to be used to solve the tasks at hand. Algorithm 2 implemented at each stage of Algorithm 1 has been developed by the authors by using the Pareto optimality method but supplemented by taking into account the features and objectives of the current tasks set for the business. The use of such algorithms has made it possible to build efficient business models enabling not only to obtain an economic effect inherent to each efficiency improvement area, but also to ensure additional growth thereof driven by the properties of the developed algorithms.

A model for forecasting deviations of external and internal environmental factors at an industrial enterprise from planned values is proposed. This model is based on an ensemble of artificial neural networks. Improving the accuracy of such forecasts is a pressing research challenge, as accuracy plays a key role in developing enterprise production programs, enabling the sound development of competitive strategies for relationships with suppliers and customers. Forecast accuracy is significantly affected by instability in internal environmental factors (data directly characterizing production processes in terms of their impact on output volumes and product quality) and external factors (demand volume, delivery times, and the quality of components and raw materials). In the research problem statement, instability was understood not as the variability of factor values per se, but as fluctuations in their generalized characteristics relating to the entire data set. Such characteristics include irregular data receipt and the presence of anomalies in them. The novelty of the research results lies in the proposed structure of the neural network model for forecasting deviations of external and internal environmental factors from planned indicators in the face of irregular data receipt and the presence of anomalies in the data, as well as the algorithm for its application. The model is based on an ensemble of three neural network submodels built on convolutional and recurrent neural network architectures that forecast factors in the internal and external environments (taking into account decomposition into micro and macro environments) of the enterprise. The mutual influence of the instability of these factors is taken into account in the model by using a long short-term memory network at its output to aggregate the results of the submodels to produce the final forecast. The results of the model experiment showed that taking into account the instability of factors allows for increased accuracy in forecasting deviations of external and internal environmental factors from planned values.