The quality of regression models must be evaluated by many indicators. Quality criteria can be the minimum of square sum or absolute values of deviations of the predicted values from the true ones, the adequacy of value and sign of the coefficients in the regression equations, the model robustness, the minimum of signs necessary to fulfil other indicators, and much more. When constructing regression equations using standard programmes, it is quite difficult to simultaneously take into account several of the listed indicators. The aim of the article is to demonstrate that building regression models based on mathematical programming problems allows simultaneously considering a large set of requirements for the solution quality within one model. The scientific novelty lies in the fact that this approach makes it possible to create more complex regression models that take into account the specifics of particular practical problems. For example, in the general sample, there may be different trends at the same time. In this case, it is necessary to find out how many regression equations are required to describe the available observations with a given accu-racy. A special case of such a formulation is piecewise linear regression. Another example can be the need to predict multiple output parameters with a minimal set of identical input parameters. The article presents the practical results of applying the author’s approach to solving regression problems in agglomeration production and forecasting financial results for the banking sector

The spread of a new coronavirus infection in the last two years together with HIV infection preserves and even increases the potential for the spread of tuberculosis in the world. Sverdlovsk oblast (SO) of Russian Federation is the region with high levels of HIV and tuberculosis (TB). The search for new methods of forecasting of the future epidemic situation for tuberculosis has become particularly relevant. The aim was to develop an effective method for predicting the epidemic situation of tuberculosis using an artificial intelligence (AI) method in the format of a dynamic simulation model based on AI technologies. Statistical data was loaded from the state statistical reporting on TB patients for the period 2007–2017. The parameters were controlled through a system of inequalities. The proposed SDM made it possible to identify and reliably calculate trends of TB epidemiological indicators. Comparison of the predicted values made in 2017 with the actual values of 2018–2021 revealed a reliable coincidence of the trend of movement of TB epidemiological indicators in the region, the maximum deviation was no more than 14.82%. The forecast results obtained with SDM are quite suitable for practical use. Especially, in operational resource planning of measures to counteract the spread of tuberculosis at the regional level.

In this article is described an application of various machine learning (ML) methods to obtain decision rules and its interpretation to a problem of recognition of activity of the tuberculosis process. The research data base included 489 patients registered in anti-tuberculosis institutions in Tyumen and Yekaterinburg. The conducted modeling by machine learning methods allowed to highlight 7 most informative features (the presence of calcifications, age, the content of leukocytes, hemoglobin, eosinophils, α2-fraction of globulins, γ-fraction of globulins) together with classification accuracy of 95% for both active and inactive patients. The research result may be interesting for medical specialists, data scientists and to all those interested in problems at the intersection of medicine and machine learning.