Mykola Prodaniuk

The formation of project teams, the allocation of resources, the assessment of specialists' competencies, and the forecasting of project results all require analysing a significant number of interrelated factors. Traditional approaches to IT project management often rely on expert assessments and managers' experience, leading to subjectivity in decision-making and reduced team performance. In this regard, the relevant area of research is the use of intelligent consulting systems capable of analysing large amounts of data, considering multiple criteria, and providing sound recommendations for forming project teams and assessing their effectiveness. The article analyses various approaches to creating decision support systems in the IT industry. To automate the process of forming project teams in the IT industry, the concept of intelligent consulting systems (IAS) has been proposed. The main components of the intelligent consulting system — the knowledge base, the data analysis module, the decision-making mechanism and the consultation module — are considered. An approach to formalising the task of forming a project team has also been developed, treating the selection of specialists as the problem of choosing the optimal combination of candidates from a set of available specialists. To describe the characteristics of specialists, a competence model was used, represented as a vector of parameters reflecting proficiency across various skills. Modern approaches to forming project teams, based on data on specialists' competencies, experience, availability, and team compatibility, are also analyzed. It is shown that hybrid approaches combining machine learning methods and decision support models will increase the efficiency of team-building processes. The results will serve as a theoretical basis for the further development of an intelligent consulting system for forming project teams in the IT industry.

This article discusses the practical aspects of applying logistic regression for binary data classification. Logistic regression determines the probability of an object belonging to one of two classes. This probability is calculated with the help of a sigmoid function, the argument of which is a linear convolution of the feature vector of the object with the weighting coefficients obtained during the minimization of the logarithmic loss function. Predicted class labels are determined by comparing the calculated probability with a given threshold value. The logistic regression study was performed using the computer simulation method. For this, a software complex was developed, the work of which reproduces the main stages of logistic regression: preparation of input data, training, testing with determination of quality metrics of binary classification, application of the logistic regression method for data classification in practice. The paper examines the effect of overlapping and imbalance of classes in the input data set on the efficiency of binary classification. The overlapping of classes is modeled by the formation of input data based on two shifted relative to each other density functions of the normal distribution of random variables. Class imbalance is simulated by the probability of switching between these features. It is shown that when the distance between the mathematical expectations of the density functions of the normal distribution decreases or when the dispersion of random variables increases, the overlapping of relevant classes increases, which leads to an increase in the number of objects that the classifier can assign to one or another class. Approaching the probability of switching between the distribution functions of random variables to the extreme values of the unit interval leads to an increase in class imbalance, which is manifested in an increase in the number of elements of the input data set labeled with the label of the same class. It has been experimentally confirmed that the AUC ROC metric, popular in binary classification problems, is dependent on the degree of class overlap and relatively resistant to class imbalance.

This article reviews the theoretical aspects of logistic regression for binary data classification, including data preparation processes, training, testing, and model evaluation metrics. Requirements for input data sets are formulated, methods of coding categorical data are described, methods of scaling input features are defined and substantiated. A scheme for learning logistic regression using the gradient descent method has been developed to minimize the loss function by the appropriate adjustment of the weights of the features of the sample of objects intended for classification. Features of the construction of recurrent methods of classical and stochastic gradient descent are determined. The requirements for the organization of the data sample for the multi-stage learning model in order to avoid overtraining or undertraining of logistic regression are described. The scheme of testing the trained logistic regression is given and the main quality metrics of binary classification are described. The influence of the height of the classification threshold on the efficiency of logistic regression was noted. According to the results of the work, the directions of perspective research of logistic regression are outlined.

In this article, the mathematical justification of logistic regression as an effective and simple to implement method of machine learning is performed. A review of literary sources was conducted in the direction of statistical processing, analysis and classification of data using the logistic regression method, which confirmed the popularity of this method in various subject areas. The logistic regression method was compared with the linear and probit regression methods regarding the possibility of predicting the probabilities of events. In this context, the disadvantages of linear regression and the advantages and affinity of logit and probit regression methods are noted. It is indicated that the possibility of forecasting probabilities and binary classification by the method of logistic regression is provided by the use of a sigmoid function with the property of compressive transformation of an argument with an unlimited numerical value into a limited range from 0 to 1 real value of the function. The derivation of the sigmoid function in two different ways is described: based on the model of the logarithm of the odds of events and the model of logistic population growth. Based on the method of maximum likelihood, the construction of a logarithmic loss function was demonstrated, the use of which made it possible to move from a multi-extremal nonlinear regression problem to a unimodal optimization problem. Methods of regularization of the loss function are presented to control the complexity and prevent retraining of the logistic regression model.

This paper proposes a new application of the stochastic game model to solve the problem of self- organization of the Hamiltonian cycle of a graph. To do this, at the vertices of the undirected graph are placed game agents, whose pure strategies are options for choosing one of the incident edges. A random selection of strategies by all agents forms a set of local paths that begin at each vertex of the graph. Current player payments are defined as loss functions that depend on the strategies of neighboring players that control adjacent vertices of the graph. These functions are formed from a penalty for the choice of opposing strategies by neighboring players and a penalty for strategies that have reduced the length of the local path. Random selection of players’ pure strategies is aimed at minimizing their average loss functions. The generation of sequences of pure strategies is performed by a discrete distribution built on the basis of dynamic vectors of mixed strategies. The elements of the vectors of mixed strategies are the probabilities of choosing the appropriate pure strategies that adaptively take into account the values of current losses. The formation of vectors of mixed strategies is determined by the Markov recurrent method, for the construction of which the gradient method of stochastic approximation is used. During the game, the method increases the value of the probabilities of choosing those pure strategies that lead to a decrease in the functions of average losses. For given methods of forming current payments, the result of the stochastic game is the formation of patterns of self-organization in the form of cyclically oriented strategies of game agents. The conditions of convergence of the recurrent method to collectively optimal solutions are ensured by observance of the fundamental conditions of stochastic approximation. The game task is extended to random graphs. To do this, the vertices are assigned the probabilities of recovery failures, which cause a change in the structure of the graph at each step of the game. Realizations of a random graph are adaptively taken into account when searching for Hamiltonian cycles. Increasing the probability of failure slows down the convergence of the stochastic game. Computer simulation of the stochastic game provided patterns of self-organization of agents’ strategies in the form of several local cycles or a global Hamiltonian cycle of the graph, depending on the ways of forming the current losses of players. The reliability of experimental studies is confirmed by the repetition of implementations of self-organization patterns for different sequences of random variables. The results of the study can be used in practice for game-solving NP-complex problems, transport and communication problems, for building authentication protocols in distributed information systems, for collective decision-making in conditions of uncertainty.