Результаты поиска по 'regression models':
Найдено статей: 20
  1. Tikhov M.S., Borodina T.S.
    Mathematical model and computer analysis of tests for homogeneity of “dose–effect” dependence
    Computer Research and Modeling, 2012, v. 4, no. 2, pp. 267-273

    The given work is devoted to the comparison of two tests for homogeneity: chi-square test based on contingency tables of 2 × 2 and test for homogeneity based on asymptotic distributions of the summarized square error of a distribution function estimators in the model of ”dose–effect” dependence. The evaluation of test power is performed by means of computer simulation. In order to design efficiency functions the method of kernel regression estimator based on Nadaray–Watson estimator is used.

    Views (last year): 6.
  2. Maksimova O.V., Grigoryev V.I.
    Four-factor computing experiment for the random walk on a two-dimensional square field
    Computer Research and Modeling, 2017, v. 9, no. 6, pp. 905-918

    Nowadays the random search became a widespread and effective tool for solving different complex optimization and adaptation problems. In this work, the problem of an average duration of a random search for one object by another is regarded, depending on various factors on a square field. The problem solution was carried out by holding total experiment with 4 factors and orthogonal plan with 54 lines. Within each line, the initial conditions and the cellular automaton transition rules were simulated and the duration of the search for one object by another was measured. As a result, the regression model of average duration of a random search for an object depending on the four factors considered, specifying the initial positions of two objects, the conditions of their movement and detection is constructed. The most significant factors among the factors considered in the work that determine the average search time are determined. An interpretation is carried out in the problem of random search for an object from the constructed model. The important result of the work is that the qualitative and quantitative influence of initial positions of objects, the size of the lattice and the transition rules on the average duration of search is revealed by means of model obtained. It is shown that the initial neighborhood of objects on the lattice does not guarantee a quick search, if each of them moves. In addition, it is quantitatively estimated how many times the average time of searching for an object can increase or decrease with increasing the speed of the searching object by 1 unit, and also with increasing the field size by 1 unit, with different initial positions of the two objects. The exponential nature of the growth in the number of steps for searching for an object with an increase in the lattice size for other fixed factors is revealed. The conditions for the greatest increase in the average search duration are found: the maximum distance of objects in combination with the immobility of one of them when the field size is changed by 1 unit. (that is, for example, with $4 \times 4$ at $5 \times 5$) can increase the average search duration in $e^{1.69} \approx 5.42$. The task presented in the work may be relevant from the point of view of application both in the landmark for ensuring the security of the state, and, for example, in the theory of mass service.

    Views (last year): 21.
  3. Mikheev A.V., Kazakov B.N.
    A New Method For Point Estimating Parameters Of Simple Regression
    Computer Research and Modeling, 2014, v. 6, no. 1, pp. 57-77

    A new method is described for finding parameters of univariate regression model: the greatest cosine method. Implementation of the method involves division of regression model parameters into two groups. The first group of parameters responsible for the angle between the experimental data vector and the regression model vector are defined by the maximum of the cosine of the angle between these vectors. The second group includes the scale factor. It is determined by means of “straightening” the relationship between the experimental data vector and the regression model vector. The interrelation of the greatest cosine method with the method of least squares is examined. Efficiency of the method is illustrated by examples.

    Views (last year): 2. Citations: 4 (RSCI).
  4. Yudin N.E.
    Modified Gauss–Newton method for solving a smooth system of nonlinear equations
    Computer Research and Modeling, 2021, v. 13, no. 4, pp. 697-723

    In this paper, we introduce a new version of Gauss–Newton method for solving a system of nonlinear equations based on ideas of the residual upper bound for a system of nonlinear equations and a quadratic regularization term. The introduced Gauss–Newton method in practice virtually forms the whole parameterized family of the methods solving systems of nonlinear equations and regression problems. The developed family of Gauss–Newton methods completely consists of iterative methods with generalization for cases of non-euclidean normed spaces, including special forms of Levenberg–Marquardt algorithms. The developed methods use the local model based on a parameterized proximal mapping allowing us to use an inexact oracle of «black–box» form with restrictions for the computational precision and computational complexity. We perform an efficiency analysis including global and local convergence for the developed family of methods with an arbitrary oracle in terms of iteration complexity, precision and complexity of both local model and oracle, problem dimensionality. We present global sublinear convergence rates for methods of the proposed family for solving a system of nonlinear equations, consisting of Lipschitz smooth functions. We prove local superlinear convergence under extra natural non-degeneracy assumptions for system of nonlinear functions. We prove both local and global linear convergence for a system of nonlinear equations under Polyak–Lojasiewicz condition for proposed Gauss– Newton methods. Besides theoretical justifications of methods we also consider practical implementation issues. In particular, for conducted experiments we present effective computational schemes for the exact oracle regarding to the dimensionality of a problem. The proposed family of methods unites several existing and frequent in practice Gauss–Newton method modifications, allowing us to construct a flexible and convenient method implementable using standard convex optimization and computational linear algebra techniques.

  5. Mizgulin V.V., Kosulnikov V.V., Kadushnikov R.M.
    The optimization approach to simulation modeling of microstructures
    Computer Research and Modeling, 2013, v. 5, no. 4, pp. 597-606

    The paper presents an optimization approach to microstructure simulation. Porosity function was optimized by numerical method, grain-size model was optimized by complex method based on criteria of model quality. Methods have been validated on examples. Presented new regression model of model quality. Actual application of proposed method is 3D reconstruction of core sample microstructure. Presented results suggest to prolongation of investigations. 

    Views (last year): 4. Citations: 7 (RSCI).
  6. Kondratyev M.A.
    Forecasting methods and models of disease spread
    Computer Research and Modeling, 2013, v. 5, no. 5, pp. 863-882

    The number of papers addressing the forecasting of the infectious disease morbidity is rapidly growing due to accumulation of available statistical data. This article surveys the major approaches for the shortterm and the long-term morbidity forecasting. Their limitations and the practical application possibilities are pointed out. The paper presents the conventional time series analysis methods — regression and autoregressive models; machine learning-based approaches — Bayesian networks and artificial neural networks; case-based reasoning; filtration-based techniques. The most known mathematical models of infectious diseases are mentioned: classical equation-based models (deterministic and stochastic), modern simulation models (network and agent-based).

    Views (last year): 71. Citations: 19 (RSCI).
  7. Prokoptsev N.G., Alekseenko A.E., Kholodov Y.A.
    Traffic flow speed prediction on transportation graph with convolutional neural networks
    Computer Research and Modeling, 2018, v. 10, no. 3, pp. 359-367

    The short-term prediction of road traffic condition is one of the main tasks of transportation modelling. The main purpose of which are traffic control, reporting of accidents, avoiding traffic jams due to knowledge of traffic flow and subsequent transportation planning. A number of solutions exist — both model-driven and data driven had proven to be successful in capturing the dynamics of traffic flow. Nevertheless, most space-time models suffer from high mathematical complexity and low efficiency. Artificial Neural Networks, one of the prominent datadriven approaches, show promising performance in modelling the complexity of traffic flow. We present a neural network architecture for traffic flow prediction on a real-world road network graph. The model is based on the combination of a recurrent neural network and graph convolutional neural network. Where a recurrent neural network is used to model temporal dependencies, and a convolutional neural network is responsible for extracting spatial features from traffic. To make multiple few steps ahead predictions, the encoder-decoder architecture is used, which allows to reduce noise propagation due to inexact predictions. To model the complexity of traffic flow, we employ multilayered architecture. Deeper neural networks are more difficult to train. To speed up the training process, we use skip-connections between each layer, so that each layer teaches only the residual function with respect to the previous layer outputs. The resulting neural network was trained on raw data from traffic flow detectors from the US highway system with a resolution of 5 minutes. 3 metrics: mean absolute error, mean relative error, mean-square error were used to estimate the quality of the prediction. It was found that for all metrics the proposed model achieved lower prediction error than previously published models, such as Vector Auto Regression, LSTM and Graph Convolution GRU.

    Views (last year): 36.
  8. Oleynik E.B., Ivashina N.V., Shmidt Y.D.
    Migration processes modelling: methods and tools (overview)
    Computer Research and Modeling, 2021, v. 13, no. 6, pp. 1205-1232

    Migration has a significant impact on the shaping of the demographic structure of the territories population, the state of regional and local labour markets. As a rule, rapid change in the working-age population of any territory due to migration processes results in an imbalance in supply and demand on labour markets and a change in the demographic structure of the population. Migration is also to a large extent a reflection of socio-economic processes taking place in the society. Hence, the issues related to the study of migration factors, the direction, intensity and structure of migration flows, and the prediction of their magnitude are becoming topical issues these days.

    Mathematical tools are often used to analyze, predict migration processes and assess their consequences, allowing for essentially accurate modelling of migration processes for different territories on the basis of the available statistical data. In recent years, quite a number of scientific papers on modelling internal and external migration flows using mathematical methods have appeared both in Russia and in foreign countries in recent years. Consequently, there has been a need to systematize the currently most commonly used methods and tools applied in migration modelling to form a coherent picture of the main trends and research directions in this field.

    The presented review considers the main approaches to migration modelling and the main components of migration modelling methodology, i. e. stages, methods, models and model classification. Their comparative analysis was also conducted and general recommendations on the choice of mathematical tools for modelling were developed. The review contains two sections: migration modelling methods and migration models. The first section describes the main methods used in the model development process — econometric, cellular automata, system-dynamic, probabilistic, balance, optimization and cluster analysis. Based on the analysis of modern domestic and foreign publications on migration, the most common classes of modelsregression, agent-based, simulation, optimization, probabilistic, balance, dynamic and combined — were identified and described. The features, advantages and disadvantages of different types of migration process models were considered.

  9. Makhov S.A.
    The long-term empirical macro model of world dynamics
    Computer Research and Modeling, 2013, v. 5, no. 5, pp. 883-891

    The work discusses the methodological basis and problems of modeling of world dynamics. Outlines approaches to the construction of a new simulation model of global development and the results of the simulation. The basis of the model building is laid empirical approach which based on the statistical analysis of the main socio-economic indicators. On the basis of this analysis identified the main variables. Dynamic equations (in continuous differential form) were written for these variables. Dependencies between variables were selected based on the dynamics of indicators in the past and on the basis of expert assessments, while econometric techniques were used, based on regression analysis. Calculations have been performed for the resulting dynamic equations system, the results are presented in the form of a trajectories beam for those indicators that are directly observable, and for which statistics are available. Thus, it is possible to assess the scatter of the trajectories and understand the predictive capability of this model.

    Views (last year): 4. Citations: 3 (RSCI).
  10. Naumov I.V., Otmakhova Y.S., Krasnykh S.S.
    Methodological approach to modeling and forecasting the impact of the spatial heterogeneity of the COVID-19 spread on the economic development of Russian regions
    Computer Research and Modeling, 2021, v. 13, no. 3, pp. 629-648

    The article deals with the development of a methodological approach to forecasting and modeling the socioeconomic consequences of viral epidemics in conditions of heterogeneous economic development of territorial systems. The relevance of the research stems from the need for rapid mechanisms of public management and stabilization of adverse epidemiological situation, taking into account the spatial heterogeneity of the spread of COVID-19, accompanied by a concentration of infection in large metropolitan areas and territories with high economic activity. The aim of the work is to substantiate a methodology to assess the spatial heterogeneity of the spread of coronavirus infection, find poles of its growth, emerging spatial clusters and zones of their influence with the assessment of inter-territorial relationships, as well as simulate the effects of worsening epidemiological situation on the dynamics of economic development of regional systems. The peculiarity of the developed approach is the spatial clustering of regional systems by the level of COVID-19 incidence, conducted using global and local spatial autocorrelation indices, various spatial weight matrices, and L.Anselin mutual influence matrix based on the statistical information of the Russian Federal State Statistics Service. The study revealed a spatial cluster characterized by high levels of infection with COVID-19 with a strong zone of influence and stable interregional relationships with surrounding regions, as well as formed growth poles which are potential poles of further spread of coronavirus infection. Regression analysis using panel data not only confirmed the impact of COVID-19 incidence on the average number of employees in enterprises, the level of average monthly nominal wages, but also allowed to form a model for scenario prediction of the consequences of the spread of coronavirus infection. The results of this study can be used to form mechanisms to contain the coronavirus infection and stabilize socio-economic at macroeconomic and regional level and restore the economy of territorial systems, depending on the depth of the spread of infection and the level of economic damage caused.

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International Interdisciplinary Conference "Mathematics. Computing. Education"