{"id":2931,"date":"2023-10-09T15:38:24","date_gmt":"2023-10-09T10:38:24","guid":{"rendered":"http:\/\/vestnik.polytech.tj\/?p=2931"},"modified":"2023-10-09T15:40:30","modified_gmt":"2023-10-09T10:40:30","slug":"simulation-modelling-methods-in-machine-learning-algo-rithms","status":"publish","type":"post","link":"https:\/\/vestnik.polytech.tj\/?p=2931&lang=en","title":{"rendered":"SIMULATION MODELLING METHODS IN MACHINE LEARNING ALGO-RITHMS"},"content":{"rendered":"

<\/p>\n

\n
\n
<\/p>\n
\n
\n
<\/p>\n
\n
\n

Authors<\/span><\/strong><\/p>\n

          <\/strong>Nizamitdinov A.I<\/strong>. <\/strong>— <\/strong>Doctor of philosophy<\/em> (PhD), Senior Lecturer<\/em>,<\/em> Department of Digital <\/em>Economy<\/em> Polytechnic Institute of Tajik Technical University, Khujand, Republic of Tajikistan, <\/em>ahlidin@gmail.com<\/a><\/em><\/p>\n

Annotation<\/strong><\/span><\/p>\n

      <\/em>The paper discusses machine learning algorithms, in particular non-parametric models of multivariate regression analysis. In particular, models such as generalized additive regression models, penalty generalized additive models, and thin-plate splines are considered. One of the problems in nonlinear fitting problems is the comparison and selection of the optimal method for approximating the data. Approximation with different types of data requires a more detailed consideration of model selection. The most difficult in these problems is to select the model with the smallest error metric. For the analysis, 5 different functions from previously published studies were selected and regression models were used to estimate them. The data are multivariate values calculated from the functions and random components from different distribution functions added to the function values. These data were subsequently used for fitting with non-parametric regression models. Using a simulation method, data were selected from each function with 100 values and 100 repetitions. The results of the function approximation performed are evaluated using the log_10( MSE) mean square error. The results of the estimation criterion are compared using box-plots to determine the most appropriate technique.<\/em><\/p>\n

Key words<\/em><\/strong><\/span><\/p>\n

  thin-plate splines, generalized additive models, penalized generalized additive models, simulation study.<\/em><\/p>\n<\/div>\n<\/div>\n

<\/div>\n<\/div>\n<\/div>\n

<\/p>\n

\n
\n
<\/p>\n
\n
\n\n\n\n
\n

Language<\/p>\n

english<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

<\/p>\n

\n
\n\n\n\n
\n

Type<\/p>\n

technical<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

<\/p>\n

\n
\n\n\n\n
\n

Year<\/p>\n

2022<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

<\/p>\n

\n
\n\n\n\n
\n

Page<\/p>\n

21<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

<\/div>\n<\/div>\n<\/div>\n

<\/div>\n<\/div>\n<\/div>\n

<\/p>\n

\n
\n
<\/p>\n
\n
\n
<\/p>\n
\n
\n

References<\/strong><\/span><\/p>\n

    \n
  1. \n
      \n
    1. Smith, M. and Kohn, R. <\/em>—<\/em> A Bayesian approach to nonparametric bivariate regression<\/em>.<\/em> Journal of the American Statistical Association, <\/em>2007, <\/em>92, 1522-1535.<\/em><\/li>\n
    2. Wood, S.N. <\/em>— <\/em>Thin plate regression splines<\/em>.<\/em> Journal of the Royal Statistical Society B, <\/em>2003, <\/em>65, 95-114.<\/em><\/li>\n
    3. Fan, J. and Gijbels, I. Local Polynomial Modelling and Its Applications<\/em>.<\/em> 1996, <\/em>London : Chapman and Hall.<\/em><\/li>\n
    4. Hastie, T. and Tibshirani, R. Generalized additive models, <\/em>1990, <\/em>London: Chapman and Hall.<\/em><\/li>\n
    5. Duchon, J. Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: Construction Theory of Functions of Several Variables. 1977.<\/em> Berlin: Springer.<\/em><\/li>\n
    6. Eilers P.H.C., and Marx B.D.<\/em> —<\/em> Flexible smoothing using B-splines and penalized likelihood (with comments and rejoinders), Statistical Science, 1996<\/em>, <\/em>11(2), 89-121.<\/em><\/li>\n
    7. Eilers P.H.C., and Marx B.D.<\/em> —<\/em> Direct generalized additive modeling with penalized likelihood, Computational Statistics and Data Analysis, 1998<\/em>, <\/em>28, 193-209.<\/em><\/li>\n
    8. Wood, S.N. <\/em>— <\/em>Mgcv: GAMs and generalized ridge regression in R, R News, 2001<\/em>,<\/em>1, 20-25.<\/em><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

      <\/div>\n<\/div>\n<\/div>\n

      <\/div>\n<\/div>\n<\/div>\n

      <\/p>\n

      \n
      \n
      <\/p>\n
      \n
      \n
      <\/p>\n
      \n
      \n

      Publication date<\/span><\/strong><\/h2>\n

      09\/22\/2023<\/p>\n<\/div>\n<\/div>\n

      <\/div>\n<\/div>\n<\/div>\n

      <\/div>\n<\/div>\n<\/div>\n

      <\/p>\n","protected":false},"excerpt":{"rendered":"

      Authors           Nizamitdinov A.I. — Doctor of philosophy (PhD), Senior Lecturer, Department of Digital Economy Polytechnic Institute of Tajik Technical University, Khujand, Republic of Tajikistan, ahlidin@gmail.com Annotation       The paper discusses machine learning algorithms, in particular non-parametric models of multivariate regression analysis. In particular, models such as generalized additive regression models, penalty generalized additive models, and thin-plate splines are considered. One of the problems in nonlinear fitting problems is the comparison and selection of the optimal method for approximating the data. Approximation with different…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[161],"tags":[384],"class_list":["post-2931","post","type-post","status-publish","format-standard","hentry","category-bulletin-of-pittu-2022","tag-bulletin-of-pittu-2022-3"],"acf":[],"featured_image_src":null,"author_info":{"display_name":"ilhomjonqodirov02","author_link":"https:\/\/vestnik.polytech.tj\/?author=1"},"_links":{"self":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts\/2931","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2931"}],"version-history":[{"count":3,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts\/2931\/revisions"}],"predecessor-version":[{"id":2934,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=\/wp\/v2\/posts\/2931\/revisions\/2934"}],"wp:attachment":[{"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2931"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2931"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vestnik.polytech.tj\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2931"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}