{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T04:45:50Z","timestamp":1780634750984,"version":"3.54.1"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:00:00Z","timestamp":1687910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"crossref","award":["2021\/12706-1"],"award-info":[{"award-number":["2021\/12706-1"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Evol. Learn. Optim."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>\n            Symbolic Regression searches for a parametric model with the optimal value of the parameters that best fits a set of samples to a measured target. The desired solution has a balance between accuracy and interpretability. Commonly, there is no constraint in the way the functions are composed in the expression or where the numerical parameters are placed, which can potentially lead to expressions that require a nonlinear optimization to find the optimal parameters. The representation called Interaction-Transformation alleviates this problem by describing expressions as a linear regression of the composition of functions applied to the interaction of the variables. One advantage is that any model that follows this representation is linear in its parameters, allowing an efficient computation. More recently, this representation was extended by applying a univariate function to the rational function of two Interaction-Transformation expressions, called\n            <jats:italic>Transformation-Interaction-Rational<\/jats:italic>\n            (\n            <jats:italic>TIR<\/jats:italic>\n            ). The use of this representation was shown to be competitive with the current literature of Symbolic Regression. In this article, we make a detailed analysis of these results using the SRBench benchmark. For this purpose, we split the datasets into different categories to understand the algorithm behavior in different settings. We also test the use of nonlinear optimization to adjust the numerical parameters instead of Ordinary Least Squares. We find through the experiments that TIR has some difficulties handling high-dimensional and noisy datasets, especially when most of the variables are composed of random noise. These results point to new directions for improving the evolutionary search of TIR expressions.\n          <\/jats:p>","DOI":"10.1145\/3597312","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T12:03:51Z","timestamp":1684152231000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Transformation-Interaction-Rational Representation for Symbolic Regression: A Detailed Analysis of SRBench Results"],"prefix":"10.1145","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2741-8736","authenticated-orcid":false,"given":"Fabr\u00edcio Olivetti","family":"De Fran\u00e7a","sequence":"first","affiliation":[{"name":"Universidade Federal do ABC, Center for Mathematics, Computing and Cognition, Heuristics, Analysis and Learning Laboratory (HAL), Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2023,6,28]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/cec48606.2020.9185521"},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/cec.2018.8477951"},{"key":"e_1_3_2_4_1","first-page":"108","volume-title":"ECML PKDD Workshop: Languages for Data Mining and Machine Learning","author":"Buitinck Lars","year":"2013","unstructured":"Lars Buitinck, Gilles Louppe, Mathieu Blondel, Fabian Pedregosa, Andreas Mueller, Olivier Grisel, Vlad Niculae, Peter Prettenhofer, Alexandre Gramfort, Jaques Grobler, Robert Layton, Jake VanderPlas, Arnaud Joly, Brian Holt, and Ga\u00ebl Varoquaux. 2013. API design for machine learning software: Experiences from the scikit-learn project. In ECML PKDD Workshop: Languages for Data Mining and Machine Learning. 108\u2013122."},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3377929.3398099"},{"key":"e_1_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1162\/evco_a_00285"},{"key":"e_1_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3512290.3528695"},{"key":"e_1_3_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2020.10.062"},{"key":"e_1_3_2_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347963"},{"key":"e_1_3_2_10_1","doi-asserted-by":"publisher","DOI":"10.1017\/9781139161879"},{"key":"e_1_3_2_11_1","unstructured":"Alexandre Goldsztejn. 2008. Modal intervals revisited part 1: A generalized interval natural extension. 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