{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T18:03:04Z","timestamp":1760551384926,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T00:00:00Z","timestamp":1614297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Air quality modelling that relates meteorological, car traffic, and pollution data is a fundamental problem, approached in several different ways in the recent literature. In particular, a set of such data sampled at a specific location and during a specific period of time can be seen as a multivariate time series, and modelling the values of the pollutant concentrations can be seen as a multivariate temporal regression problem. In this paper, we propose a new method for symbolic multivariate temporal regression, and we apply it to several data sets that contain real air quality data from the city of Wroc\u0142aw (Poland). Our experiments show that our approach is superior to classical, especially symbolic, ones, both in statistical performances and the interpretability of the results.<\/jats:p>","DOI":"10.3390\/a14030076","type":"journal-article","created":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T06:47:20Z","timestamp":1614322040000},"page":"76","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Feature and Language Selection in Temporal Symbolic Regression for Interpretable Air Quality Modelling"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9312-1175","authenticated-orcid":false,"given":"Estrella","family":"Lucena-S\u00e1nchez","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Ferrara, 44121 Ferrara, Italy"},{"name":"Department of Physics, Informatics, and Mathematics, University of Modena and Reggio Emilia, 41121 Modena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9221-879X","authenticated-orcid":false,"given":"Guido","family":"Sciavicco","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Ferrara, 44121 Ferrara, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9260-102X","authenticated-orcid":false,"given":"Ionel Eduard","family":"Stan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Ferrara, 44121 Ferrara, Italy"},{"name":"Department of Mathematical, Physical, and Computer Sciences, University of Parma, 43121 Parma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Holnicki, P., Tainio, M., Ka\u0142uszko, A., and Nahorski, Z. (2017). Burden of mortality and disease attributable to multiple air pollutants in Warsaw, Poland. Int. J. Environ. Res. Public Health, 14.","DOI":"10.3390\/ijerph14111359"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0013-9351(89)80012-X","article-title":"Lung function and chronic exposure to air pollution: A cross-sectional analysis of NHANES II","volume":"50","author":"Schwartz","year":"1989","journal-title":"Environ. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1467-985X.2006.00410.x","article-title":"Model choice in time series studies of air pollution and mortality","volume":"169","author":"Peng","year":"2006","journal-title":"J. R. Stat. Soc. Ser. A Stat. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1289\/ehp.00108347","article-title":"Associations between air pollution and mortality in Phoenix, 1995\u20131997","volume":"108","author":"Mar","year":"2000","journal-title":"Environ. Health Perspect."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.envint.2018.08.025","article-title":"The Australian Child Health and Air Pollution Study (ACHAPS): A national population-based cross-sectional study of long-term exposure to outdoor air pollution, asthma, and lung function","volume":"120","author":"Knibbs","year":"2018","journal-title":"Environ. Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1080\/10473289.2000.10464167","article-title":"Effect of the fine fraction of particulate matter versus the coarse mass and other pollutants on daily mortality in Santiago, Chile","volume":"50","author":"Cifuentes","year":"2000","journal-title":"J. Air Waste Manag. Assoc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.ecoinf.2018.12.001","article-title":"Spatio-temporal learning in predicting ambient particulate matter concentration by multi-layer perceptron","volume":"49","author":"Chianese","year":"2019","journal-title":"Ecol. Inform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1016\/j.scitotenv.2017.11.291","article-title":"PM10 concentration forecasting in the metropolitan area of Oviedo (Northern Spain) using models based on SVM, MLP, VARMA and ARIMA: A case study","volume":"621","author":"Nieto","year":"2018","journal-title":"Sci. Total Environ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1080\/10473289.2005.10464708","article-title":"Assessing spatial variability of ambient nitrogen dioxide in Montreal, Canada, with a land-use regression model","volume":"55","author":"Gilbert","year":"2005","journal-title":"J. Air Waste Manag. Assoc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2422","DOI":"10.1021\/es0606780","article-title":"Application of land use regression to estimate long-term concentrations of traffic-related nitrogen oxides and fine particulate matter","volume":"41","author":"Henderson","year":"2007","journal-title":"Environ. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7561","DOI":"10.1016\/j.atmosenv.2008.05.057","article-title":"A review of land-use regression models to assess spatial variation of outdoor air pollution","volume":"42","author":"Hoek","year":"2008","journal-title":"Atmos. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lucena-S\u00e1nchez, E., Jim\u00e9nez, F., Sciavicco, G., and Kaminska, J. (2020, January 27\u201329). Simple Versus Composed Temporal Lag Regression with Feature Selection, with an Application to Air Quality Modeling. Proceedings of the Conference on Evolving and Adaptive Intelligent Systems, Bari, Italy.","DOI":"10.1109\/EAIS48028.2020.9122765"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.scitotenv.2018.09.196","article-title":"A random forest partition model for predicting NO2 concentrations from traffic flow and meteorological conditions","volume":"651","author":"Kaminska","year":"2015","journal-title":"Sci. Total Environ."},{"key":"ref_14","unstructured":"Breiman, L., Friedman, J., Olshen, R., and Stone, C. (1984). Classification and Regression Trees, Chapman and Hall\/CRC."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/BF00116835","article-title":"The CN2 Induction Algorithm","volume":"3","author":"Clark","year":"1989","journal-title":"Mach. Learn."},{"key":"ref_16","unstructured":"Sciavicco, G., and Stan, I. (2020, January 23\u201325). Knowledge Extraction with Interval Temporal Logic Decision Trees. Proceedings of the 27th International Symposium on Temporal Representation and Reasoning, Bozen-Bolzano, Italy."},{"key":"ref_17","unstructured":"Lucena-S\u00e1nchez, E., Sciavicco, G., and Stan, I. (2020, January 25). Symbolic Learning with Interval Temporal Logic: The Case of Regression. Proceedings of the 2nd Workshop on Artificial Intelligence and Formal Verification, Logic, Automata, and Synthesis , Bozen-Bolzano, Italy."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1145\/115234.115351","article-title":"A Propositional Modal Logic of Time Intervals","volume":"38","author":"Halpern","year":"1991","journal-title":"J. ACM"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1145\/182.358434","article-title":"Maintaining Knowledge about Temporal Intervals","volume":"26","author":"Allen","year":"1983","journal-title":"Commun. ACM"},{"key":"ref_20","unstructured":"Witten, I.H., Frank, E., and Hall, M.A. (2017). Data Mining: Practical Machine Learning Tools and Techniques, Morgan Kaufmann. [4th ed.]."},{"key":"ref_21","unstructured":"John, G. (1995, January 20\u201321). Robust Decision Trees: Removing Outliers from Databases. Proceedings of the 1st International Conference on Knowledge Discovery and Data Mining, Montreal, QC, Canada."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Maronna, R., Martin, D., and Yohai, V. (2006). Robust Statistics: Theory and Methods, Wiley.","DOI":"10.1002\/0470010940"},{"key":"ref_23","unstructured":"Box, G., Jenkins, G., Reinsel, G., and Ljung, G. (2016). Time Series Analysis: Forecasting and Control, Wiley."},{"key":"ref_24","first-page":"1157","article-title":"An introduction to variable and feature selection","volume":"3","author":"Guyon","year":"2003","journal-title":"J. Mach. Learn. Res."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Siedlecki, W., and Sklansky, J. (1993). A note on genetic algorithms for large-scale feature selection. Handbook of Pattern Recognition and Computer Vision, World Scientific.","DOI":"10.1142\/9789814343138_0005"},{"key":"ref_26","unstructured":"Vafaie, H., and Jong, K.D. (1992, January 10\u201313). Genetic algorithms as a tool for feature selection in machine learning. Proceedings of the 4th Conference on Tools with Artificial Intelligence, Arlington, VA, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.knosys.2009.02.006","article-title":"A filter model for feature subset selection based on genetic algorithm","volume":"22","author":"ElAlamil","year":"2009","journal-title":"Knowl. Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Anirudha, R., Kannan, R., and Patil, N. (2014, January 15\u201317). Genetic algorithm based wrapper feature selection on hybrid prediction model for analysis of high dimensional data. Proceedings of the 9th International Conference on Industrial and Information Systems, Gwalior, India.","DOI":"10.1109\/ICIINFS.2014.7036522"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1016\/j.patrec.2007.05.011","article-title":"A hybrid genetic algorithm for feature selection wrapper based on mutual information","volume":"28","author":"Huang","year":"2007","journal-title":"Pattern Recognit. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/5254.671091","article-title":"Feature subset selection using a genetic algorithm","volume":"13","author":"Yang","year":"1998","journal-title":"IEEE Intell. Syst. Their Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.neucom.2016.12.045","article-title":"Multi-objective evolutionary feature selection for online sales forecasting","volume":"234","author":"Sciavicco","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/TEVC.2013.2290086","article-title":"A survey of multiobjective evolutionary algorithms for data mining: Part I","volume":"18","author":"Mukhopadhyay","year":"2014","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"131","DOI":"10.3233\/IDA-1997-1302","article-title":"Feature Selection for Classification","volume":"1","author":"Dash","year":"1997","journal-title":"Intell. Data Anal."},{"key":"ref_34","unstructured":"Ishibuchi, H., and Nakashima, T. (2000, January 8\u201312). Multi-objective pattern and feature selection by a genetic algorithm. Proceedings of the Genetic and Evolutionary Computation Conference, Las Vegas, NV, USA."},{"key":"ref_35","first-page":"1","article-title":"A multi-objective genetic algorithm approach to feature selection in neural and fuzzy modeling","volume":"3","author":"Emmanouilidis","year":"2001","journal-title":"Evol. Optim."},{"key":"ref_36","unstructured":"Liu, J., and Iba, H. (2002, January 12\u201317). Selecting informative genes using a multiobjective evolutionary algorithm. Proceedings of the Congress on Evolutionary Computation, Honolulu, HI, USA."},{"key":"ref_37","unstructured":"Pappa, G.L., Freitas, A.A., and Kaestner, C. (2002, January 11\u201314). Attribute selection with a multi-objective genetic algorithm. Proceedings of the 16th Brazilian Symposium on Artificial Intelligence, Porto de Galinhas\/Recife, Brazil."},{"key":"ref_38","unstructured":"Shi, S., Suganthan, P., and Deb, K. (2004, January 7\u20138). Multiclass protein fold recognition using multiobjective evolutionary algorithms. Proceedings of the Symposium on Computational Intelligence in Bioinformatics and Computational Biology, La Jolla, CA, USA."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Collette, Y., and Siarry, P. (2004). Multiobjective Optimization: Principles and Case Studies, Springer.","DOI":"10.1007\/978-3-662-08883-8"},{"key":"ref_40","unstructured":"Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms, Wiley."},{"key":"ref_41","first-page":"760","article-title":"JMetal: A Java Framework for Multi-Objective Optimization","volume":"42","author":"Durillo","year":"2011","journal-title":"Av. Eng. Softw."},{"key":"ref_42","unstructured":"Johnson, R.A., and Bhattacharyya, G.K. (2019). Statistics: Principles and Methods, Wiley. [8th ed.]."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013). An Introduction to Statistical Learning: With Applications in R, Springer.","DOI":"10.1007\/978-1-4614-7138-7"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Gilpin, L.H., Bau, D., Yuan, B.Z., Bajwa, A., Specter, M., and Kagal, L. (2018, January 1\u20133). Explaining Explanations: An Overview of Interpretability of Machine Learning. Proceedings of the IEEE 5th International Conference on Data Science and Advanced Analytics, Turin, Italy.","DOI":"10.1109\/DSAA.2018.00018"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/3\/76\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:29:15Z","timestamp":1760160555000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/3\/76"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,26]]},"references-count":44,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["a14030076"],"URL":"https:\/\/doi.org\/10.3390\/a14030076","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2021,2,26]]}}}