Discovering interpretable structure in longitudinal predictors via coefficient trees
We consider the regression setting in which the response variable is not longitudinal (i.e., it is observed once for each case), but it is assumed to depend functionally on a set of predictors that are observed longitudinally, which is a specific form of functional predictors. In this situation, we...
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| Published in: | Advances in data analysis and classification Vol. 18; no. 4; pp. 911 - 951 |
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| Format: | Journal Article |
| Language: | English |
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01.12.2024
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| ISSN: | 1862-5347, 1862-5355 |
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| Abstract | We consider the regression setting in which the response variable is not longitudinal (i.e., it is observed once for each case), but it is assumed to depend functionally on a set of predictors that are observed longitudinally, which is a specific form of functional predictors. In this situation, we often expect that the same predictor observed at nearby time points are more likely to be associated with the response in the same way. In such situations, we can exploit those aspects and discover groups of predictors that share the same (or similar) coefficient according to their temporal proximity. We propose a new algorithm called coefficient tree regression for data in which the non-longitudinal response depends on longitudinal predictors to efficiently discover the underlying temporal characteristics of the data. The approach results in a simple and highly interpretable tree structure from which the hierarchical relationships between groups of predictors that affect the response in a similar manner based on their temporal proximity can be observed, and we demonstrate with a real example that it can provide a clear and concise interpretation of the data. In numerical comparisons over a variety of examples, we show that our approach achieves substantially better predictive accuracy than existing competitors, most likely due to its inherent form of dimensionality reduction that is automatically discovered when fitting the model, in addition to having interpretability advantages and lower computational expense. |
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| AbstractList | We consider the regression setting in which the response variable is not longitudinal (i.e., it is observed once for each case), but it is assumed to depend functionally on a set of predictors that are observed longitudinally, which is a specific form of functional predictors. In this situation, we often expect that the same predictor observed at nearby time points are more likely to be associated with the response in the same way. In such situations, we can exploit those aspects and discover groups of predictors that share the same (or similar) coefficient according to their temporal proximity. We propose a new algorithm called coefficient tree regression for data in which the non-longitudinal response depends on longitudinal predictors to efficiently discover the underlying temporal characteristics of the data. The approach results in a simple and highly interpretable tree structure from which the hierarchical relationships between groups of predictors that affect the response in a similar manner based on their temporal proximity can be observed, and we demonstrate with a real example that it can provide a clear and concise interpretation of the data. In numerical comparisons over a variety of examples, we show that our approach achieves substantially better predictive accuracy than existing competitors, most likely due to its inherent form of dimensionality reduction that is automatically discovered when fitting the model, in addition to having interpretability advantages and lower computational expense. |
| Author | Malthouse, Edward C. Apley, Daniel W. Sürer, Özge |
| Author_xml | – sequence: 1 givenname: Özge orcidid: 0000-0003-4854-9759 surname: Sürer fullname: Sürer, Özge email: surero@miamioh.edu organization: Department of Information Systems and Analytics, Miami University – sequence: 2 givenname: Daniel W. surname: Apley fullname: Apley, Daniel W. organization: Industrial Engineering and Management Sciences, Northwestern University – sequence: 3 givenname: Edward C. surname: Malthouse fullname: Malthouse, Edward C. organization: Industrial Engineering and Management Sciences, Northwestern University |
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| Cites_doi | 10.1080/21670811.2021.1948347 10.1145/568518.568520 10.1109/TPAMI.2013.72 10.1007/s10618-010-0179-5 10.1007/s10994-022-06179-8 10.1145/882082.882086 10.1007/3-540-44794-6_10 10.1145/3178876.3186162 10.4310/SII.2010.v3.n4.a13 10.1145/1557019.1557122 10.1007/s10618-014-0349-y 10.1145/2020408.2020587 10.1007/s11747-019-00710-5 10.1093/bioinformatics/btm125 10.1061/(ASCE)CO.1943-7862.0001047 10.1038/s42256-019-0048-x 10.1080/01621459.2014.892882 10.1016/j.eswa.2022.117423 10.4310/SII.2009.v2.n3.a10 10.1002/cem.2849 10.1007/s10994-021-06091-7 10.1111/biom.12300 10.1111/j.1467-9868.2005.00532.x 10.1002/sam.11569 10.24432/C5XS4Q 10.1016/j.dss.2019.113141 10.18637/jss.v033.i01 10.1016/j.jmva.2004.02.012 10.1016/j.cor.2023.106152 10.1007/3-540-70659-3_2 10.1111/j.1467-9868.2005.00490.x 10.1214/07-AOS584 10.1007/s10618-015-0425-y 10.1109/ICDM.2006.49 10.1145/3331184.3331247 10.1093/biomet/asp020 10.1002/sam.11534 10.32614/CRAN.package.TSrepr 10.1146/annurev-statistics-041715-033624 10.1111/j.1541-0420.2007.00843.x 10.1007/s10618-007-0064-z 10.24432/C58C86 |
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