{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:40:22Z","timestamp":1760128822945,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,7]],"date-time":"2023-07-07T00:00:00Z","timestamp":1688688000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"USDA","award":["USDA 2020-67021-32855","USDA-020-67021-32855","IIS-1838207","CNS 1901218","OIA-2134901"],"award-info":[{"award-number":["USDA 2020-67021-32855","USDA-020-67021-32855","IIS-1838207","CNS 1901218","OIA-2134901"]}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["USDA 2020-67021-32855","USDA-020-67021-32855","IIS-1838207","CNS 1901218","OIA-2134901"],"award-info":[{"award-number":["USDA 2020-67021-32855","USDA-020-67021-32855","IIS-1838207","CNS 1901218","OIA-2134901"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Path-specific effect analysis is a powerful tool in causal inference. This paper provides a definition of causal counterfactual path-specific importance score for the structural causal model (SCM). Different from existing path-specific effect definitions, which focus on the population level, the score defined in this paper can quantify the impact of a decision variable on an outcome variable along a specific pathway at the individual level. Moreover, the score has many desirable properties, including following the chain rule and being consistent. Finally, this paper presents an algorithm that can leverage these properties and find the k-most important paths with the highest importance scores in a causal graph effectively.<\/jats:p>","DOI":"10.3390\/computation11070133","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:35:21Z","timestamp":1688949321000},"page":"133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantifying Causal Path-Specific Importance in Structural Causal Model"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0418-4877","authenticated-orcid":false,"given":"Xiaoxiao","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of California, Davis, CA 95616, USA"}]},{"given":"Minda","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}]},{"given":"Fanyu","family":"Meng","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Davis, CA 95616, USA"}]},{"given":"Xin","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Davis, CA 95616, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2493-1366","authenticated-orcid":false,"given":"Zhaodan","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA"}]},{"given":"Xin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1037\/0022-3514.51.6.1173","article-title":"The moderator\u2013mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations","volume":"51","author":"Baron","year":"1986","journal-title":"J. Personal. Soc. Psychol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1126\/science.1105809","article-title":"Causal protein-signaling networks derived from multiparameter single-cell data","volume":"308","author":"Sachs","year":"2005","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1111\/ecoj.12593","article-title":"Identification and estimation of dynamic causal effects in macroeconomics using external instruments","volume":"128","author":"Stock","year":"2018","journal-title":"Econ. J."},{"key":"ref_4","unstructured":"Chiappa, S. (February, January 27). Path-specific counterfactual fairness. Proceedings of the AAAI Conference on Artificial Intelligence, Honolulu, HI, USA."},{"key":"ref_5","first-page":"3399","article-title":"PC-fairness: A unified framework for measuring causality-based fairness","volume":"32","author":"Wu","year":"2019","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, X., Meng, F., Liu, X., Kong, Z., and Chen, X. (2023). Causal explanation for reinforcement learning: Quantifying state and temporal importance. Appl. Intell.","DOI":"10.1007\/s10489-023-04649-7"},{"key":"ref_7","unstructured":"Chikahara, Y., Sakaue, S., Fujino, A., and Kashima, H. (2021, January 13\u201315). Learning individually fair classifier with path-specific causal-effect constraint. Proceedings of the International Conference on Artificial Intelligence and Statistics, PMLR, Online."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, H., Geng, Z., Sun, X., Yu, Y., and Xue, F. (2020). A novel path-specific effect statistic for identifying the differential specific paths in systems epidemiology. BMC Genet., 21.","DOI":"10.1186\/s12863-020-00876-w"},{"key":"ref_9","unstructured":"Avin, C., Shpitser, I., and Pearl, J. (August, January 30). Identifiability of Path-Specific Effects. Proceedings of the 19th International Joint Conference on Artificial Intelligence, Edinburgh, Scotland."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pearl, J. (2009). Causality; Causality: Models, Reasoning, and Inference, Cambridge University Press.","DOI":"10.1017\/CBO9780511803161"},{"key":"ref_11","unstructured":"Glymour, M., Pearl, J., and Jewell, N.P. (2016). Causal Inference in Statistics: A Primer, John Wiley & Sons."},{"key":"ref_12","unstructured":"Rothenh\u00e4usler, D., and Yu, B. (2019). Incremental causal effects. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3070","DOI":"10.1086\/702172","article-title":"Marginal treatment effects from a propensity score perspective","volume":"127","author":"Zhou","year":"2019","journal-title":"J. Political Econ."},{"key":"ref_14","unstructured":"Zhou, X., and Opacic, A. (2022). Marginal Interventional Effects. arXiv."},{"key":"ref_15","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., and Stein, C. (2022). Introduction to Algorithms, MIT Press."},{"key":"ref_16","unstructured":"Jungnickel, D., and Jungnickel, D. (2005). Graphs, Networks and Algorithms, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yen, S.H., Du, D.H.C., and Ghanta, S. (1989, January 25\u201329). Efficient algorithms for extracting the k most critical paths in timing analysis. Proceedings of the 26th ACM\/IEEE Design Automation Conference, Las Vegas, NV, USA.","DOI":"10.1145\/74382.74497"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1001\/jama.1994.03510350050036","article-title":"Independent risk factors for atrial fibrillation in a population-based cohort: The Framingham Heart Study","volume":"271","author":"Benjamin","year":"1994","journal-title":"JAMA"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"20150027","DOI":"10.1515\/jci-2015-0027","article-title":"Interventional approach for path-specific effects","volume":"5","author":"Lin","year":"2017","journal-title":"J. Causal Inference"},{"key":"ref_20","unstructured":"Malinsky, D., Shpitser, I., and Richardson, T. (2019, January 16\u201318). A potential outcomes calculus for identifying conditional path-specific effects. Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, Naha, Japan."},{"key":"ref_21","unstructured":"Zhang, J., and Bareinboim, E. (2018, January 6\u201310). Non-parametric path analysis in structural causal models. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, Monterey, CA, USA."},{"key":"ref_22","unstructured":"Gong, H., and Zhu, K. (2021). Path-specific Effects Based on Information Accounts of Causality. arXiv."},{"key":"ref_23","unstructured":"Janzing, D., Bl\u00f6baum, P., Minorics, L., and Faller, P. (2020). Quantifying causal contributions via structure preserving interventions. arXiv."},{"key":"ref_24","unstructured":"Wang, J., Wiens, J., and Lundberg, S. (2021, January 25\u201327). Shapley flow: A graph-based approach to interpreting model predictions. Proceedings of the International Conference on Artificial Intelligence and Statistics, Valencia, Spain."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2324","DOI":"10.1214\/13-AOS1145","article-title":"Quantifying causal influences","volume":"41","author":"Janzing","year":"2013","journal-title":"Ann. Statist."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bartle, R. (1995). The Elements of Integration and Lebesgue Measure, Wiley Classics Library; Wiley.","DOI":"10.1002\/9781118164471"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/7\/133\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:08:09Z","timestamp":1760126889000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/7\/133"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,7]]},"references-count":26,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["computation11070133"],"URL":"https:\/\/doi.org\/10.3390\/computation11070133","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2023,7,7]]}}}