{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T10:08:36Z","timestamp":1777543716515,"version":"3.51.4"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:00:00Z","timestamp":1559260800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:00:00Z","timestamp":1559260800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100006192","name":"Advanced Scientific Computing Research","doi-asserted-by":"publisher","award":["DE-SC-0011077"],"award-info":[{"award-number":["DE-SC-0011077"]}],"id":[{"id":"10.13039\/100006192","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ben L. Fryrear Fellowship in Computational Science"},{"DOI":"10.13039\/100006502","name":"Defense Sciences Office, DARPA","doi-asserted-by":"publisher","award":["DARPA-BAA-15-13"],"award-info":[{"award-number":["DARPA-BAA-15-13"]}],"id":[{"id":"10.13039\/100006502","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s11222-019-09876-y","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T13:02:32Z","timestamp":1559307752000},"page":"237-253","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Inverse regression for ridge recovery: a data-driven approach for parameter reduction in computer experiments"],"prefix":"10.1007","volume":"30","author":[{"given":"Andrew","family":"Glaws","sequence":"first","affiliation":[]},{"given":"Paul G.","family":"Constantine","sequence":"additional","affiliation":[]},{"given":"R. Dennis","family":"Cook","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,5,31]]},"reference":[{"key":"9876_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21506-8","volume-title":"Understanding Analysis","author":"S Abbott","year":"2001","unstructured":"Abbott, S.: Understanding Analysis, 2nd edn. Springer, New York (2001)","edition":"2"},{"issue":"1906","key":"9876_CR2","doi-asserted-by":"crossref","first-page":"4385","DOI":"10.1098\/rsta.2009.0110","volume":"367","author":"KP Adragni","year":"2009","unstructured":"Adragni, K.P., Cook, R.D.: Sufficient dimension reduction and prediction in regression. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 367(1906), 4385\u20134405 (2009)","journal-title":"Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"issue":"8","key":"9876_CR3","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.2514\/1.J050247","volume":"48","author":"D Allaire","year":"2010","unstructured":"Allaire, D., Willcox, K.: Surrogate modeling for uncertainty assessment with application to aviation environmental system models. AIAA J. 48(8), 1791\u20131803 (2010)","journal-title":"AIAA J."},{"key":"9876_CR4","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/978-3-642-32677-6_10","volume-title":"Uncertainty Quantification in Scientific Computing","author":"P Challenor","year":"2012","unstructured":"Challenor, P.: Using emulators to estimate uncertainty in complex models. In: Dienstfrey, A.M., Boisvert, R.F. (eds.) Uncertainty Quantification in Scientific Computing, pp. 151\u2013164. Springer, Berlin, Heidelberg (2012)"},{"issue":"3","key":"9876_CR5","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1111\/1467-9574.00056","volume":"51","author":"JT Chang","year":"1997","unstructured":"Chang, J.T., Pollard, D.: Conditioning as disintegration. Stat. Neerl. 51(3), 287\u2013317 (1997)","journal-title":"Stat. Neerl."},{"issue":"2","key":"9876_CR6","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s00365-011-9147-6","volume":"35","author":"A Cohen","year":"2012","unstructured":"Cohen, A., Daubechies, I., DeVore, R., Kerkyacharian, G., Picard, D.: Capturing ridge functions in high dimensions from point queries. Constr. Approx. 35(2), 225\u2013243 (2012)","journal-title":"Constr. Approx."},{"key":"9876_CR7","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611973860","volume-title":"Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies","author":"PG Constantine","year":"2015","unstructured":"Constantine, P.G.: Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies. SIAM, Philadelphia (2015)"},{"key":"9876_CR8","doi-asserted-by":"crossref","unstructured":"Constantine, P.G., Eftekhari, A., Wakin, M.B.: Computing active subspaces efficiently with gradient sketching. In: 2015 IEEE 6th International Workshop on Computational Advances in Multi-sensor Adaptive Processing (CAMSAP), pp. 353\u2013356. (2015)","DOI":"10.1109\/CAMSAP.2015.7383809"},{"key":"9876_CR9","doi-asserted-by":"crossref","first-page":"79","DOI":"10.21105\/joss.00079","volume":"1","author":"PG Constantine","year":"2016","unstructured":"Constantine, P.G., Howard, R., Glaws, A., Grey, Z., Diaz, P., Fletcher, L.: Python active-subspaces utility library. J. Open Source Softw. 1, 79 (2016)","journal-title":"J. Open Source Softw."},{"key":"9876_CR10","unstructured":"Constantine, P.G., del Rosario, Z., Iaccarino, G.: Data-driven dimensional analysis: algorithms for unique and relevant dimensionless groups. (2017a). arXiv:1708.04303"},{"key":"9876_CR11","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.cma.2017.07.038","volume":"326","author":"PG Constantine","year":"2017","unstructured":"Constantine, P.G., Eftekhari, A., Hokanson, J., Ward, R.: A near-stationary subspace for ridge approximation. Comput. Methods Appl. Mech. Eng. 326, 402\u2013421 (2017b)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"425","key":"9876_CR12","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1080\/01621459.1994.10476459","volume":"89","author":"RD Cook","year":"1994","unstructured":"Cook, R.D.: On the interpretation of regression plots. J. Am. Stat. Assoc. 89(425), 177\u2013189 (1994a)","journal-title":"J. Am. Stat. Assoc."},{"key":"9876_CR13","unstructured":"Cook, R.D.: Using dimension-reduction subspaces to identify important inputs in models of physical systems. In: Proceedings of the Section on Physical and Engineering Sciences, pp. 18\u201325. American Statistical Association, Alexandria, VA (1994b)"},{"issue":"435","key":"9876_CR14","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1080\/01621459.1996.10476968","volume":"91","author":"RD Cook","year":"1996","unstructured":"Cook, R.D.: Graphics for regressions with a binary response. J. Am. Stat. Assoc. 91(435), 983\u2013992 (1996)","journal-title":"J. Am. Stat. Assoc."},{"key":"9876_CR15","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316931","volume-title":"Regression Graphics: Ideas for Studying Regression Through Graphics","author":"RD Cook","year":"1998","unstructured":"Cook, R.D.: Regression Graphics: Ideas for Studying Regression Through Graphics. Wiley, New York (1998)"},{"issue":"9\u201310","key":"9876_CR16","doi-asserted-by":"crossref","first-page":"2109","DOI":"10.1080\/03610920008832598","volume":"29","author":"RD Cook","year":"2000","unstructured":"Cook, R.D.: SAVE: a method for dimension reduction and graphics in regression. Commun. Stat. Theory Methods 29(9\u201310), 2109\u20132121 (2000)","journal-title":"Commun. Stat. Theory Methods"},{"issue":"485","key":"9876_CR17","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1198\/jasa.2009.0106","volume":"104","author":"RD Cook","year":"2009","unstructured":"Cook, R.D., Forzani, L.: Likelihood-based sufficient dimension reduction. J. Am. Stat. Assoc. 104(485), 197\u2013208 (2009)","journal-title":"J. Am. Stat. Assoc."},{"issue":"414","key":"9876_CR18","first-page":"328","volume":"86","author":"RD Cook","year":"1991","unstructured":"Cook, R.D., Weisberg, S.: Sliced inverse regression for dimension reduction: comment. J. Am. Stat. Assoc. 86(414), 328\u2013332 (1991)","journal-title":"J. Am. Stat. Assoc."},{"key":"9876_CR19","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1063\/1.3060498","volume":"10","author":"T Cowling","year":"1957","unstructured":"Cowling, T., Lindsay, R.B.: Magnetohydrodynamics. Phys. Today 10, 40 (1957)","journal-title":"Phys. Today"},{"key":"9876_CR20","unstructured":"Donoho, D.L.: High-dimensional data analysis: the curses and blessings of dimensionality. In: AMS Conference on Math Challenges of the 21st Century (2000)"},{"issue":"2","key":"9876_CR21","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/0047-259X(86)90083-7","volume":"20","author":"ML Eaton","year":"1986","unstructured":"Eaton, M.L.: A characterization of spherical distributions. J. Multivar. Anal. 20(2), 272\u2013276 (1986)","journal-title":"J. Multivar. Anal."},{"key":"9876_CR22","volume-title":"Real Analysis: Modern Techniques and Their Applications","author":"GB Folland","year":"1999","unstructured":"Folland, G.B.: Real Analysis: Modern Techniques and Their Applications, 2nd edn. Wiley, New York (1999)","edition":"2"},{"issue":"2","key":"9876_CR23","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s10208-012-9115-y","volume":"12","author":"M Fornasier","year":"2012","unstructured":"Fornasier, M., Schnass, K., Vybiral, J.: Learning functions of few arbitrary linear parameters in high dimensions. Found. Comput. Math. 12(2), 229\u2013262 (2012)","journal-title":"Found. Comput. Math."},{"issue":"376","key":"9876_CR24","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1080\/01621459.1981.10477729","volume":"76","author":"JH Friedman","year":"1980","unstructured":"Friedman, J.H., Stuetzle, W.: Projection pursuit regression. J. Am. Stat. Assoc. 76(376), 817\u2013823 (1980)","journal-title":"J. Am. Stat. Assoc."},{"key":"9876_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-11259-6","volume-title":"Handbook of Uncertainty Quantification","author":"R Ghanem","year":"2016","unstructured":"Ghanem, R., Higdon, D., Owhadi, H.: Handbook of Uncertainty Quantification. Springer, Berlin (2016)"},{"key":"9876_CR26","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/s11222-018-9816-4","volume":"29","author":"A Glaws","year":"2018","unstructured":"Glaws, A., Constantine, P.G.: Gauss\u2013Christoffel quadrature for inverse regression: applications to computer experiments. Stat. Comput. 29, 429\u2013447 (2018)","journal-title":"Stat. Comput."},{"issue":"5","key":"9876_CR27","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1002\/sam.11355","volume":"10","author":"A Glaws","year":"2017","unstructured":"Glaws, A., Constantine, P.G., Shadid, J., Wildey, T.M.: Dimension reduction in magnetohydrodynamics power generation models: dimensional analysis and active subspaces. Stat. Anal. Data Min. 10(5), 312\u2013325 (2017)","journal-title":"Stat. Anal. Data Min."},{"key":"9876_CR28","doi-asserted-by":"crossref","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"GH Golub","year":"2013","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 4th edn. JHU Press, Baltimore (2013)","edition":"4"},{"key":"9876_CR29","volume-title":"Deep Learning","author":"I Goodfellow","year":"2016","unstructured":"Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016)"},{"key":"9876_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-84858-7","volume-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"T Hastie","year":"2009","unstructured":"Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer, New York (2009)","edition":"2"},{"key":"9876_CR31","unstructured":"Hokanson, J., Constantine, P.: Data-driven polynomial ridge approximation using variable projection. (2017). arXiv:1702.05859"},{"issue":"4","key":"9876_CR32","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1023\/A:1012771025575","volume":"21","author":"DR Jones","year":"2001","unstructured":"Jones, D.R.: A taxonomy of global optimization methods based on response surfaces. J. Glob. Optim. 21(4), 345\u2013383 (2001)","journal-title":"J. Glob. Optim."},{"key":"9876_CR33","first-page":"261","volume-title":"Handbook of Statistics","author":"JR Koehler","year":"1996","unstructured":"Koehler, J.R., Owen, A.B.: Computer experiments. In: Ghosh, S., Rao, C.R. (eds.) Handbook of Statistics, vol. 13(9), pp. 261\u2013308. Elsevier, Amsterdam (1996)"},{"issue":"414","key":"9876_CR34","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1080\/01621459.1991.10475035","volume":"86","author":"KC Li","year":"1991","unstructured":"Li, K.C.: Sliced inverse regression for dimension reduction. J. Am. Stat. Assoc. 86(414), 316\u2013327 (1991)","journal-title":"J. Am. Stat. Assoc."},{"issue":"420","key":"9876_CR35","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1080\/01621459.1992.10476258","volume":"87","author":"KC Li","year":"1992","unstructured":"Li, K.C.: On principal Hessian directions for data visualization and dimension reduction: another application of Stein\u2019s lemma. J. Am. Stat. Assoc. 87(420), 1025\u20131039 (1992)","journal-title":"J. Am. Stat. Assoc."},{"key":"9876_CR36","doi-asserted-by":"crossref","DOI":"10.1201\/9781315119427","volume-title":"Sufficient Dimension Reduction: Methods and Applications with R","author":"B Li","year":"2018","unstructured":"Li, B.: Sufficient Dimension Reduction: Methods and Applications with R. CRC Press, Philadelphia (2018)"},{"issue":"3","key":"9876_CR37","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1214\/aos\/1176347254","volume":"17","author":"K-C Li","year":"1989","unstructured":"Li, K.-C., Duan, N.: Regression analysis under link violation. Ann. Stat. 17(3), 1009\u20131052 (1989)","journal-title":"Ann. Stat."},{"key":"9876_CR38","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.jcp.2016.05.040","volume":"321","author":"W Li","year":"2016","unstructured":"Li, W., Lin, G., Li, B.: Inverse regression-based uncertainty quantification algorithms for high-dimensional models: theory and practice. J. Comput. Phys. 321, 259\u2013278 (2016)","journal-title":"J. Comput. Phys."},{"key":"9876_CR39","volume-title":"Response Surface Methodology: Process and Product Optimization Using Designed Experiments","author":"RH Myers","year":"1995","unstructured":"Myers, R.H., Montgomery, D.C.: Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Wiley, New York (1995)"},{"key":"9876_CR40","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/j.ress.2017.06.026","volume":"167","author":"Q Pan","year":"2017","unstructured":"Pan, Q., Dias, D.: Sliced inverse regression-based sparse polynomial chaos expansions for reliability analysis in high dimensions. Reliab. Eng. Syst. Saf. 167, 484\u2013493 (2017). (Special section: applications of probabilistic graphical models in dependability, diagnosis and prognosis)","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"9876_CR41","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781316408124","volume-title":"Ridge Functions","author":"A Pinkus","year":"2015","unstructured":"Pinkus, A.: Ridge Functions. Cambridge University Press, Cambridge (2015)"},{"issue":"7","key":"9876_CR42","doi-asserted-by":"crossref","first-page":"W07401","DOI":"10.1029\/2011WR011527","volume":"48","author":"S Razavi","year":"2012","unstructured":"Razavi, S., Tolson, B.A., Burn, D.H.: Review of surrogate modeling in water resources. Water Resour. Res. 48(7), W07401 (2012)","journal-title":"Water Resour. Res."},{"issue":"4","key":"9876_CR43","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1214\/ss\/1177012413","volume":"4","author":"J Sacks","year":"1989","unstructured":"Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4(4), 409\u2013423 (1989)","journal-title":"Stat. Sci."},{"key":"9876_CR44","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3799-8","volume-title":"The Design and Analysis of Computer Experiments","author":"TJ Santner","year":"2003","unstructured":"Santner, T.J., Williams, B.J., Notz, W.I.: The Design and Analysis of Computer Experiments. Springer, New York (2003)"},{"key":"9876_CR45","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611973228","volume-title":"Uncertainty Quantification: Theory, Implementation, and Applications","author":"RC Smith","year":"2013","unstructured":"Smith, R.C.: Uncertainty Quantification: Theory, Implementation, and Applications. SIAM, Philadelphia (2013)"},{"key":"9876_CR46","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-23395-6","volume-title":"Introduction to Uncertainty Quantification","author":"T Sullivan","year":"2015","unstructured":"Sullivan, T.: Introduction to Uncertainty Quantification. Springer, New York (2015)"},{"key":"9876_CR47","volume-title":"Complexity and Information","author":"JF Traub","year":"1998","unstructured":"Traub, J.F., Werschulz, A.G.: Complexity and Information. Cambridge University Press, Cambridge (1998)"},{"issue":"3","key":"9876_CR48","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.acha.2014.01.002","volume":"37","author":"H Tyagi","year":"2014","unstructured":"Tyagi, H., Cevher, V.: Learning non-parametric basis independent models from point queries via low-rank methods. Appl. Comput. Harmon. Anal. 37(3), 389\u2013412 (2014)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"4","key":"9876_CR49","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1115\/1.2429697","volume":"129","author":"GG Wang","year":"2006","unstructured":"Wang, G.G., Shan, S.: Review of metamodeling techniques in support of engineering design optimization. J. Mech. Des. 129(4), 370\u2013380 (2006)","journal-title":"J. Mech. Des."},{"key":"9876_CR50","doi-asserted-by":"crossref","DOI":"10.1002\/0471704091","volume-title":"Applied Linear Regression","author":"S Weisberg","year":"2005","unstructured":"Weisberg, S.: Applied Linear Regression, 3rd edn. Wiley, New York (2005)","edition":"3"},{"issue":"8","key":"9876_CR51","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.1016\/j.jmva.2008.01.006","volume":"99","author":"X Yin","year":"2008","unstructured":"Yin, X., Li, B., Cook, R.D.: Successive direction extraction for estimating the central subspace in a multiple-index regression. J. Multivar. Anal. 99(8), 1733\u20131757 (2008)","journal-title":"J. Multivar. Anal."},{"issue":"3","key":"9876_CR52","doi-asserted-by":"crossref","first-page":"1948","DOI":"10.1002\/2016WR019518","volume":"53","author":"J Zhang","year":"2017","unstructured":"Zhang, J., Li, W., Lin, G., Zeng, L., Wu, L.: Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method. Water Resour. Res. 53(3), 1948\u20131962 (2017)","journal-title":"Water Resour. Res."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-019-09876-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-019-09876-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-019-09876-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T03:13:17Z","timestamp":1694920397000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-019-09876-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,31]]},"references-count":52,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["9876"],"URL":"https:\/\/doi.org\/10.1007\/s11222-019-09876-y","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,31]]},"assertion":[{"value":"27 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 May 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}