Global Sensitivity Analysis via Optimal Transport

References

• Altschuler J, Weed J, Rigollet P (2017) Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration. Advances in Neural Information Processing Systems (Curran Associates, Red Hook, NY), 1965–1975.Google Scholar
• Altschuler J, Bach F, Rudi A, Niles-Weed J (2019) Massively scalable Sinkhorn distances via the Nyström method. Adv. Neural Inform. Processing Systems 32:1–11.Google Scholar
• Barr J, Rabitz H (2022) A generalized kernel method for global sensitivity analysis. SIAM/ASA J. Uncertainty Quantification 10(1):27–54.Crossref, Google Scholar
• Barton RR (2016) Tutorial: Simulation metamodeling. Proc. 2015 Winter Simul. Conf. (IEEE, Piscataway, NJ), 1765–1779.Google Scholar
• Baucells M, Borgonovo E (2013) Invariant probabilistic sensitivity analysis. Management Sci. 59(11):2536–2549.Link, Google Scholar
• Berger D, Herkenhoff K, Huang C, Mongey S (2022) Testing and reopening in an SEIR model. Rev. Econom. Dynam. 43:1–21.Crossref, Google Scholar
• Bertsimas D, Shtern S, Sturt B (2022a) A data-driven approach to multistage stochastic linear optimization. Management Sci. 69(1):51–74.Link, Google Scholar
• Bertsimas D, Shtern S, Sturt B (2022b) Technical note—Two-stage sample robust optimization. Oper. Res. 70(1):624–640.Link, Google Scholar
• Binois M, Gramacy RB (2021) HetGP: Heteroskedastic Gaussian process modeling and sequential design in R. J. Statist. Software 98(13):1–44.Crossref, Google Scholar
• Binois M, Gramacy RB, Ludkovski M (2018) Practical heteroscedastic Gaussian process modeling for large simulation experiments. J. Comput. Graphical Statist. 27(4):808–821.Crossref, Google Scholar
• Blanchet J, Kang Y (2021) Sample out-of-sample inference based on Wasserstein distance. Oper. Res. 69(3):985–1013.Link, Google Scholar
• Borgonovo E, Tarantola S, Plischke E, Morris MD (2014) Transformations and invariance in the sensitivity analysis of computer experiments. J. Roy. Statist. Soc. B 76:925–947.Crossref, Google Scholar
• Broadie M, Du Y, Moallemi CC (2011) Efficient risk estimation via nested sequential simulation. Management Sci. 57(6):1172–1194.Link, Google Scholar
• Broadie M, Du Y, Moallemi CC (2015) Risk estimation via regression. Oper. Res. 63(5):1077–1097.Link, Google Scholar
• Cambanis S, Huang S, Simons G (1981) On the theory of elliptically contoured distributions. J. Multivariate Anal. 11:368–385.Crossref, Google Scholar
• Cambanis S, Simons G, Stout W (1976) Inequalities for E k(X, Y) when the marginals are fixed. Z. Wahrscheinlichkeitstheor. Verwandte Geb. 36(4):285–294.Crossref, Google Scholar
• Carlsson JG, Behroozi M, Mihic K (2018) Wasserstein distance and the distributionally robust TSP. Oper. Res. 66(6):1603–1624.Link, Google Scholar
• Chatterjee S (2021) A new coefficient of correlation. J. Amer. Statist. Assoc. 116(536):2009–2022.Crossref, Google Scholar
• Chen Y, Georgiou TT, Pavon M (2021) Stochastic control liaisons: Richard Sinkhorn meets Gaspard Monge on a Schrödinger bridge. SIAM Rev. 63(2):249–313.Crossref, Google Scholar
• Chen Z, Sim M, Xiong P (2020) Robust stochastic optimization made easy with RSOME. Management Sci. 66(8):3329–3339.Link, Google Scholar
• Chen L, Kyng R, Liu YP, Peng R, Gutenberg MP, Sachdeva S (2022) Maximum flow and minimum-cost flow in almost-linear time. Preprint, submitted March 1, https://arxiv.org/abs/2203.00671.Google Scholar
• Chizat L, Roussillon P, Léger F, Vialard F-X, Peyré G (2020) Faster Wasserstein distance estimation with the Sinkhorn divergence. Advances in Neural Information Processing Systems (Curran Associates Inc., Red Hook, NY).Google Scholar
• Cuturi M (2013) Sinkhorn distances: Lightspeed computation of optimal transportation distances. Adv. Neural Inform. Processing Systems 26:2292–2300.Google Scholar
• da Veiga S (2021) Kernel-based ANOVA decomposition and Shapley effects – Application to global sensitivity analysis. Preprint, submitted January 13, https://hal.science/hal-03108628v1/file/KernelANOVA.pdf.Google Scholar
• Deb N, Ghosal P, Sen B (2020) Measuring association on topological spaces using kernels and geometric graphs. Preprint, submitted October 5, https://arxiv.org/abs/2010.01768.Google Scholar
• Du Z, Wang L, Bai Y, Wang X, Pandey A, Fitzpatrick MC, Chinazzi M, et al. (2022) Cost-effective proactive testing strategies during COVID-19 mass vaccination: A modelling study. Lancet Regional Health Amer. 8:1–10.Google Scholar
• Felli JC, Hazen GB (1998) Sensitivity analysis and the expected value of perfect information. Med. Decision Making 18:95–109.Crossref, Google Scholar
• Figalli A, Glaudo F (2021) An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows (European Mathematical Society, Zurich).Crossref, Google Scholar
• Fort JC, Klein T, Lagnoux A (2021) Global sensitivity analysis and Wasserstein spaces. SIAM/ASA J. Uncertainty Quantification 9(2):880–921.Crossref, Google Scholar
• Fraiman R, Gamboa F, Moreno L (2020) Sensitivity indices for output on a Riemannian manifold. Internat. J. Uncertainty Quantification 10(4):297–314.Crossref, Google Scholar
• Gamboa F, Klein T, Lagnoux A (2018) Sensitivity analysis based on Cramér–von Mises distance. SIAM/ASA J. Uncertainty Quantification 6(2):522–548.Crossref, Google Scholar
• Gamboa F, Janon A, Klein T, Lagnoux A (2014) Sensitivity analysis for multidimensional and functional outputs. Electronic J. Statist. 8:573–603.Crossref, Google Scholar
• Gamboa F, Klein T, Lagnoux A, Moreno L (2021) Sensitivity analysis in general metric spaces. Reliability Engrg. System Safety 212:107611.Crossref, Google Scholar
• Gamboa F, Janon A, Klein T, Lagnoux A, Prieur C (2016) Statistical inference for Sobol pick-freeze Monte Carlo method. Statistics 50(4):881–902.Crossref, Google Scholar
• Gelbrich M (1990) On a formula for the L2 Wasserstein metric between measures on Euclidean Hilbert spaces. Math. Nachrichten 147:185–203.Crossref, Google Scholar
• Genevay A, Peyré G, Cuturi M (2018) Learning generative models with Sinkhorn divergences. Storkey A, Perez-Cruz F, eds. Proc. Twenty-First Internat. Conf. Artificial Intelligence Statist. AISTATS 2018, vol. 84 (PMLR, New York), 1608–1617.Google Scholar
• Givens CR, Shortt RM (1984) A class of Wasserstein metrics for probability distributions. Michigan Math. J. 31:231–240.Crossref, Google Scholar
• Glasserman P, Wang Y (1998) Leadtime-inventory trade-offs in assemble-to-order systems. Oper. Res. 46(6):858–871.Link, Google Scholar
• Gordy MB, Juneja S (2010) Nested simulation in portfolio risk measurement. Management Sci. 56(10):1833–1848.Link, Google Scholar
• Hanasusanto GA, Kuhn D (2018) Conic programming reformulations of two-stage distributionally robust linear programs over Wasserstein balls. Oper. Res. 66(3):849–869.Link, Google Scholar
• Hillier FS, Lieberman G (2012) Introduction to Operations Research, 7th ed. (McGraw-Hill, New York).Google Scholar
• Hitchcock FL (1940) The distribution of a product from several sources to numerous localities. MIT J. Math. Physics 20:224–230.Crossref, Google Scholar
• Hong LJ, Nelson BL (2006) Discrete optimization via simulation using COMPASS. Oper. Res. 54(1):115–129.Link, Google Scholar
• Hong LJ, Juneja S, Liu G (2017) Kernel smoothing for nested estimation with application to portfolio risk measurement. Oper. Res. 65(3):657–673.Link, Google Scholar
• Hu Z, Cao J, Hong LJ (2012) Robust simulation of global warming policies using the DICE model. Management Sci. 58(12):2190–2206.Link, Google Scholar
• Ishigami T, Homma T (1990) An importance quantification technique in uncertainty analysis for computer models. Proc. First Internat. Sympos. Uncertainty Model. Anal. (IEEE, Piscataway, NJ), 398–403.Google Scholar
• Janati H, Muzellec B, Peyré G, Cuturi M (2020) Entropic optimal transport between unbalanced Gaussian measures has a closed form. Preprint, submitted June 3, https://arxiv.org/abs/2006.02572.Google Scholar
• Kleijnen JPC (2010) Sensitivity analysis of simulation models. Cochran JJ, Cox LA Jr, Keskinocak P, Kharoufeh JP, Cole Smith J, eds. Wiley Encyclopedia of Operations Research and Management Science (Wiley, Hoboken, NJ), 1–10.Google Scholar
• Kleijnen JPC, Helton JC (1999) Statistical analyses of scatterplots to identify important factors in large-scale simulations. 2: Robustness of techniques. Reliability Engrg. System Safety 65(2):187–197.Crossref, Google Scholar
• Knight PA (2008) The Sinkhorn-Knopp algorithm: Convergence and applications. SIAM J. Matrix Anal. Appl. 30(1):261–275.Crossref, Google Scholar
• Kuhn HW (1955) The Hungarian method for the assignment problem. Nav. Res. Logist. Quart. 2(1–2):83–97.Crossref, Google Scholar
• Kuhn HW (1956) Variants of the Hungarian method for assignment problems. Nav. Res. Logist. Quart. 3(4):253–258.Crossref, Google Scholar
• Lamboni M, Monod H, Makowski D (2011) Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models. Reliability Engrg. System Safety 96(4):450–459.Crossref, Google Scholar
• Landsman ZM, Valdez EA (2003) Tail conditional expectations for elliptical distributions. N. Amer. Actuarial J. 7(4):55–71.Crossref, Google Scholar
• Luenberger DG, Ye Y (2016) Linear and Nonlinear Programming, 4th ed. (Springer, Cham, Switzerland).Crossref, Google Scholar
• Luo F, Mehrotra S (2019) Decomposition algorithm for distributionally robust optimization using Wasserstein metric with an application to a class of regression models. Eur. J. Oper. Res. 278(1):20–35.Crossref, Google Scholar
• Marrel A, Saint-Geours N, De Lozzo M (2017) Sensitivity analysis of spatial and/or temporal phenomena. Ghanem R, Higdon D, Owhadi H, eds. Handbook of Uncertainty Quantification (Springer Verlag, Cham, Switzerland), 1327–1357.Crossref, Google Scholar
• Mohajerin Esfahani P, Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Program. 171(1–2):1–52.Crossref, Google Scholar
• Móri TF, Székely GJ (2019) Four simple axioms of dependence measures. Metrika 82(1):1–16.Crossref, Google Scholar
• Nguyen VA, Kuhn D, Esfahani PM (2022) Distributionally robust inverse covariance estimation: The Wasserstein shrinkage estimator. Oper. Res. 70(1):490–515.Link, Google Scholar
• Nordhaus W (2017) Integrated assessment models of climate change. NBER Reporter 3:1–4.Google Scholar
• Owen AB (2014) Sobol’ indices and Shapley value. SIAM/ASA J. Uncertainty Quantification 2(1):245–251.Crossref, Google Scholar
• Pearson K (1905) On the General Theory of Skew Correlation and Non-Linear Regression, of Mathematical Contributions to the Theory of Evolution, Drapers’ Company Research Memoirs, vol. XIV (Dulau & Co., London).Google Scholar
• Peyré G, Cuturi M (2019) Computational optimal transport. Foundations Trends Machine Learn. 11(5–6):355–607.Crossref, Google Scholar
• Puccetti G (2017) An algorithm to approximate the optimal expected inner product of two vectors with given marginals. J. Math. Anal. Appl. 451(1):132–145.Crossref, Google Scholar
• Rahman S (2016) The f-sensitivity index. SIAM/ASA J. Uncertainty Quantification 4(1):130–162.Crossref, Google Scholar
• Razavi S, Jakeman A, Saltelli A, Prieur C, Iooss B, Borgonovo E, Plischke E, et al. (2021) The future of sensitivity analysis: An essential discipline for systems modeling and policy support. Environ. Model. Software 137(104954):1–22.Google Scholar
• Rényi A (1959) On measures of dependence. Acta Math. Acad. Sci. Hungaricae 10:441–451.Crossref, Google Scholar
• Saltelli A (2002) Making best use of model valuations to compute sensitivity indices. Comput. Phys. Commun. 145:280–297.Crossref, Google Scholar
• Saltelli A, Bammer G, Bruno I, Charters E, Di Fiore M, Didier E, Espeland WN, et al. (2020) Five ways to ensure that models serve society: A manifesto. Nature 582:482–484.Crossref, Google Scholar
• Sobol’ IM (1993) Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Experiments 1:407–414.Google Scholar
• Strong M, Oakley JE (2013) An efficient method for computing single-parameter partial expected value of perfect information. Med. Decision Making 33(6):755–766.Crossref, Google Scholar
• Subramanyam A, Mufalli F, Laínez-Aguirre JM, Pinto JM, Gounaris CE (2021) Robust multiperiod vehicle routing under customer order uncertainty. Oper. Res. 69(1):30–60.Link, Google Scholar
• Vallender SS (1974) Calculation of the Wasserstein distance between probability distributions on the line. Theory Probab. Appl. 18(4):784–786.Crossref, Google Scholar
• Villani C (2008) Optimal Transport: Old and New (Springer Verlag, Berlin).Google Scholar
• Wagner HM (1995) Global sensitivity analysis. Oper. Res. 43(6):948–969.Link, Google Scholar
• Wang Z, You K, Song S, Zhang Y (2020) Wasserstein distributionally robust shortest path problem. Eur. J. Oper. Res. 284(1):31–43.Crossref, Google Scholar
• Wiesel J (2022) Measuring association with Wasserstein distances. Bernoulli 28(4):2816–2832.Crossref, Google Scholar
• Xie J, Frazier P, Chick S (2012) Assemble to order simulator. SimOptWebsite.Google Scholar
• Zhang Y, Zhang Z, Lim A, Sim M (2021) Robust data-driven vehicle routing with time windows. Oper. Res. 69(2):469–485.Link, Google Scholar