{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T10:44:45Z","timestamp":1778496285296,"version":"3.51.4"},"publisher-location":"Cham","reference-count":56,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030983185","type":"print"},{"value":"9783030983192","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-030-98319-2_10","type":"book-chapter","created":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T07:03:13Z","timestamp":1653030193000},"page":"205-221","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Scalable Control Variates for Monte Carlo Methods Via Stochastic Optimization"],"prefix":"10.1007","author":[{"given":"Shijing","family":"Si","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris. J.","family":"Oates","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew B.","family":"Duncan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lawrence","family":"Carin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7ois-Xavier","family":"Briol","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,5,21]]},"reference":[{"key":"10_CR1","doi-asserted-by":"crossref","unstructured":"Andrad\u00f3ttir, S., Heyman, D.P., Ott, T.J.: Variance reduction through smoothing and control variates for Markov chain simulations. ACM Trans. Model. Comput. Simul. 3(3), 167\u2013189 (1993)","DOI":"10.1145\/174153.174154"},{"key":"10_CR2","doi-asserted-by":"crossref","unstructured":"Assaraf, R., Caffarel, M.: Zero-variance principle for Monte Carlo algorithms. Phys. Rev. Lett. 83(23), 4682 (1999)","DOI":"10.1103\/PhysRevLett.83.4682"},{"key":"10_CR3","doi-asserted-by":"crossref","unstructured":"Baker, J., Fearnhead, P., Fox, E.B., Nemeth, C.: Control variates for stochastic gradient MCMC. Stat. Comput. 29, 599\u2013615 (2019)","DOI":"10.1007\/s11222-018-9826-2"},{"key":"10_CR4","doi-asserted-by":"crossref","unstructured":"Barbour, A.D.: Stein\u2019s method and Poisson process convergence. J. Appl. Probab. 25, 175\u2013184 (1988)","DOI":"10.1017\/S0021900200040341"},{"key":"10_CR5","unstructured":"Barp, A., Briol, F.X., Duncan, A.B., Girolami, M., Mackey, L.: Minimum Stein discrepancy estimators. In: Neural Information Processing Systems, pp. 12964\u201312976 (2019)"},{"key":"10_CR6","unstructured":"Barp, A., Oates, C.J., Porcu, E., Girolami, M.: A Riemannian-Stein Kernel Method. arXiv:1810.04946 (2018)"},{"key":"10_CR7","doi-asserted-by":"crossref","unstructured":"Belomestny, D., Iosipoi, L., Moulines, E., Naumov, A., Samsonov, S.: Variance reduction for Markov chains with application to MCMC. Stat. Comput. 30, 973\u2013997 (2020)","DOI":"10.1007\/s11222-020-09931-z"},{"key":"10_CR8","doi-asserted-by":"crossref","unstructured":"Belomestny, D., Iosipoi, L., Zhivotovskiy, N.: Variance reduction via empirical variance minimization: convergence and complexity. Doklady Math. 98, 494\u2013497 (2018)","DOI":"10.1134\/S1064562418060261"},{"key":"10_CR9","unstructured":"Belomestny, D., Moulines, E., Shagadatov, N., Urusov, M.: Variance Reduction for MCMC Methods Via Martingale Representations (2019). arXiv:1903.0737"},{"key":"10_CR10","doi-asserted-by":"crossref","unstructured":"Briol, F.X., Oates, C.J., Girolami, M., Osborne, M.A., Sejdinovic, D.: Probabilistic integration: a role in statistical computation? (with discussion). Stat. Sci. 34(1), 1\u201322 (2019)","DOI":"10.1214\/18-STS660"},{"key":"10_CR11","unstructured":"Brosse, N., Durmus, A., Meyn, S., Moulines, E.: Diffusion approximations and control variates for MCMC (2018). arXiv:1808.01665"},{"key":"10_CR12","doi-asserted-by":"crossref","unstructured":"Chen, L.H.Y., Goldstein, L., Shao, Q.M.: Normal Approximation by Stein\u2019s Method. Springer, Berlin (2010)","DOI":"10.1007\/978-3-642-15007-4_13"},{"key":"10_CR13","unstructured":"Chen, W.Y., Barp, A., Briol, F.X., Gorham, J., Girolami, M., Mackey, L., Oates, C.J.: Stein point Markov chain Monte Carlo. In: International Conference on Machine Learning, PMLR 97, pp. 1011\u20131021 (2019)"},{"key":"10_CR14","unstructured":"Chen, W.Y., Mackey, L., Gorham, J., Briol, F.X., Oates, C.J.: Stein points. In: Proceedings of the International Conference on Machine Learning, PMLR 80:843\u2013852 (2018)"},{"key":"10_CR15","unstructured":"Chwialkowski, K., Strathmann, H., Gretton, A.: A kernel test of goodness of fit. Int. Conf. Mach. Learn. 48, 2606\u20132615 (2016)"},{"key":"10_CR16","doi-asserted-by":"crossref","unstructured":"Dellaportas, P., Kontoyiannis, I.: Control variates for estimation based on reversible Markov chain Monte Carlo samplers. J. R. Stat. Soc. Ser. B: Stat. Methodol. 74(1), 133\u2013161 (2012)","DOI":"10.1111\/j.1467-9868.2011.01000.x"},{"key":"10_CR17","doi-asserted-by":"crossref","unstructured":"Friel, N., Mira, A., Oates, C.J.: Exploiting multi-core architectures for reduced-variance estimation with intractable likelihoods. Bayesian Anal. 11(1), 215\u2013245 (2014)","DOI":"10.1214\/15-BA948"},{"key":"10_CR18","unstructured":"Genz, A.: Testing multidimensional integration routines. In: Proceedings of the International Conference on Tools, Methods and Languages for Scientific and Engineering Computation, pp. 81\u201394 (1984)"},{"key":"10_CR19","doi-asserted-by":"crossref","unstructured":"Gorham, J., Duncan, A., Mackey, L., Vollmer, S.: Measuring sample quality with diffusions. Ann. Appl. Probab. 29(5), 2884\u20132928 (2019)","DOI":"10.1214\/19-AAP1467"},{"key":"10_CR20","unstructured":"Gorham, J., Mackey, L.: Measuring sample quality with Stein\u2019s method. In: Advances in Neural Information Processing Systems, pp. 226\u2013234 (2015)"},{"key":"10_CR21","unstructured":"Gorham, J., Mackey, L.: Measuring sample quality with kernels. In: Proceedings of the International Conference on Machine Learning, pp. 1292\u20131301 (2017)"},{"key":"10_CR22","unstructured":"Grathwohl, W., Choi, D., Wu, Y., Roeder, G., Duvenaud, D.: Backpropagation through the void: Optimizing control variates for black-box gradient estimation. In: International Conference on Learning Representations (2018)"},{"key":"10_CR23","unstructured":"Greensmith, E., Bartlett, P.L., Baxter, J.: Variance reduction techniques for gradient estimates in reinforcement learning. J. Mach. Learn. Res. 5, 1471\u20131530 (2004)"},{"key":"10_CR24","doi-asserted-by":"crossref","unstructured":"Hammer, H., Tjelmeland, H.: Control variates for the Metropolis-Hastings algorithm. Scand. J. Stat. 35(3), 400\u2013414 (2008)","DOI":"10.1111\/j.1467-9469.2008.00601.x"},{"key":"10_CR25","doi-asserted-by":"crossref","unstructured":"Henderson, S.G., Glynn, P.W.: Approximating martingales for variance reduction in Markov process simulation. Math. Oper. Res. 27(2), 253\u2013271 (2002)","DOI":"10.1287\/moor.27.2.253.329"},{"key":"10_CR26","doi-asserted-by":"crossref","unstructured":"Hickernell, F.J., Lemieux, C., Owen, A.B.: Control variates for quasi-Monte Carlo. Stat. Sci. 20(1), 1\u201331 (2005)","DOI":"10.1214\/088342304000000468"},{"key":"10_CR27","doi-asserted-by":"crossref","unstructured":"Kennedy, M.C., Hagan, A.O.: Bayesian calibration of computer models. J. R. Stat. Soc. Ser. B: Stat. Methodol. 63(3), 425\u2013464 (2001)","DOI":"10.1111\/1467-9868.00294"},{"key":"10_CR28","unstructured":"Leluc, R., Portier, F., Segers, J.: Control variate selection for Monte Carlo integration (2019). arXiv:1906.10920"},{"key":"10_CR29","doi-asserted-by":"crossref","unstructured":"Ley, C., Swan, Y.: Parametric Stein operators and variance bounds. Braz. J. Probab. Stat. 30(2) (2016)","DOI":"10.1214\/14-BJPS271"},{"key":"10_CR30","unstructured":"Liu, H., Feng, Y., Mao, Y., Zhou, D., Peng, J., Liu, Q.: Action-dependent control variates for policy optimization via Stein\u2019s identity. In: International Conference on Learning Representation (2018)"},{"key":"10_CR31","unstructured":"Liu, Q., Lee, J.D.: Black-box importance sampling. In: Proceedings of the International Conference on Artificial Intelligence and Statistics, pp. 952\u2013961 (2017)"},{"key":"10_CR32","unstructured":"Liu, Q., Lee, J.D., Jordan, M.I.: A kernelized Stein discrepancy for goodness-of-fit tests and model evaluation. In: International Conference on Machine Learning, pp. 276\u2013284 (2016)"},{"key":"10_CR33","unstructured":"Liu, Q., Wang, D.: Stein variational gradient descent: a general purpose Bayesian inference algorithm. In: Advances in Neural Information Processing Systems (2016)"},{"key":"10_CR34","unstructured":"Liu, S., Kanamori, T., Jitkrittum, W., Chen, Y.: Fisher efficient inference of intractable models. In: Neural Information Processing Systems, pp. 8793\u20138803 (2019)"},{"key":"10_CR35","doi-asserted-by":"crossref","unstructured":"Mira, A., Solgi, R., Imparato, D.: Zero variance Markov chain Monte Carlo for Bayesian estimators. Stat. Comput. 23(5), 653\u2013662 (2013)","DOI":"10.1007\/s11222-012-9344-6"},{"key":"10_CR36","doi-asserted-by":"publisher","unstructured":"M\u00fcller, T., Rousselle, F., Keller, A., Nov\u00e1k, J.: Neural control variates. ACM Trans. Graph. 39(6), 243:1\u2013243:19 (2020). https:\/\/doi.org\/10.1145\/3414685.3417804","DOI":"10.1145\/3414685.3417804"},{"key":"10_CR37","doi-asserted-by":"crossref","unstructured":"Newton, N.J.: Variance reduction for simulated diffusions. SIAM J. Appl. Math. 54(6), 1780\u20131805 (1994)","DOI":"10.1137\/S0036139992236220"},{"key":"10_CR38","doi-asserted-by":"crossref","unstructured":"Oates, C.J., Cockayne, J., Briol, F.X., Girolami, M.: Convergence rates for a class of estimators based on Stein\u2019s identity. Bernoulli 25(2), 1141\u20131159 (2019)","DOI":"10.3150\/17-BEJ1016"},{"key":"10_CR39","doi-asserted-by":"crossref","unstructured":"Oates, C.J., Girolami, M., Chopin, N.: Control functionals for Monte Carlo integration. J. R. Stat. Soc. B: Stat. Methodol. 79(3), 695\u2013718 (2017)","DOI":"10.1111\/rssb.12185"},{"key":"10_CR40","doi-asserted-by":"crossref","unstructured":"Oates, C.J., Papamarkou, T., Girolami, M.: The controlled thermodynamic integral for Bayesian model comparison. J. Am. Stat. Assoc. (2016)","DOI":"10.1080\/01621459.2015.1021006"},{"key":"10_CR41","doi-asserted-by":"crossref","unstructured":"O\u2019Hagan, A.: Bayes-Hermite quadrature. J. Stat. Plan. Inference 29, 245\u2013260 (1991)","DOI":"10.1016\/0378-3758(91)90002-V"},{"key":"10_CR42","unstructured":"Paisley, J., Blei, D., Jordan, M.: Variational Bayesian inference with stochastic search. In: International Conference on Machine Learning (2012)"},{"key":"10_CR43","doi-asserted-by":"crossref","unstructured":"Papamarkou, T., Mira, A., Girolami, M.: Zero variance differential geometric Markov chain Monte Carlo algorithms. Bayesian Anal. 9(1), 97\u2013128 (2014)","DOI":"10.1214\/13-BA848"},{"key":"10_CR44","doi-asserted-by":"crossref","unstructured":"Pardoux, E., Vertennikov, A.Y.: On the Poisson equation and diffusion approximation. I. Ann. Probab. 29(3), 1061\u20131085 (2001)","DOI":"10.1214\/aop\/1015345596"},{"key":"10_CR45","doi-asserted-by":"crossref","unstructured":"Portier, F., Segers, J.: Monte Carlo integration with a growing number of control variates. J. Appl. Probab. 56(4), 1168\u20131186 (2019)","DOI":"10.1017\/jpr.2019.78"},{"key":"10_CR46","unstructured":"Ranganath, R., Altosaar, J., Tran, D., Blei, D.M.: Operator variational inference. In: Advances in Neural Information Processing Systems, pp. 496\u2013504 (2016)"},{"key":"10_CR47","unstructured":"Ranganath, R., Gerrish, S., Blei, D.M.: Black box variational inference. In: Artificial Intelligence and Statistics, pp. 814\u2013822 (2014)"},{"key":"10_CR48","unstructured":"Riabiz, M., Chen, W., Cockayne, J., Swietach, P., Niederer, S.A., Mackey, L., Oates, C.J.: Optimal thinning of MCMC output (2020). arXiv:2005.03952"},{"key":"10_CR49","doi-asserted-by":"crossref","unstructured":"Ross, N.: Fundamentals of Stein\u2019s method. Probab. Surv. 8, 210\u2013293 (2011)","DOI":"10.1214\/11-PS182"},{"key":"10_CR50","unstructured":"Si, S., Oates, C.J., Duncan, A.B., Carin, L., Briol, F.X.: Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization (2020). arXiv:2006.07487"},{"key":"10_CR51","doi-asserted-by":"crossref","unstructured":"South, L.F., Karvonen, T., Nemeth, C., Girolami, M., Oates, C.J.: Semi-exact control functionals from Sard\u2019s method (2020). arXiv:2002.00033","DOI":"10.1093\/biomet\/asab036"},{"key":"10_CR52","unstructured":"South, L.F., Oates, C.J., Mira, A., Drovandi, C.: Regularised zero-variance control variates for high-dimensional variance reduction (2019). arXiv:1811.05073"},{"key":"10_CR53","unstructured":"Stein, C.: A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In: Proceedings of 6th Berkeley Symposium on Mathematical Statistics and Probability, pp. 583\u2013602. University of California Press (1972)"},{"key":"10_CR54","doi-asserted-by":"crossref","unstructured":"Wan, R., Zhong, M., Xiong, H., Zhu, Z.: Neural control variates for Monte Carlo variance reduction. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 533\u2013547 (2019)","DOI":"10.1007\/978-3-030-46147-8_32"},{"key":"10_CR55","unstructured":"Wang, C., Chen, X., Smola, A., Xing, E.P.: Variance reduction for stochastic gradient optimization. In: Advances in Neural Information Processing Systems, pp. 181\u2013189 (2013)"},{"key":"10_CR56","unstructured":"Yang, J., Liu, Q., Rao, V., Neville, J.: Goodness-of-fit testing for discrete distributions via Stein discrepancy. In: International Conference on Machine Learning, pp. 5561\u20135570 (2018)"}],"container-title":["Springer Proceedings in Mathematics & Statistics","Monte Carlo and Quasi-Monte Carlo Methods"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-98319-2_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T07:04:57Z","timestamp":1653030297000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-98319-2_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783030983185","9783030983192"],"references-count":56,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-98319-2_10","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"value":"2194-1009","type":"print"},{"value":"2194-1017","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"21 May 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"MCQMC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 August 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 August 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"mcqmc2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/mcqmc20.web.ox.ac.uk\/home","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}