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There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating a\n            <jats:italic>constant<\/jats:italic>\n            function---from the stochastic evaluations of the integrand---that integrates to the original integral. The integral mean value theorem states that this\n            <jats:italic>constant<\/jats:italic>\n            function should be the mean (or expectation) of the integrand. Since both interpretations result in the same estimator, little attention has been devoted to the calculus-oriented interpretation. We show that the calculus-oriented interpretation actually implies the possibility of using a more\n            <jats:italic>complex<\/jats:italic>\n            function than a\n            <jats:italic>constant<\/jats:italic>\n            one to construct a more efficient estimator for Monte Carlo integration. We build a new estimator based on this interpretation and relate our estimator to control variates with least-squares regression on the stochastic samples of the integrand. Unlike prior work, our resulting estimator is\n            <jats:italic>provably<\/jats:italic>\n            better than or equal to the conventional Monte Carlo estimator. To demonstrate the strength of our approach, we introduce a practical estimator that can act as a simple drop-in replacement for conventional Monte Carlo integration. We experimentally validate our framework on various light transport integrals. The code is available at https:\/\/github.com\/iribis\/regressionmc.\n          <\/jats:p>","DOI":"10.1145\/3528223.3530095","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T21:06:27Z","timestamp":1658523987000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Regression-based Monte Carlo integration"],"prefix":"10.1145","volume":"41","author":[{"given":"Corentin","family":"Sala\u00fcn","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrien","family":"Gruson","sequence":"additional","affiliation":[{"name":"McGill University &amp; \u00c9cole de Technologie Sup\u00e9rieure, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Binh-Son","family":"Hua","sequence":"additional","affiliation":[{"name":"VinAI Research, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Toshiya","family":"Hachisuka","sequence":"additional","affiliation":[{"name":"University of Waterloo, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gurprit","family":"Singh","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3015459"},{"key":"e_1_2_2_2_1","volume-title":"Nonlinearly Weighted First-Order Regression for Denoising Monte Carlo Renderings. 35, 4 (June","author":"Bitterli Benedikt","year":"2016","unstructured":"Benedikt Bitterli, Fabrice Rousselle, Bochang Moon, Jos\u00e9 A. 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