Regression-based Monte Carlo integration

Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists alternative interpretation in calculus where can be seen estimating a constant function---from evaluations integrand---that integrates to original integral. The integral mean theorem states that this function should (or expectation) integrand. Since both interpretations result same estimator, little attention has been devoted calculus-oriented interpretation. We show actually implies possibility more complex than one construct efficient for integration. build new based on and relate our control variates with least-squares regression samples Unlike prior work, resulting provably better or equal conventional estimator. To demonstrate strength approach, we introduce practical act simple drop-in replacement experimentally validate framework various light transport integrals. code available at https://github.com/iribis/regressionmc.