  We propose a novel multi-dimensional integration algorithm using a machine
learning (ML) technique. After training a ML regression model to mimic a target
integrand, the regression model is used to evaluate an approximation of the
integral. Then, the difference between the approximation and the true answer is
calculated to correct the bias in the approximation of the integral induced by
a ML prediction error. Because of the bias correction, the final estimate of
the integral is unbiased and has a statistically correct error estimation. The
performance of the proposed algorithm is demonstrated on six different types of
integrands at various dimensions and integrand difficulties. The results show
that, for the same total number of integrand evaluations, the new algorithm
provides integral estimates with more than an order of magnitude smaller
uncertainties than those of the VEGAS algorithm in most of the test cases.
