论文标题
一种机器学习方法，用于有效的多维整合
A machine learning approach for efficient multi-dimensional integration
论文作者
论文摘要
我们提出了一种使用机器学习（ML）技术的新型多维集成算法。在训练ML回归模型以模仿目标积分后，回归模型被用于评估积分的近似值。然后，计算近似值和真实答案之间的差异，以纠正由ML预测误差引起的积分近似的偏差。由于偏差校正，积分的最终估计值是公正的，并且具有统计正确的误差估计。在各个维度和集成困难的六种不同类型的集成类型上，证明了所提出的算法的性能。结果表明，对于集成量评估的总数，新算法提供的积分估计值比在大多数测试用例中的维加斯算法的不确定性较小的数量级不确定性。
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.
