We develop a machine learning algorithm to turn around stratification in Monte Carlo sampling. We use a different way to divide the domain space of the integrand, based on the height of the function being sampled, similar to what is done in Lebesgue integration. This means that isocontours of the function define regions that can have any shape depending on the behavior of the function. We take advantage of the capacity of neural networks to learn complicated functions in order to predict these complicated divisions and preclassify large samples of the domain space. From this preclassification we can select the required number of points to perform a number of tasks such as variance reduction, integration and even event selection. The network ultimately defines the regions with what it learned and is also used to calculate the multi-dimensional volume of each region.

翻译：我们开发了一种机器学习算法，以改进蒙特卡洛采样中的分层策略。我们采用一种不同的方式来划分被积函数的定义域空间，其依据是被采样函数的高度，类似于勒贝格积分中的做法。这意味着函数的等值线定义了区域，这些区域的形状可以取决于函数的行为而任意变化。我们利用神经网络学习复杂函数的能力，来预测这些复杂的分区并对定义域空间的大量样本进行预分类。基于这种预分类，我们可以选择所需数量的点来执行多项任务，例如方差缩减、积分乃至事件选择。该网络最终根据其学习结果定义各区域，并用于计算每个区域的多维体积。