LeStrat-Net: Lebesgue style stratification for Monte Carlo simulations powered by machine learning
This addresses a domain-specific problem for Monte Carlo simulation practitioners, but appears incremental as it adapts existing stratification concepts with machine learning.
The authors tackled the problem of stratification in Monte Carlo sampling by developing a machine learning algorithm that divides the domain space based on function height, similar to Lebesgue integration, to enable tasks like variance reduction and integration, but no concrete numerical results were provided.
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.