# A machine learning approach for efficient multi-dimensional integration

arXiv: https://arxiv.org/abs/2009.06697 · HTML: https://mlsanity.com/paper/2009.06697/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Stereotype Detection in LLMs: A Multiclass, Explainable, and Benchmark-Driven Approach](https://mlsanity.com/paper/2404.01768/) (2024)
- [High-precision regressors for particle physics](https://mlsanity.com/paper/2302.00753/) (2023)

## Abstract (arXiv)

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.