On two ways to use determinantal point processes for Monte Carlo integration

Determinantal point processes can significantly improve the accuracy of Monte Carlo integration by reducing variance. Researchers have explored two existing methods that utilize determinantal point processes to achieve more consistent estimators. The standard Monte Carlo estimator relies on independent samples, resulting in a variance of order 1/N. In contrast, determinantal point processes introduce a repulsive distribution, allowing for more efficient sampling and adapting to the target function and distribution. By replacing traditional sampling methods with determinantal point processes, the variance rates can be significantly reduced, leading to more reliable estimates. This approach has important implications for applications where accurate integration is crucial¹. The ability to improve the efficiency of Monte Carlo integration can have a significant impact on various fields, including machine learning and statistical analysis, enabling practitioners to make more informed decisions with more accurate results.