Median of Means Sampling for the Keister Function
This work addresses numerical integration challenges for researchers in computational mathematics, offering incremental improvements by validating median-of-means as an alternative to traditional methods.
The study tackled the problem of computing the Keister function integral using Randomized Quasi-Monte Carlo methods by comparing median-of-means to mean-of-means sampling, finding that median-of-means outperforms for sample sizes over 10^3 points while mean-of-means is better for smaller sizes, with results tested across dimensions 2 to 8 and sample sizes from 2^8 to 2^19.
This study investigates the performance of median-of-means sampling compared to traditional mean-of-means sampling for computing the Keister function integral using Randomized Quasi-Monte Carlo (RQMC) methods. The research tests both lattice points and digital nets as point distributions across dimensions 2, 3, 5, and 8, with sample sizes ranging from 2^8 to 2^19 points. Results demonstrate that median-of-means sampling consistently outperforms mean-of-means for sample sizes larger than 10^3 points, while mean-of-means shows better accuracy with smaller sample sizes, particularly for digital nets. The study also confirms previous theoretical predictions about median-of-means' superior performance with larger sample sizes and reflects the known challenges of maintaining accuracy in higher-dimensional integration. These findings support recent research suggesting median-of-means as a promising alternative to traditional sampling methods in numerical integration, though limitations in sample size and dimensionality warrant further investigation with different test functions and larger parameter spaces.