In Figure , we show the relative error between the exact MI and the MI computed for a few values of r, where r is the determinant of the covariance matrix describing the 2D Gaussian. As was also shown by Kraskov et al., the estimates improve with larger N, and the algorithm shows no systematic error when the Gaussians are truly uncorrelated (r=0). Because of this systematic error, Kraskov et al. recommended a value of k between 2 and 4, which shows reduced noise compared to a k value of 1, but without the large systematic bias from larger values of k. However, if one is testing for statistical independence of the datasets, Kraskov et al. recommended a value of k = N/2, since for independent data, the systematic error will be nonexistent, and a larger k value will diminish noise. This toy system shows that our GPU implementation of the algorithm is correct -producing the same results as Kraskov's original publication and the same as a correct CPU implementation. Benchmarks show a performance gain of at least three orders of magnitude for large inputs, compared to the CPU implementation, when using a GTX1080 GPU, and at least another additional order of magnitude increase when using the powerful RTX6000 Ada GPUs (Figure ).