Implements Integral Probability Measures, at the moment Maximum Mean Discrepancy with Gaussian, RQ, and IPM kernel. The package is made such that it is compatible with Flux.
mmd(GaussianKernel(γ),x,y,γ,n) Maximum Mean Discrepancy between x and y using gaussian kernel of bandwidth γ
Example
using IPMeasures
import IPMeasures: mmd, GaussianKernel
mmd(GaussianKernel(1.0),randn(2,100),randn(2,100))
0.012
IMQKernel(c) inverse multi-quadratic kernel k(d) = \frac{C}{C + d} with d being a distance used in Tolstikhin, Ilya, et al. "Wasserstein Auto-Encoders." arXiv preprint arXiv:1711.01558 (2017)
Example
using IPMeasures
import IPMeasures: mmd, IMQKernel
mmd(IMQKernel(1.0),randn(2,100),randn(2,100))
0.026
RQKernel(α) Maximum Mean Discrepancy between x and y rq kernel from Bińkowski, Mikołaj, et al. "Demystifying MMD GANs." (2018).
Example
using IPMeasures
import IPMeasures: mmd, RQKernel
mmd(RQKernel(1.0),randn(2,100),randn(2,100))
0.026
Furthermore, we ha estimation of Null Hypothesis of kernel k of samples x from n random draws of subsets of size l
null_distribution(k::AbstractKernel, x, n, l)
estimates the null distribution