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