IPMeasures.jl

Implements Integral Probability Measures, such as Maximum Mean Discrepancy (MMD) with Gaussian, RQ, and IPM kernels, as well as the KL divergence of conditional Gaussians (based on ConditionalDists.jl). The package is compatible with Flux.jl and uses the Distances.jl interface.

Examples

Maximum Mean Discrepancy between x and y using gaussian kernel of bandwidth γ

using IPMeasures: mmd, GaussianKernel

x = randn(2,100)
y = randn(2,100)
γ = 1.0
mmd(GaussianKernel(γ),x,y)
0.012

IMQKernel(c) inverse multi-quadratic kernel k(d) = C/(C+d) with d being a distance as used in [Tolstikhin, Ilya, et al. "Wasserstein Auto-Encoders." (2017)](arXiv preprint arXiv:1711.01558)

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).

using IPMeasures
import IPMeasures: mmd, RQKernel
mmd(RQKernel(1.0),randn(2,100),randn(2,100))
0.026

Furthermore, we have 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