## IPMeasures.jl

Implementation of Integral Probability Measures in Julia
Author aicenter
Popularity
12 Stars
Updated Last
1 Year Ago
Started In
June 2018

# 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

### Required Packages

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