MMD: Compute the MMD between two samples

In AnthonyEbert/EasyMMD: Allows users to compute the Maximum Mean Discrepancy (MMD) between two samples.

Compute the MMD between two samples

Description

This function returns the estimator for the two-sample MMD.

Usage

MMD(
  y,
  x,
  y_kmmd = NULL,
  var = 1,
  bias = FALSE,
  threshold = Inf,
  approx_exp = 0,
  sigma = NULL,
  w_y = NULL,
  w_x = NULL
)

Arguments

y	either a numeric vector or matrix with number of rows equal to number of observations and number of columns equal to dimension of observations.
x	either a numeric vector or matrix with number of rows equal to number of observations and number of columns equal to dimension of observations.
y_kmmd	precomputed first term in MMD calculation.
var	matrix kernel variance covariance matrix.
bias	logical; if TRUE the biased MMD is computed rather than the unbiased MMD. This can be useful since the biased MMD is always positive.
threshold	numeric filter out values for exponentiation.
approx_exp	integer; if 0 the usual function for the exponential distribution is used; if 1 a much faster but less accurate version of the exponential distribution is used.
sigma	numeric DEPRECATED square root of variance.
w_y	numeric weights for y
w_x	numeric weights for x

References

Gretton, Arthur, et al. "A kernel method for the two-sample-problem." Advances in neural information processing systems. 2007.

Examples

set.seed(1)
y <- rnorm(2000)
x <- rnorm(2000, 5)

MMD_1 <- MMD(y, x)
MMD_1

# Precompute y_kmmd for faster speed
y_kmmd <- kmmd(y)

MMD_2 <- MMD(y, x, y_kmmd)
MMD_2


system.time(MMD_1 <- MMD(y, x))
system.time(MMD_2 <- MMD(y, x, y_kmmd))

# Different var

MMD_4 <- MMD(y, x, var = 0.25)

# Matrix version
library(mvtnorm)

x <- rmvnorm(100, c(0,0), diag(c(2,2)))
sigma <- matrix(c(2,1.5,1.5,2), ncol=2)
y <- rmvnorm(100, c(0,0), sigma = sigma)

MMD(y, x, var = diag(c(0.5, 0.5)), bias = TRUE)

AnthonyEbert/EasyMMD documentation built on March 29, 2022, 8:55 p.m.