Sliced Wasserstein Distance Between Two Empirical Distributions

Estimate the sliced Wasserstein distance between two empirical distributions represented as matrices using Monte Carlo simulation.

Optionally, a matrix thetas can be supplied. Each row of thetas will be interpreted as a projection direction. These rows do not have to be unit vectors, allowing users to transform the projection directions rather than the matrices.

Usage

sliced_wasserstein(x, y, p = 2, thetas = NULL, L = 50, seed = NULL)

Arguments

x, y: Matrices representing empirical distributions.
p: Order of sliced Wasserstein distance.
thetas: Optionally, a matrix, each row of which represents a projection direction.
L: If no thetas are provided, L random projection directions are generated.
seed: Optional random seed.

Value

Estimated sliced Wasserstein distance of order p between x and y.

Examples

M1 <- matrix(rnorm(50), ncol = 5)
M2 <- matrix(rnorm(250), ncol = 5)
sliced_wasserstein(M1, M2) # random projection directions
#> [1] 0.6550946
cardinal_axes <- diag(1, 5)
sliced_wasserstein(M1, M2, thetas = cardinal_axes)
#> [1] 0.5931266
first_two_axes <- cardinal_axes[1:2, ]
sliced_wasserstein(M1, M2, thetas = first_two_axes)
#> [1] 0.6565441