MMD Two-Sample Test

Tests whether two samples come from the same distribution using the Maximum Mean Discrepancy (MMD). Uses a permutation test for inference.

Usage

mmd_test(
  x,
  y,
  kernel = kernel_spec(),
  n_permutations = 500L,
  alpha = 0.05,
  seed = NULL
)

Arguments

x

Numeric vector, matrix, or data.frame. First sample.

y

Numeric vector, matrix, or data.frame. Second sample.

kernel

Kernel specification. Default is RBF with median heuristic.

n_permutations

Integer. Number of permutations. Default is 500.

alpha

Numeric. Significance level. Default is 0.05.

seed

Integer or NULL. Random seed for reproducibility.

Value

An object of class "kernel_test_result" with components:

statistic

The observed MMD^2 statistic (unbiased).

p_value

Permutation p-value. The field is named p_value (with an underscore), not p.value; read result$p_value, or call tidy() for the broom-canonical p.value column.

method

"MMD".

n

Total sample size (n_x + n_y).

n_permutations

Number of permutations used.

null_distribution

Vector of permuted MMD^2 values.

kernel_x

Kernel specification used.

call

The matched call.

References

Gretton, A., Borgwardt, K. M., Rasch, M. J., Scholkopf, B., & Smola, A. (2012). A kernel two-sample test. JMLR, 13, 723-773.

See also

Other independence and two-sample tests: hsic_test()

Examples

set.seed(42)

# Same distribution
x <- matrix(rnorm(200), 100, 2)
y <- matrix(rnorm(200), 100, 2)
result <- mmd_test(x, y)
print(result)
#> 
#>    MMD Test
#> 
#> Statistic: -0.00292249 
#> P-value:   0.6327 
#> N:         200 
#> Perms:     500 
#> Kernel X:  rbf (bw = 1.601)
#> 

# Different distributions
y_shifted <- matrix(rnorm(200, mean = 1), 100, 2)
result <- mmd_test(x, y_shifted)
print(result)
#> 
#>    MMD Test
#> 
#> Statistic: 0.269115 
#> P-value:   0.0020 
#> N:         200 
#> Perms:     500 
#> Kernel X:  rbf (bw = 1.838)
#>