Tests whether two variables are independent using the Hilbert-Schmidt Independence Criterion (HSIC). Uses a permutation test for inference.
Usage
hsic_test(
x,
y,
kernel_x = kernel_spec(),
kernel_y = kernel_spec(),
n_permutations = 500L,
alpha = 0.05,
seed = NULL
)Arguments
- x
Numeric vector, matrix, or data.frame. First variable.
- y
Numeric vector, matrix, or data.frame. Second variable.
- kernel_x
Kernel specification for
x. Default is RBF with median heuristic.- kernel_y
Kernel specification for
y. Default is RBF with median heuristic.- n_permutations
Integer. Number of permutations for the null distribution. 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 HSIC test statistic.
- p_value
Permutation p-value.
- method
"HSIC".- n
Sample size.
- n_permutations
Number of permutations used.
- null_distribution
Vector of permuted HSIC values.
- kernel_x, kernel_y
Kernel specifications used (with resolved bandwidths).
- call
The matched call.
References
Gretton, A., Fukumizu, K., Teo, C. H., Song, L., Scholkopf, B., & Smola, A. J. (2008). A kernel statistical test of independence. NeurIPS, 20.
See also
Other independence and two-sample tests:
mmd_test()
Examples
set.seed(42)
n <- 200
x <- rnorm(n)
# Dependent case
y_dep <- x^2 + rnorm(n, sd = 0.5)
result <- hsic_test(x, y_dep)
print(result)
#>
#> HSIC Test
#>
#> Statistic: 0.0220599
#> P-value: 0.0020
#> N: 200
#> Perms: 500
#> Kernel X: rbf (bw = 0.9284)
#> Kernel Y: rbf (bw = 0.9302)
#>
# Independent case
y_ind <- rnorm(n)
result <- hsic_test(x, y_ind)
print(result)
#>
#> HSIC Test
#>
#> Statistic: 0.000759494
#> P-value: 0.5908
#> N: 200
#> Perms: 500
#> Kernel X: rbf (bw = 0.9284)
#> Kernel Y: rbf (bw = 0.91)
#>