HSIC independence test with gamma approximation

Faithful port of hsic_test_gamma() (hsic.py). O(n^2) in the sample size because it forms the full n x n Gram matrices; not recommended for n in the thousands.

Usage

hsic_test_gamma(X, Y)

Arguments

X

numeric vector or matrix (n x d)

Y

numeric vector or matrix with the same number of rows as X

Value

list(stat = HSIC test statistic, p = gamma-approximated p-value)

Details

Either argument may be a matrix (n x d); its columns are combined into a single Gaussian kernel over row-wise Euclidean distances, exactly as in the upstream multivariate implementation (used by RESIT, which tests a residual against the joint distribution of several predictors). The variables are not standardized beforehand (upstream behavior), so with wildly different column scales the largest-scale column dominates the distance.

The gamma-approximation variance estimator is only defined for n >= 6 (its closed form divides by (n-1)(n-2)(n-3)); below that this errors instead of silently returning a NaN p-value that would otherwise propagate into NA-valued rejection decisions in callers. A constant input (zero variance in every column) carries no dependence information, so it is treated as trivially independent (p = 1) rather than routed through the degenerate kernel-width / centered-Gram-matrix computation.