gpuCorPerm: Permutation Tests of Correlations, With a GPU

In gputools: GPU Drop-Ins for Statistics on Wide Data

Permutation Tests of Correlations, With a GPU

Description

Tests every correlation between the columns of x and those of y (or among the columns of x) by permutation: the rows of y are shuffled B times and each correlation's p-value is how often a shuffle gives one as strong. It also gives p-values adjusted for testing all the pairs at once, by Westfall and Young's maxT. Permutation p-values need no assumption of normality, which for small samples and skewed data the t test of gpuCor makes; each shuffle costs a whole correlation matrix, which the GPU computes in one matrix product.

Usage

gpuCorPerm(x, y = NULL, B = 1000L, method = "pearson",
		precision = getOption("gputools.precision", "single"))

Arguments

x	a numeric matrix whose columns are the variables, with no missing values.
y	a numeric matrix with the same number of rows, or NULL for x with itself.
B	the number of permutations. The smallest p-value possible is 1 / (B + 1).
method	"pearson" or "spearman".
precision	"single" or "double": the floating point precision the GPU computes in; see gpuCor.

Details

The permutations are drawn with sample.int, so set.seed makes the results reproducible. Each is applied to the rows of y (of a copy of x when y is NULL), and all of a permutation's correlations are computed from it, so the tests share their permutations, as the maxT adjustment needs.

The p-value of a correlation r is (1 + b) / (1 + B), where b of the B permutations gave a correlation with |r_b| \ge |r|: two-sided, and counting the observed data as one of the permutations (Phipson and Smyth 2010), so that it is never zero. The adjusted p-value counts instead the permutations whose largest |r_b| over all the tests reaches |r|: single-step maxT (Westfall and Young 1993), which controls the family-wise error rate.

The whole ncol(x) by ncol(y) matrix is held on the GPU, twice; for wider data, split the columns of y (the maxT adjustment is then within each part).

Value

A list:

coefficients	the correlations, as cor gives them.
p.value	the permutation p-values.
p.adjusted	the maxT adjusted p-values.
permutations	B.

With y = NULL the diagonal is NA.

References

Westfall, P. H. and Young, S. S. (1993) Resampling-Based Multiple Testing. Wiley.

Phipson, B. and Smyth, G. K. (2010) Permutation p-values should never be zero. Statistical Applications in Genetics and Molecular Biology 9, 39.

See Also

gpuCor, cor.test

Examples

set.seed(1)
# 15 samples of skewed data; one real association
x <- matrix(rexp(15 * 40), 15, 40)
y <- matrix(rexp(15 * 30), 15, 30)
y[, 1] <- y[, 1] + 2 * x[, 1]
res <- gpuCorPerm(x, y, B = 2000)
res$p.value[1, 1]
res$p.adjusted[1, 1]
min(res$p.adjusted[-1, -1])

gputools documentation built on Oct. 24, 2026, 5:07 p.m.