dcor_large: Distance correlation with optional blockwise computation

In dcorBSS: Distance-Correlation Based Methods for Blind Source Separation and Dependence Analysis

Distance correlation with optional blockwise computation

Description

Computes the distance correlation between x and y. If block_size = NULL, the standard full pairwise-distance computation is used. If block_size is a positive integer, a blockwise algorithm is used that avoids allocating the full n \times n distance matrices.

Usage

dcor_large(x, y, block_size = NULL)

Arguments

x	A numeric vector or numeric matrix. Rows are observations.
y	A numeric vector or numeric matrix. Rows are observations.
block_size	Either NULL or one positive integer. If NULL, the standard full computation is used, except in the univariate case where dccpp is used. If positive, the blockwise computation is used with that block size.

Details

If block_size = NULL and both inputs are univariate, the computation is delegated to the optimized dccpp implementation. In this special case, the computational complexity is of order O(n \log n), whereas the standard and blockwise multivariate implementations both have quadratic complexity.

Vectors are treated as one-column matrices.

Distance correlation is obtained by combining squared distance covariance terms for (x, y), (x, x), and (y, y).

If block_size is a positive integer, the same quantities are computed block by block. The rows of x and y are partitioned into consecutive blocks of size at most block_size. Distances are then computed only for one block pair at a time, and the contributions needed for distance covariance are accumulated across all block pairs. This can greatly reduce memory requirements for large n.

The block size does not need to divide the sample size. If the sample size is not a multiple of block_size, the final block is simply smaller.

The blockwise computation is intended for larger data sets where forming the full pairwise distance matrices may be memory intensive. It computes the same sample quantity as the standard version, up to possible small differences from floating-point arithmetic. It mainly reduces memory usage; the computational complexity remains of order O(n^2).

Smaller block sizes use less memory but may be somewhat slower. Larger block sizes use more memory and approach the standard full computation.

Value

A numeric scalar, the distance correlation.

References

Székely, G. J., Rizzo, M. L., and Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances. Annals of Statistics, 35(6), 2769–2794. doi:10.1214/009053607000000505.

Székely, G. J. and Rizzo, M. L. (2009). Brownian distance covariance. Annals of Applied Statistics, 3(4), 1236–1265. doi:10.1214/09-AOAS312.

Chaudhuri, A. and Hu, W. (2019). A fast algorithm for computing distance correlation. Computational Statistics & Data Analysis, 135, 15–24. doi:10.1016/j.csda.2019.01.016.

Examples

n <- 100
x <- matrix(rnorm(n * 3), n, 3)
y <- matrix(rnorm(n * 2), n, 2)

r1 <- dcor_large(x, y)
r2 <- dcor_large(x, y, block_size = 32L)

r1
r2
all.equal(r1, r2, tolerance = 1e-10)

dcorBSS documentation built on Nov. 10, 2026, 5:07 p.m.