Add M nearest-neighbour Chatterjee correlation (#990)#1414
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Summary
Implements the revised (M nearest-neighbour) Chatterjee rank correlation of
Lin & Han (2021), addressing #990. Adds a new function
chatterjee_correlation_mnn(u, v, M)alongside the existingchatterjee_correlation, with the same C++11 and C++17 overload structure.The original coefficient has a detection boundary of n^(-1/4) for independence
testing, well short of the parametric n^(-1/2) rate. By using the M right
nearest neighbours of each point (rather than the single right neighbour) and
letting M grow with n, the revised statistic consistently estimates the same
dependence measure while approaching near-parametric efficiency. See Lin & Han,
On boosting the power of Chatterjee's rank correlation, Biometrika 110(2)
(2023) 283–299, arXiv:2108.06828.
Design notes
Separate function rather than an extended signature. The M-NN statistic
uses
min(R_i, R_j)and a different normalisation, so even at M = 1 it is notidentical to
chatterjee_correlation. A distinct function avoids silentlychanging existing results and keeps the statistical intent explicit.
Mis a required argument with no default.Rank base. The internal
rank()returns 0-based ranks; the paper'sformula uses 1-based ranks. The offset cancels in the existing M = 1 statistic
(which uses
|R_i - R_{i+1}|) but not undermin(.,.), so it is appliedexplicitly. This is noted in a comment where it matters.
Complexity. O(n log n + nM). Near-linear for small M; tends to O(n²) as
M → n.
Parallel path. The outer index loop is partitioned across threads into
disjoint ranges, each reading the shared rank vector read-only (indices up to
i + M may fall in a neighbouring range; there are no writes). This differs
from the M = 1 parallel path, which splits the data array for the
difference-based transform.
Ties / degenerate input. Like
chatterjee_correlation, the functionassumes distinct Y (continuous data). A constant Y returns a quiet NaN; this
is detected on the input directly, since
rank()collapses tied values.Choice of M. The asymptotic null variance is minimised at M ~ sqrt(n); the
choice is documented but left to the caller.
Tests
Added to
test_chatterjee_correlation.cpp, coveringfloat,double, andlong double:and strictly decreasing dependence), which require no external reference.
and Y.
The sequential path was verified locally under
b2withcxxstd=14andcxxstd=17(clang, arm64).