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fix knn chebyshev exactness - #91
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htymjun
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Nov 1, 2026
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- fix: Make the k-NN estimators exact for the Chebyshev metric
- chore: Bump version to 1.2.0
Verification against brute-force references and Kraskov, Stoegbauer & Grassberger, PRE 69, 066138 (2004) revealed five defects: 1. nanoflann's searchLevel() combines per-dimension cell offsets by summing them, which is a lower bound only for additive metrics. For the Chebyshev metric the cell distance is the maximum, so cells with true neighbours were pruned and k-NN radii were too large (~9% of the points in 2-D, 32% in 4-D). All estimators were affected. The new ChebyshevKDTree hides findNeighbors() with an exact L-infinity search; nanoflann itself is unchanged. 2. Points with zero marginal counts were dropped from the average, biasing I(1) for k = 1. Only degenerate points (eps == 0) are skipped. 3. 1-D marginal counts compared x_j < v + eps, so rounding could count the boundary point; the edges are now re-tested in difference form. 4. shannon_entropy used the Euclidean unit-ball constant with Chebyshev distances (bias of -0.24 nats in 2-D, -1.13 in 4-D); c_d = 1 now. 5. information_flow_causal_map accepted per-variable tau although several code paths read only tau[0]; a non-uniform tau now raises ValueError. After the fix, mutual_info, conditional_mutual_info, shannon_entropy, KL_div, Theiler-window MI, information_flow, transfer_entropy and all information_flow_causal_map paths agree with exhaustive-distance references to 1e-12. Before the fix, the mean I(1) of independent variables was down to -0.11 nats (|z| up to 297), Fig. 4 of Kraskov et al. was missed by 0.10-0.18 nats, and I(X1; X2..X8) for equicorrelated Gaussians (r = 0.9) gave 0.549 instead of 1.086. After the fix the independence conjecture holds within 2 sem in 45 cases, Fig. 4 and Fig. 5 match the digitized paper values within 0.0006 and 0.004, and Fig. 14 matches the exact values within 0.007. The exact search is slower: x1.2-1.3 for the 2-D joint space of 1-D variables, x5 in 4-D. Tests: test_knn_exact.py (brute-force agreement, multi-dimensional entropy and MI, tau validation) and test_ksg_kraskov.py (independence, Figs. 4 and 5, exact MI; draws Figs. 4, 5 and 14 into tests/results/kraskov.png). test_MI.py now covers rho = 0.1-0.9 and k = 1-30 with statistical tolerances. The pre-fix build fails 10 of the 11 Kraskov tests. Co-Authored-By: Claude Opus 5.5 <[email protected]>
The k-NN fixes change the numerical output of every estimator. Co-Authored-By: Claude Opus 5.5 <[email protected]>
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