How to Choose a Conditional Independence Test

Choosing the right conditional independence (CI) test depends on the type of your data and the assumptions you are willing to make about the underlying dependence. citk ships 19 tests organised under the six survey families plus four adapter strategies; this guide gives a practical mapping from data + assumptions to tests.

Key Considerations

1. Data Type

• All continuous:

  • fisherz_citk: linear, Gaussian — fastest baseline.

  • spearman: monotonic but not necessarily linear — robust non-parametric alternative.

  • kci: kernel-based, captures arbitrary non-linear dependence.

  • rcit, rcot: random-Fourier-feature approximations to KCI; faster on larger samples.

  • cmiknn: kNN-based conditional mutual information with local-permutation p-values.

• All discrete (categorical):

  • gsq (G-test) or chisq (Chi-Square): classical contingency-table tests.

  • dummy_fisherz: one-hot encoding adapter that aggregates Fisher-Z calls; competitive when categorical cardinalities are moderate.

• Mixed continuous + discrete:

  • cmiknn_mixed: mixed-type kNN CMI estimator (tigramite).

  • mcmiknn: another mixed-type kNN CMI implementation (vendored from upstream hpi-epic/mCMIkNN).

  • regci: parametric likelihood-ratio test using GLM regression chosen per response type (continuous → linear, discrete → logistic).

  • ci_mm: symmetric likelihood-ratio test from R MXM that runs both regression directions and combines them.

  • gcm, wgcm, pcm: ML-residualisation tests using random forest regression (via pycomets); flexible, asymptotically calibrated, and the RF nuisance regressions handle continuous, discrete, or mixed inputs natively.

  • disc_chisq, disc_gsq: equal-frequency discretisation adapters around classical discrete tests.

  • hartemink_chisq: information-preserving Hartemink discretisation (via R bnlearn) + Chi-Square; better dependence preservation than equal-frequency binning.

2. Relationship Type

• Linear: fisherz_citk is the computationally efficient choice when both Gaussianity and linearity hold.

• Monotonic: spearman works on ranks; robust to non-linearities as long as the relationship is monotonic.

• Non-linear / complex: kernel tests (kci, rcit, rcot), kNN-based tests (cmiknn, cmiknn_mixed, mcmiknn), and ML-residualisation tests (gcm, wgcm, pcm) are all designed to detect arbitrary dependence at higher computational cost. wgcm and pcm add power on alternatives where the dependence is localised in the conditioning space or where the predictor is weakly identified.

3. Sample Size

• Small samples: classical tests (fisherz_citk, spearman, chisq, gsq) are most reliable; non-parametric and ML-based tests need more data for stable estimation.

• Large samples: kernel tests (especially exact kci) become expensive — prefer rcit/rcot for random-feature approximations, or gcm/wgcm/pcm for ML-residualisation with linear cost.

• Very large samples: kci is roughly quadratic in \(n\); consider capping or switching to a faster family.

Summary Table

Test Name	Family	Data Type	Relationship Type	Key Assumption(s)
fisherz_citk	Partial Correlation	Continuous	Linear	Approximate Gaussianity
spearman	Partial Correlation	Continuous	Monotonic	Monotonicity
chisq	Contingency Table	Discrete	Any	Adequate cell counts
gsq	Contingency Table	Discrete	Any	Adequate cell counts
regci	Regression	Mixed or continuous	Any (within model class)	Correct GLM specification per variable type; requires tigramite
ci_mm	Regression	Mixed	Any (within model class)	Correct linear/logistic per variable; requires rpy2 + R MXM
cmiknn	Nearest Neighbor	Continuous	Any	Sample size adequate for kNN density estimation; requires tigramite
cmiknn_mixed	Nearest Neighbor	Mixed	Any	Variable types declared via data_type; requires tigramite
mcmiknn	Nearest Neighbor	Mixed	Any	Vendored upstream mCMIkNN; no extra install required
kci	Kernel	Continuous	Any	Suitable kernel choice; cost is at least quadratic in \(n\)
rcit	Kernel	Continuous	Any	Random-feature approximation; requires rpy2 + R RCIT
rcot	Kernel	Continuous	Any	Random-feature approximation with reduced-dim conditioning; requires rpy2 + R RCIT
gcm	Machine-Learning-Based	Mixed or continuous	Any	Consistent nuisance regression; requires pycomets
wgcm	Machine-Learning-Based	Mixed or continuous	Any (esp. localised)	Consistent nuisance regression + sample splitting; requires pycomets
pcm	Machine-Learning-Based	Mixed or continuous	Any (assumption-lean)	Consistent residualisation; requires pycomets
disc_chisq	Adapter Strategies	Mixed or continuous	Any	Discretisation preserves dependence; ChiSq cell-count rule
disc_gsq	Adapter Strategies	Mixed or continuous	Any	Discretisation preserves dependence; GSq cell-count rule
dummy_fisherz	Adapter Strategies	Mixed or discrete	Any (encoded space)	One-hot encoding fidelity; combined p-values approximation
hartemink_chisq	Adapter Strategies	Mixed or continuous	Any	Information-preserving discretisation; requires rpy2 + R bnlearn