Conditional independence tests

Two tests are bundled. Both implement the CITest protocol, so you can also write your own and pass it as ci_test= to CDANs.

Picking a test

Test	Cost	Assumes	Use when
FisherZ	O(n)	linear, Gaussian	data is approximately linear-Gaussian
KCITest	O(n³)	none	dependencies may be nonlinear; surrogate-dependence check

Pick by name (ci_test="fisherz" or "kci") or by passing an instance for custom configuration.

CITest

Bases: Protocol

Protocol that every conditional-independence test must implement.

pvalue

pvalue(x: ndarray, y: ndarray, z: ndarray | None = None) -> float

Return the p-value of testing X ⊥ Y | Z.

Parameters:

Name	Type	Description	Default
x	ndarray	(n_samples,) or (n_samples, d_x) array.	required
y	ndarray	(n_samples,) or (n_samples, d_y) array.	required
z	ndarray | None	(n_samples, d_z) array of conditioning variables, or None for an unconditional test.	None

Returns:

Type	Description
float	p-value in [0, 1]. Larger values mean stronger evidence for independence.

FisherZ

Fisher's Z conditional independence test (partial correlation based).

KCITest

KCITest(
    width_heuristic: str = "empirical",
    width: float | None = None,
    epsilon: float = 0.001,
)

Kernel-based Conditional Independence test (Zhang et al., 2011).

Suitable for both linear and nonlinear, Gaussian and non-Gaussian relationships. Substantially slower than :class:FisherZ — O(n^3) per call — so prefer FisherZ for linear-Gaussian benchmarks and reach for KCI when the residual structure is plausibly nonlinear.

Parameters:

Name	Type	Description	Default
width_heuristic	str	How to set the Gaussian kernel bandwidth. "empirical" (default) uses the sample-size-dependent constants from the reference KCI implementation. "median" uses the median pairwise-distance heuristic. "manual" requires width to be passed.	'empirical'
width	float | None	Manual precision parameter 1 / sigma^2. Used only when width_heuristic="manual".	None
epsilon	float	Regularization for the conditional residualization step. 1e-3 matches the reference.	0.001

get_ci_test

get_ci_test(name: str | CITest, **kwargs) -> CITest

Resolve a CI test by name, or return one already given.

Parameters:

Name	Type	Description	Default
name	str | CITest	Either a string ("fisherz" or "kci") or an object that already implements the :class:CITest protocol.	required
**kwargs		Forwarded to the test constructor when name is a string.	{}

Returns:

Type	Description
CITest	A ready-to-use CI test instance.