# Kernel-based conditional independence (KCI) test and independence test

Kernel-based conditional independence (KCI) test and independence test 1. To test if x and y are conditionally or unconditionally independent on Z. For unconditional independence tests, Z is set to the empty set.

## Usage

    from causal-learn.utils.cit import kci
    p = kci(data, X, Y, condition_set, kernelX, kernelY, kernelZ)

## Parameters

X, Y, and condition_set: data matrices of size number_of_samples * dimensionality. Z could be None.

KernelX/Y/Z (condition_set): [‘GaussianKernel’, ‘LinearKernel’, ‘PolynomialKernel’]. (For ‘PolynomialKernel’, the default degree is 2. Currently, users can change it by setting the ‘degree’ of ‘class PolynomialKernel()’.

## Returns

p: the p value.

1

  Zhang, K., Peters, J., Janzing, D., & Schölkopf, B. (2011, July). Kernel-based Conditional Independence Test and Application in Causal Discovery. In 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011) (pp. 804-813). AUAI Press.