Kernel Conditional Independence Tests

[rflperry]

Testing for conditional independence, X \indep Y | Z, is a common problem within causal discovery and feature selection. The following two kernel-based methods are able to perform this test without too many assumptions.

Kernel Conditional Independence (KCI) Test [paper][matlab code]

• Well known and commonly used in practice from my understanding.
• Computes kernel matrices in each of the variables X, Y, Z to compute a test statistic.
• Approximates the null distribution using a Gamma distribution. No permutation test available.
• [Edit] Python code in this package

A Permutation-Based Kernel Conditional Independence (KCIP) Test [paper][matlab code]

• Potentially an improvement to KCI but not as widely used or known, partially due to speed constraints.
• Computes kernel matrices in each of the variables X, Y, Z.
• Also provides a two-layer bootstrap permutation test by:
  • Finding a permutation Y' of Y based on minimizing the permuted Z distances.
  • Performing a two-sample test (MMD) on the original (X, Y, X) and permuted (X, Y', Z)
• Improves upon KCI when it's null is not well specified (compelx, higher-dimension Z), or if Z can be clustered well or is discrete.
• Also provides analytic approximates the null distribution using a Gamma distribution.

A nonparametric test based on regression error (FIT) [paper] [python code]

• A bit more fringe than KCI/KCIP but provides good simulation comparisons between all three methods plus more.
• Uses a nonparametric regression (in their case, a decision tree) to examine the change in predictive power based on including versus excluding some variables Z.
• Uses the mean squared error as a test statistic and an analytic Gaussian/T-test approach to compute a pvalue
• Seemingly efficient for large samples sizes as compared to other kernel based approaches.
• Interesting connections in that trees/forests are adaptive kernel methods and extensions to forests/honesty/leaf permutations.

[zdbzdb123123]

Interested

[sampan501]

@zdbzdb123123 which one? Once you have decided, please make a new issue with the description and link to this issue

[zdbzdb123123]

KCI, and will do

[rflperry]

I also discovered a package with python code, matlab wrappers.

1. KCI code
2. KCIP code
   The package has some other things, including a small notebook with simulations to test the tools.

[MatthewZhao26]

Interested in FIT