We introduce PairSwap-ICI, a novel testing algorithm to assess the conditional independence of $X$ and $Y$ given $Z$, under the assumption that $X$ is stochastically increasing in $Z$.

• simulations/
  Contains code to reproduce the results in Section 5 of the paper.
  Example: Simulation studies for evaluating the power and type-I error control of PairSwap-ICI test.

• real_data_analysis/
  Contains code to reproduce the results in Section 6, analyzing real-world dataset (a diabetes example).

• utils/
  Contains utility functions required for the implementation of the PairSwap-ICI test.

• cross_bin_matching
  Implements cross-bin matching for a user-specified number of bins $K$.

• neighbour_matching Implements neighbour matching, which matches $(Y,Z)$ tuples based on their nearest neighbours in $Z$-space.

• PairSwapICI_test Computes the $p$-value for the PairSwap-ICI test, given a dataset of $(X,Y,Z)$ and a matching strategy $M$ (e.g., neighbour or cross-bin matching).

• marg_indep_test Tests the marginal independence hypothesis $H_0:X\perp Y$, given a dataset of $(X,Y,Z)$.

Clone the repository to get started:

git clone https://github.com/jake-soloff/shape-constrained-CIT.git
cd shape-constrained-CIT

Ensure you have the required Python libraries installed (e.g., numpy, scipy). Use the following command to install them:

pip install -r requirements.txt

Below are examples for computing $p$-values using PairSwap-ICI test with different matching strategies.

Given $n$ samples of $(X,Y,Z)$ (each univariate), implement the PairSwap-ICI test with neighbour matching as follows:

from utils import neighbour_matching, PairSwapICI_test

# Generate or load your data (X, Y, Z)
# X, Y, Z = ...

# Create neighbour matching
M = neighbour_matching(Y, Z)

# Compute the p-value
p = PairSwapICI_test(X, Y, M, nperm)

To use cross-bin matching, choose a desired number of bins $K$:

from utils import cross_bin_matching, PairSwapICI_test

# Generate or load your data (X, Y, Z)
# X, Y, Z = ...

# Create cross-bin matching with your chosen number of bins K
K = 10  # Example: 10 bins
M = cross_bin_matching(Y, Z, K)

# Compute the p-value
p = PairSwapICI_test(X, Y, M)