Latent representation based Conditional Independence Test (LCIT)

This is the implementation of our papers:

• Bao Duong and Thin Nguyen. Conditional Independence Testing via Latent Representation Learning. In IEEE International Conference on Data Mining (ICDM), 2022.
• Bao Duong and Thin Nguyen. Normalizing flows for conditional independence testing. Knowledge and Infomation System 66, 357–380 (2024).

Dependencies

• Common packages: numpy, pandas, scikit-learn, seaborn, scipy, tqdm, yaml.
• For LCIT: PyTorch 1.12, PyTorch-Lightning 1.5.3.
• (Optional) For KCIT: causal-learn 0.1.2.3 (https://github.com/cmu-phil/causal-learn).
• (Optional) For CCIT: CCIT 0.4 (https://github.com/rajatsen91/CCIT).

Alternatively, the pixi.lock and pixi.toml files can be used to reproduce our workable environment via pixi install (see pixi for more details).

Demo

import numpy as np, seaborn as sns, matplotlib.pyplot as plt
from src.citests import LCIT
np.random.seed(0)

# Case 1 (Conditional Independent): X <- Z -> Y
N, d = 200, 3
Z = np.random.uniform(-2, 2, size=(N, d))
X = Z @ np.random.randn(d) + np.random.uniform(-0.2, 0.2, size=N)
Y = Z @ np.random.randn(d) + np.random.uniform(-0.2, 0.2, size=N)

e_x, e_y, p_value = LCIT(X, Y, Z, return_latents=True)
sns.jointplot(x=e_x, y=e_y)
plt.show()
print(f'{p_value = :.2f}') # 0.51
if p_value > 0.05:
    print('[Correct] Failed to reject H0 (X _||_ Y | Z)')
else:
    print('[Incorrect] Reject H0 (X _||_ Y | Z)')

# Case 2 (Conditional Dependent): X -> Z -> Y <- X
N, d = 1000, 10
X = np.random.uniform(-0.2, 0.2, size=N)
Z = np.outer(X, np.random.randn(d) * 5) + np.random.uniform(-0.2, 0.2, size=(N, d))
Y = X * np.random.randn() + Z @ np.random.randn(d) + np.random.uniform(-0.2, 0.2, size=N)

p_value = LCIT(X, Y, Z, n_components=16, hidden_sizes=[4, 4])
print(f'{p_value = :.2f}') # 0.00
if p_value > 0.1:
    print('[Incorrect] Failed to reject H0 (X _||_ Y | Z)')
else:
    print('[Correct] Reject H0 (X _||_ Y | Z)')

See demo.py for more details.

Running experiments

For example, to run the "Effect of sample size" experiment (Figure 4 in the paper):

python experiments/exp_samplesize/main.py --methods LCIT SCIT --n_jobs=8

where available methods are CCIT, KCIT, SCIT, and LCIT; n_jobs is the number of parallel jobs to run.

Modifiable configurations are stored in experiments/exp_*/config/, and result dataframes are stored in experiments/exp_*/results/ after the command is finished.

Citation

If you find our code helpful, please cite us as:

@inproceedings{duong2022conditional,
	author = {Bao Duong and Thin Nguyen},
	booktitle = {2022 IEEE International Conference on Data Mining (ICDM)},
	pages = {121-130},
	title = {Conditional Independence Testing via Latent Representation Learning},
	year = {2022}
}