ANM Mixture Model (ANM-MM)

Python implementation of the following paper

Causal Inference and Mechanism Clustering of A Mixture of Additive Noise Models.
Hu, Shoubo, Zhitang Chen, Vahid Partovi Nia, Laiwan Chan, and Yanhui Geng.
Advances in Neural Information Processing Systems. (NeurIPS) 2018.

Prerequisites

• numpy
• scipy
• sklearn

We test the code using Anaconda 4.3.30 64-bit for python 2.7 on Windows 10. Any later version should still work perfectly.

Running the tests

After installing all required packages, you can run test.py to see whether ANM-MM() could work normally.

The test code does the following:

1. it generates 100 observations (a (100, 2) numpy array) from two exponential functions. The first column is the cause X and the second is the effect Y.
2. ANM-MM is applied on the generated data to first conduct clustering and then infer the causal direction.

Apply ANM-MM on your data

Usage

Import ANM-MM using

from ANMMM import ANMMM_cd, ANMMM_clu

Apply ANM-MM on your data

# causal inference
direction = ANMMM_cd(data, lda)

# mechanism clustering
labels = ANMMM_clu(data, label, lda)

Description

Input of function ANMMM_cd() and ANMMM_clu()

Argument	Description
data	Numpy array with 2 columns and any number of rows. Rows represent i.i.d. samples, The variables in the first and second column are called X and Y, respectively.
label	List of true labels of each observation.
lda	The parameter λ which controls the importance of HSIC term.

Output of function ANMMM_cd()

Argument	Description
direction	1 - the first column is the cause; -1 - the second column is the cause; 0 - can not tell.

Output of function ANMMM_clu()

Argument	Description
labels	List of estimated clustering labels of each observation.

Authors

• Shoubo Hu - shoubo [dot] sub [at] gmail [dot] com
• Zhitang Chen - chenzhitang2 [at] huawei [dot] com

See also the list of contributors who participated in this project.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

• Hat tip to James Hensman for his elegant GP-LVM code.