High-dimensional causal discovery from Inverse Covariance matrices by Independence-based Decomposition (ICID).

This package implements the ICID algorithm, which consists of the following two consecutive steps:

(IC) S* = argmin loss(S) - logdet(S) + lambda_1 |S|_1,
            subject to S > 0 (symmetric positive definite),

(ID) B* = argmin |S* - phi(B)|^2 + lambda_1' |B|_1,
            subject to B in DAG and supp(B) \subset supp(S).

For the ID problem, phi(B) = (1/s)(I-B)(I-B)' is a quadratic matrix function of B.

Core functions

• icid/icid.py - Implementation of the ICID algorithm
• icid/SparseMatDecomp.py - Computation of the Independence-based Decomposition of an input inverse covariance matrix
• icid/Loram.py - Computation of proximal mappings with respect to the DAG characteristic function h.

Requirements

• Python 3.6+
• numpy
• scipy
• scikit-learn : the module GraphLasso (named GraphicalLasso in more recent version of scikit-learn) is used for the step (IC).
• python-igraph: Install igraph C core and pkg-config first.
• pywt: for the soft-threshod function (TODO: copy this function individually to remove this unnecessary dependency)
• NOTEARS/utils.py - graph simulation, data simulation, and accuracy evaluation from [Zheng et al. 2018]

Running a demo

$ cd icid-exp/
$ make 
$ python demo_icid.py