Home

Awesome

DAGs with NO TEARS :no_entry_sign::droplet:

[Update 12/8/22] Interested in faster and more accurate structure learning? See our new DAGMA library from NeurIPS 2022.

This is an implementation of the following papers:

[1] Zheng, X., Aragam, B., Ravikumar, P., & Xing, E. P. (2018). DAGs with NO TEARS: Continuous optimization for structure learning (NeurIPS 2018, Spotlight).

[2] Zheng, X., Dan, C., Aragam, B., Ravikumar, P., & Xing, E. P. (2020). Learning sparse nonparametric DAGs (AISTATS 2020, to appear).

<!-- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://arxiv.org/abs/1803.01422) ([NeurIPS 2018](https://nips.cc/Conferences/2018/), Spotlight) [Xun Zheng](https://www.cs.cmu.edu/~xunzheng/), [Bryon Aragam](https://www.bryonaragam.com/), [Pradeep Ravikumar](https://www.cs.cmu.edu/~pradeepr/), [Eric Xing](https://www.cs.cmu.edu/~epxing/). -->

If you find this code useful, please consider citing:

@inproceedings{zheng2018dags,
    author = {Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric P.},
    booktitle = {Advances in Neural Information Processing Systems},
    title = {{DAGs with NO TEARS: Continuous Optimization for Structure Learning}},
    year = {2018}
}

@inproceedings{zheng2020learning,
    author = {Zheng, Xun and Dan, Chen and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric P.},
    booktitle = {International Conference on Artificial Intelligence and Statistics},
    title = {{Learning sparse nonparametric DAGs}},
    year = {2020}
}

tl;dr Structure learning in <60 lines

Check out linear.py for a complete, end-to-end implementation of the NOTEARS algorithm in fewer than 60 lines.

This includes L2, Logistic, and Poisson loss functions with L1 penalty.

Introduction

A directed acyclic graphical model (aka Bayesian network) with d nodes defines a distribution of random vector of size d. We are interested in the Bayesian Network Structure Learning (BNSL) problem: given n samples from such distribution, how to estimate the graph G?

A major challenge of BNSL is enforcing the directed acyclic graph (DAG) constraint, which is combinatorial. While existing approaches rely on local heuristics, we introduce a fundamentally different strategy: we formulate it as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. In other words,

<img width="460" alt="characterization" src="https://user-images.githubusercontent.com/1810194/47379174-2eb1af00-d6c8-11e8-8dae-4626690127b9.png"/>

where h is a smooth function whose level set exactly characterizes the space of DAGs.

Requirements

Contents (New version)

Running a simple demo

The simplest way to try out NOTEARS is to run a simple example:

$ git clone https://github.com/xunzheng/notears.git
$ cd notears/
$ python notears/linear.py

This runs the l1-regularized NOTEARS on a randomly generated 20-node Erdos-Renyi graph with 100 samples. Within a few seconds, you should see output like this:

{'fdr': 0.0, 'tpr': 1.0, 'fpr': 0.0, 'shd': 0, 'nnz': 20}

The data, ground truth graph, and the estimate will be stored in X.csv, W_true.csv, and W_est.csv.

Running as a command

Alternatively, if you have a CSV data file X.csv, you can install the package and run the algorithm as a command:

$ pip install git+git://github.com/xunzheng/notears
$ notears_linear X.csv

The output graph will be stored in W_est.csv.

Examples: Erdos-Renyi graph

Examples: Scale-free graph

Other implementations