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This is the official repository of the paper Efficient Neural Causal Discovery without Acyclicity Constraints by Phillip Lippe, Taco Cohen, and Efstratios Gavves. Presented at the International Conference on Learning Representations (ICLR), 2022.

Learning the structure of a causal graphical model using both observational and interventional data is a fundamental problem in many scientific fields. A promising direction is continuous optimization for score-based methods, which efficiently learn the causal graph in a data-driven manner. However, to date, those methods require slow constrained optimization to enforce acyclicity or lack convergence guarantees. In this work, we present ENCO, an efficient structure learning method leveraging observational and interventional data. ENCO formulates the graph search as an optimization of independent edge likelihoods with the edge orientation being modeled as a separate parameter. Consequently, we can provide convergence guarantees of ENCO under mild conditions without constraining the score function with respect to acyclicity. In experiments, we show that ENCO handles various graph settings well, and even recovers graphs with up to 1,000 nodes in less than nine hours of compute using a single GPU (NVIDIA RTX3090) while having less than one mistake on average out of 1 million possible edges. Further, ENCO can handle and detect latent confounders.

The code is written in PyTorch (1.9) and Python 3.8. Higher versions of PyTorch and Python are expected to work as well.

We recommend to use conda for installing the requirements. If you haven't installed conda yet, you can find instructions here. The steps for installing the requirements are:

1. Create a new environment from the provided YAML file:

   conda env create -f environment.yml
   

   The environment installs PyTorch with CUDA 11.1. Adjust the CUDA version if you want to install it with CUDA 10.2, or remove it from the environment file if you want to install it on a CPU-only system.

2. Activate the environment

   conda activate enco
   

To reproduce the experiments in the paper, we provide datasets of causal graphs for the synthetic, confounder, and real-world experiments. The datasets can be download by executing download_datasets.sh (requires approx. 600MB disk space). Alternatively, the datasets can be accessed through this link (unzip the file in the causal_graphs folder).

The repository is structured in three main folders:

• causal_graphs contains all utilities for creating, visualizing and handling causal graphs that we experiment on.
• causal_discovery contains the code of ENCO for structure learning.
• experiments contains all utilities to run experiments with ENCO on various causal graphs.

Details on running experiments as well as the commands for reproducing the experiments in the paper can be found in the experiments folder.

We created a quick walkthrough tutorial that goes through the most important functions/components in the repository in walkthrough.ipynb. In short, ENCO can be applied as follows:

from causal_graphs.graph_generation import generate_categorical_graph, get_graph_func  # Functions for generating new graphs
from causal_discovery.enco import ENCO

# Create a graph on which ENCO should be applied
graph = generate_categorical_graph(num_vars=8, 
                                   min_categs=10,
                                   max_categs=10,
                                   graph_func=get_graph_func('random'),
                                   edge_prob=0.4,
                                   seed=42)

# Create ENCO object
enco_module = ENCO(graph=graph)
if torch.cuda.is_available():
    enco_module.to(torch.device('cuda:0'))

# Run causal discovery
predicted_adj_matrix = enco_module.discover_graph(num_epochs=10)

If you use this code, please consider citing our work:

@inproceedings{lippe2022enco,
 author = {Lippe, Phillip and Cohen, Taco and Gavves, Efstratios},
 booktitle = {International Conference on Learning Representations},
 title = {Efficient Neural Causal Discovery without Acyclicity Constraints},
 url = {https://openreview.net/forum?id=eYciPrLuUhG},
 year = {2022}
}