This repository contains the inference and simulation codes accompying the paper: X. Lou, Y. Hu, X. Li, Learning Linear Polytree Structural Equation Model, TMLR, 2025.

The majority of the code is written in Python 3 along with several assisting R scripts.

For Python, it requires netwowrkx and graphviz, pydot (for visualizing graphs only) packages in addition to standard packages such as numpy, scipy.

For R, we use the package bnlearn for the implementation of the comparative hill-climbing algorithm and benchmark data.

The code also requires a \data and \figure sub-folders to store results.

infer_polytree.py contains the functions for learning the CPDAG from data based on a linear polytree model, as well as functions for randomly generate polytree models and visualizing the graphs.

example_infer_vs_hc.py gives a simple example of applying the Chow-Liu algorithm to learn a polytree on a randomly generated SEM data, and compare the result with other algorithms (hill climbing, PC, polytree adapted PC).

polytree_simulation_vs_hc_PC.py test the performance of the Chow-Liu algorithm to learn randomly generated polytree models under various parameters p, n, r_min ($\rho_\min$), din_max (see the paper for details). The code produces Fig.1,2 of the paper (using pre-computed simulation data run_id=3,4). Note, the code may take a while to run with a large number of n and ntrial.

alarm_data.py applies the Chow-Liu algorithm to the benchmark data ALARM Beinlich et al. (1989), which is a DAG with 37 nodes and 46 edges. It produces Fig.3 of the paper.

asia_data.py applies the Chow-Liu algorithm to the benchmark data ASIA, Lauritzen and Spiegelhalter (1988), which is a DAG with 8 nodes and 8 edges. It produces Fig.4 of the paper.

earthquake_data.py applies the Chow-Liu algorithm to the benchmark data EARTHQUAKE, Korb and Nicholson, (2010). It produces Fig.5 of the paper.

The DAG benchmark ALARM data is downloaded from the online resources of the paper The Max-Min Hill-Climbing Bayesian Network Structure Learning Algorithm I. Tsamardinos, L. E. Brown, C. F. Aliferis, Machine Learning, 2006.

The DAG benchmark AISA and EARTHQUAKE data are from the R package bnlearn bnlearn and its Bayesian Network Repository.

We use a simple Pyhton implementation of the Kruskal MST algorithm from Pedro Lobato@GitHub, kruskal.py. We found it is faster than the buildt-in function from networkx.

Please give citations to the paper: X. Lou, Y. Hu, X. Li, Learning Linear Polytree Structural Equation Model, TMLR, 2025.