Bayesian inference in decomposable graphical models using sequential Monte Carlo methods

This library contains Bayesian inference in decomposable (triangulated) graphical models based on sequential Monte Carlo methods. Currently supported functionalities include:

• Bayesian structure learning for discrete log-linear and Gaussian data.

• Estimation of the number of decomopsable graphs with a given number of nodes.

• Predictive classification using Bayesian model averaging (BMA).

• Random generation of junction trees (the Christmas tree algorithm).

Installation

If graphviz is not installed, you can install it from brew / aptitude / pacman for example

$ brew install graphviz

On Ubuntu you might need to run

sudo apt-get install python-dev graphviz libgraphviz-dev pkg-config

Then run

$ pip install trilearn

It is also possible to pull trilearn as a docker image by

$ docker pull onceltuca/trilearn

Running the tests

$ make test

Usage

See the Jupyter notebooks for examples of usage.

Scripts

Continuous data

To approximate the underlying decomposable graph posterior given the dataset sample_data/data_ar1-5.csv run

$ pgibbs_ggm_sample -N 50 -M 1000 -f sample_data/data_ar1-5.csv -o results_ggm

this will produce a file containing the Markov chain generated by the particle Gibbs algorithm. In order to analyze the chain run

$ analyze_graph_tajectories -i results_ggm -o results_ggm/plots

this will produce a bunch of files in the current directory to be analyzed.

Discrete data

The data set examples/data/czech_autoworkers.csv contains six binary variables. To generate a particle Gibbs trajectory of decomposable graphs type

$ pgibbs_loglinear_sample -N 50 -M 300 -f sample_data/czech_autoworkers.csv  -o results_loglin

and

$ analyze_graph_tajectories -i results_loglin -o results_loglin/plots

this will produce a number of files in the current directory.

Estimate the number of decomposable graphs

To estimate the number of decomposable graphs with up to 15 nodes run for example

$ count_chordal_graphs -p 15 -N 20000

Built With

• NetworkX

• NumPy

• Scipy

• Pandas

• Seaborn

Authors

• Felix L. Rios just send me an e-mail in case of any questions, felix.leopoldo.rios at gmail com

References

• J. Olsson, T. Pavlenko, and F. L. Rios. Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods. Electron. J. Statist., 13(2):2865–2897, 2019.
• J. Olsson, T. Pavlenko, F. L. Rios, Sequential sampling of junction trees for decomposable graphs, Statistics and Computing 32, 80, 2022
• T. Pavlenko, F. L. Rios, Graphical posterior predictive classifier: Bayesian model averaging with particle Gibbs, Theor. Probability and Math. Statist. 109: 81-99, 2023

License

This project is licensed under the Apache 2.0 License - see the LICENSE file for details

Acknowledgments

• Jim Holmstrom