Most real-world problems require dealing with incomplete data. Bayesian networks robustly handle missing values during inference, but learning them from incomplete datasets is not straightforward. Using the structural expectation-maximization algorithm is the most common approach to address this problem, but its main limitation is its highly demanding computational cost. As structural expectation-maximization spends most of its running time performing inference, efficient inference is essential. This can be achieved by bounding the inference complexity of the Bayesian network candidates. This paper proposes a tractable adaptation of the structural expectation-maximization algorithm that theoretically provides guarantees on its convergence. We perform experiments that support empirically our claims.
This software has been developed as a Python 2.7.15 package and includes some functionalities in Cython and C++11 (version 5.4.0). Consequently, it is needed a Python environment and internet connectivity to download additional package dependencies. Python software can be downloaded from https://www.python.org/downloads/.
We provide the steps for a clean installation in Ubuntu 16.04. This software has not been tried under Windows.
The package also uses the following dependencies.
| Library | Version | License |
|---|---|---|
| pandas | 0.23 | BSD 3 |
| numpy | 1.14.3 | BSD |
| Cython | 0.28.2 | Apache |
| cloudpickle | 0.5.3 | BSD 3 |
| scikit-learn | 0.20.2 | BSD 3 |
They can be installed through the following sentence: sudo pip install "Library" where Library must be replaced by the library to be installed.
Open the folder where you have saved TSEM project files (e.g., "~/Downloads/TSEM") and compile Cython files running the following commands in the command console:
python2.7 setup_dt.py build_ext --inplace
python2.7 setup_tw.py build_ext --inplace
python2.7 setup_et.py build_ext --inplace
python2.7 setup_cplus.py build_ext --inplace
python2.7 setup_cplus_data.py build_ext --inplace
python2.7 setup_gs.py build_ext --inplace
python2.7 setup_etc.py build_ext --inplace
File "example.py" provides a demo that shows how to use the code to: learn Bayesian networks in the presence of missing values, interpreting the returned models, and performing inference.