Learning Markov Network Structure with Decision Trees

Daniel Lowd and Jesse Davis

Online Appendix


Traditional Markov network structure learning algorithms perform a search for globally useful features. However, these algorithms are often slow and prone to finding local optima due to the large space of possible structures. Ravikumar et al. recently proposed the alternative idea of applying L1 logistic regression to learn a set of pairwise features for each variable, which are then combined into a global model. This paper presents the DTSL algorithm, which uses probabilistic decision trees as the local model. Our approach has two significant advantages: it is more efficient, and it is able to discover features that capture more complex interactions among the variables. Our approach can also be seen as a method for converting a dependency network into a consistent probabilistic model. In an extensive empirical evaluation on 13 datasets, our algorithm obtains comparable accuracy to three standard structure learning algorithms while running 1-4 orders of magnitude faster.


The structure learning code is based on the Libra project, and the weight learning code is based on the Alchemy project. Both are distributed under a modified BSD license (Libra license, Alchemy license), which permits free inclusion in other commercial or open-source projects. Other files and modifications are distributed under a similar modified BSD license.