New skeleton-based approaches for Bayesian structure learning of Bayesian networks

Authors:
AndréS R. Masegosa;SerafíN Moral
Affiliations:
Department of Computer Science and Artificial Intelligence, University of Granada, Spain;Department of Computer Science and Artificial Intelligence, University of Granada, Spain
Venue:
Applied Soft Computing
Year:
2013

Citing 12
Cited 0

Probabilistic reasoning in intelligent systems: networks of plausible inference

Probabilistic reasoning in intelligent systems: networks of plausible inference
A Bayesian Method for the Induction of Probabilistic Networks from Data

Machine Learning
Learning Bayesian Networks: The Combination of Knowledge and Statistical Data

Machine Learning
Time and sample efficient discovery of Markov blankets and direct causal relations

Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Exact Bayesian Structure Discovery in Bayesian Networks

The Journal of Machine Learning Research
The max-min hill-climbing Bayesian network structure learning algorithm

Machine Learning
Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move

Machine Learning
A Recursive Method for Structural Learning of Directed Acyclic Graphs

The Journal of Machine Learning Research
Using Markov Blankets for Causal Structure Learning

The Journal of Machine Learning Research
Local Causal and Markov Blanket Induction for Causal Discovery and Feature Selection for Classification Part I: Algorithms and Empirical Evaluation

The Journal of Machine Learning Research
Learning Bayesian networks by hill climbing: efficient methods based on progressive restriction of the neighborhood

Data Mining and Knowledge Discovery
A Bayesian stochastic search method for discovering Markov boundaries

Knowledge-Based Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

Automatically learning the graph structure of a single Bayesian network (BN) which accurately represents the underlying multivariate probability distribution of a collection of random variables is a challenging task. But obtaining a Bayesian solution to this problem based on computing the posterior probability of the presence of any edge or any directed path between two variables or any other structural feature is a much more involved problem, since it requires averaging over all the possible graph structures. For the former problem, recent advances have shown that search+score approaches find much more accurate structures if the search is constrained by a previously inferred skeleton (i.e. a relaxed structure with undirected edges which can be inferred using local search based methods). Based on similar ideas, we propose two novel skeleton-based approaches to approximate a Bayesian solution to the BN learning problem: a new stochastic search which tries to find directed acyclic graph (DAG) structures with a non-negligible score; and a new Markov chain Monte Carlo method over the DAG space. These two approaches are based on the same idea. In a first step, both employ a previously given skeleton and build a Bayesian solution constrained by this skeleton. In a second step, using the preliminary solution, they try to obtain a new Bayesian approximation but this time in an unconstrained graph space, which is the final outcome of the methods. As shown in the experimental evaluation, this new approach strongly boosts the performance of these two standard techniques proving that the idea of employing a skeleton to constrain the model space is also a successful strategy for performing Bayesian structure learning of BNs.