Falcon Optimization Algorithm for Bayesian Networks Structure Learning

In machine-learning, one of the useful scientific models for producing the structure of knowledge is Bayesian network, which can draw probabilistic dependency relationships between variables. The score and search is a method used for learning the structure of a Bayesian network. The authors apply the Falcon Optimization Algorithm (FOA) as a new approach to learning the structure of Bayesian networks. This paper uses the Reversing, Deleting, Moving and Inserting operations to adopt the FOA for approaching the optimal solution of Bayesian network structure. Essentially, the falcon prey search strategy is used in the FOA algorithm. The result of the proposed technique is compared with Pigeon Inspired optimization, Greedy Search, and Simulated Annealing using the BDeu score function. The authors have also examined the performances of the confusion matrix of these techniques utilizing several benchmark data sets. As shown by the evaluations, the proposed method has more reliable performance than the other algorithms including producing better scores and accuracy values

Scale Up Bayesian Network Learning

Bayesian networks are widely used graphical models which represent uncertain relations between the random variables in a domain compactly and intuitively. The first step of applying Bayesian networks to real-word problems is typically building the network structure. Optimal structure learning via score-and-search has become an active research topic in recent years. In this context, a scoring function is used to measure the goodness of fit of a structure to given data, and the goal is to find the structure which optimizes the scoring function. The problem has been viewed as a shortest path problem, and has been shown to be NP-hard. The complexity of the structure learning limits the usage of Bayesian networks. Thus, we propose to leverage and model correlations among variables to improve the efficiency of finding optimal structures of Bayesian networks. In particular, the shortest path problem highlights the importance of two research issues: the quality of heuristic functions for guiding the search, and the complexity of search space. This thesis introduces several techniques for addressing the issues. We present effective approaches to reducing the search space by extracting constraints directly from data. We also propose various methods to improve heuristic functions, so as to search over the most promising part of the solution space. Empirical results show that these methods significantly improve the efficiency and scalability of heuristics search-based structure learning

Tightening Bounds for Bayesian Network Structure Learning

A recent breadth-first branch and bound algorithm (BFBnB)for learning Bayesian network structures (Maloneet al. 2011) uses two bounds to prune the searchspace for better efficiency; one is a lower bound calculatedfrom pattern database heuristics, and the otheris an upper bound obtained by a hill climbing search.Whenever the lower bound of a search path exceeds theupper bound, the path is guaranteed to lead to suboptimalsolutions and is discarded immediately. This paperintroduces methods for tightening the bounds. Thelower bound is tightened by using more informed variablegroupings when creating the pattern databases, andthe upper bound is tightened using an anytime learningalgorithm. Empirical results show that these boundsimprove the efficiency of Bayesian network learning bytwo to three orders of magnitude