## Finding Optimal Bayesian Network Given a Super-Structure

Citations: | 7 - 0 self |

### BibTeX

@MISC{Perrier_findingoptimal,

author = {Eric Perrier and Seiya Imoto and Satoru Miyano and Max Chickering},

title = {Finding Optimal Bayesian Network Given a Super-Structure},

year = {}

}

### OpenURL

### Abstract

Classical approaches used to learn Bayesian network structure from data have disadvantages in terms of complexity and lower accuracy of their results. However, a recent empirical study has shown that a hybrid algorithm improves sensitively accuracy and speed: it learns a skeleton with an independency test (IT) approach and constrains on the directed acyclic graphs (DAG) considered during the search-and-score phase. Subsequently, we theorize the structural constraint by introducing the concept of super-structure S, which is an undirected graph that restricts the search to networks whose skeleton is a subgraph of S. We develop a super-structure constrained optimal search (COS): its time complexity is upper bounded by O(γm n), where γm < 2 depends on the maximal degree m of S. Empirically, complexity depends on the average degree ˜m and sparse structures allow larger graphs to be calculated. Our algorithm is faster than an optimal search by several orders and even finds more accurate results when given a sound super-structure. Practically, S can be approximated by IT approaches; significance level of the tests controls its sparseness, enabling to control the trade-off between speed and accuracy. For incomplete super-structures, a greedily post-processed version (COS+) still enables to significantly outperform other heuristic searches. Keywords: subset Bayesian networks, structure learning, optimal search, super-structure, connected 1.