The Improved Ordering-Based Search Method Incorporating with Ensemble Learning

Hao Wang

doi:10.1007/s12559-024-10251-x

2024-02-12

PRE

DOI：10.1007/s12559-024-10251-x

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摘要

En 中文

The Bayesian network provides a useful way to deal with uncertain information, which helps researchers to better understand the human cognitive process. The foundation of the Bayesian network focuses on identifying the qualitative relations between variables, which is also called structure learning. Local search in the ordering space is an effective method for learning the structure of large-scale Bayesian networks. However, the existing algorithms tend to the local optimum and stop searching for superior solutions. To tackle the problem, random perturbations are applied to the local optimum without specific strategies, resulting in many meaningless restarts that sacrifice much time but still fail to improve the results. As an extension of the local search, simulated annealing stochastically searches the solution spaces and selects relatively poor solutions with a certain probability. This paper proposes a method based on simulated annealing to learn Bayesian network structure in the ordering space, which expands the search scope by probabilistically accepting poorer solutions. Moreover, we improve simulated annealing by adding a memory module and modifying the termination condition. The memory module records the optimal solution before accepting a worse solution, which avoids losing the possible global optimal solution. The new termination condition is related to the quality of the search results, which reduces many redundant searches. Besides, we design a new restart strategy based on ensemble learning. When the search traps in the local optimum, a new ordering is obtained to restart the search by perturbing the current ordering with constraints. The constraints are generated by the results of ensemble learning on multiple structures, which help the algorithm approach the global optimum solution. Experimental results show that our proposed methods improve the accuracy and efficiency in learning the optimal structure over the benchmarks compared to the state-of-the-art algorithms.

Keyword:

Bayesian networks

Structure learning

Ensemble learning

Local search