Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to networks of moderate or higher complexity. In general, approximate solutions tend to sacrifice accuracy for speed, where the aim is to minimise the loss in accuracy and maximise the gain in speed. While some approximate algorithms are optimised to handle thousands of variables, these algorithms may still be unable to learn such high dimensional structures. Some of the most efficient score-based algorithms cast the structure learning problem as a combinatorial optimisation of candidate parent sets. This paper explores a strategy towards pruning the size of candidate parent sets, and which could form part of existing score-based algorithms as an additional pruning phase aimed at high dimensionality problems. The results illustrate how different levels of pruning affect the learning speed relative to the loss in accuracy in terms of model fitting, and show that aggressive pruning may be required to produce approximate solutions for high complexity problems.

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通过修剪候选父集近似学习高维贝叶斯网络结构

学习贝叶斯网络 (BN) 结构的基于分数的算法提供了从不同级别的近似学习到精确学习的解决方案。存在近似解决方案是因为精确学习通常不适用于中等或更高复杂度的网络。一般来说，近似解往往会为了速度而牺牲精度，其目的是最小化精度损失并最大化速度增益。虽然一些近似算法经过优化以处理数千个变量，但这些算法可能仍然无法学习这样的高维结构。一些最有效的基于分数的算法将结构学习问题视为候选父集的组合优化。本文探讨了一种修剪候选父集大小的策略，并且可以构成现有的基于分数的算法的一部分，作为针对高维问题的附加修剪阶段。结果说明了不同级别的修剪如何影响相对于模型拟合精度损失的学习速度，并表明可能需要积极修剪才能为高复杂性问题生成近似解决方案。