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Considerable progress has been made on algorithms for learning the structure of Bayesian networks from data. Model averaging by using bootstrap replicates with feature selection by thresholding is a widely used solution for learning features with high confidence. Yet, in the context of limited data many questions remain unanswered. What scoring functions are most effective for model averaging? Does the bias arising from the discreteness of the bootstrap significantly affect learning performance? Is it better to pick the single best network or to average multiple networks learnt from each bootstrap resample? How should thresholds for learning statistically significant features be selected? The best scoring functions are Dirichlet Prior Scoring Metric with small λ and the Bayesian Dirichlet metric. Correcting the bias arising from the discreteness of the bootstrap worsens learning performance. It is better to pick the single best network learnt from each bootstrap resample. We describe a permutation based method for determining significance thresholds for feature selection in bagged models. We show that in contexts with limited data, Bayesian bagging using the Dirichlet Prior Scoring Metric (DPSM) is the most effective learning strategy, and that modifying the scoring function to penalize complex networks hampers model averaging. We establish these results using a systematic study of two well-known benchmarks, specifically ALARM and INSURANCE. We also apply our network construction method to gene expression data from the Cancer Genome Atlas Glioblastoma multiforme dataset and show that survival is related to clinical covariates age and gender and clusters for interferon induced genes and growth inhibition genes. For small data sets, our approach performs significantly better than previously published methods.
Broom, B. M., Do, K. A., & Subramanian, D. (2012). Model averaging strategies for structure learning in Bayesian networks with limited data. BMC Bioinformatics, 13 Suppl 13. https://doi.org/10.1186/1471-2105-13-S13-S10