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Bayesian network structure learning for the uncertain experimentalist : with applications to network biology Eaton, Daniel James

Abstract

In this work, we address both the computational and modeling aspects of Bayesian network structure learning. Several recent algorithms can handle large networks by operating on the space of variable orderings, but for technical reasons they cannot compute many interesting structural features and require the use of a restrictive prior. We introduce a novel MCMC method that utilizes the deterministic output of the exact structure learning algorithm of Koivisto and Sood to construct a fast-mixing proposal on the space of DAGs. We show that in addition to fixing the order-space algorithms' shortcomings, our method outperforms other existing samplers on real datasets by delivering more accurate structure and higher predictive likelihoods in less compute time. Next, we discuss current models of intervention and propose a novel approach named the uncertain intervention model, whereby the targets of an intervention can be learned in parallel to the graph's causal structure. We validate our model experimentally using synthetic data generated from known ground truth. We then apply our model to two biological datasets that have been previously analyzed using Bayesian networks. On the T-cell dataset of Sachs et al. we show that the uncertain intervention model is able to better model the density of the data compared to previous techniques, while on the ALL dataset of Yeoh et al. we demonstrate that our method can be used to directly estimate the genetic effects of the disease.

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