An instance-specific algorithm for learning the structure of causal Bayesian networks containing latent variables
Almost all of the existing algorithms for learning a causal Bayesian network structure (CBN) from observational data recover a structure that models the causal relationships that are shared by the instances in a population. Although learning such population-wide CBNs accurately is useful, it is important to learn CBNs that are speciﬁc to each instance in domains in which diﬀerent instances may have varying causal structures, such as in human biology. For example, a breast cancer tumor in a patient (instance) is often a composite of causal mechanisms, where each of these individual causal mechanisms may appear relatively frequently in breast-cancer tumors of other patients, but the particular combination of mechanisms is unique to the current tumor. Therefore, it is critical to discover the speciﬁc set of causal mechanisms that are operating in each patient to understand and treat that particular patient eﬀectively. We previously introduced an instance-speciﬁc CBN structure learning method that builds a causal model for a given instance T from the features we know about T and from a training set of data on many other instances . However, that method assumes that there are no latent (hidden) confounders, that is, there are no latent variables that cause two or more of the measured variables. Unfortunately, this assumption rarely holds in practice. In the current paper, we introduce a novel instance-speciﬁc causal structure learning algorithm that uses partial ancestral graphs (PAGs) to model latent confounders. Simulations support that the proposed instance-speciﬁc method improves structure-discovery performance compared to an existing PAG-learning method called GFCI, which is not instance-speciﬁc. We also report results that provide support for instance-speciﬁc causal relationships existing in realworld datasets.
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