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Abstract:
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Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system on each other. There are two important lines of work that have currently dealt with DAG estimation in the Gaussian framework - one where the ordering is known and one where it is unknown. When the nodes exhibit a natural ordering, the problem of estimating directed graphs reduces to the problem of estimating the structure of the network. This leads to a convex problem which can be solved in a fast and efficient manner with the added advantage of convergence guarantees. On the other hand, when the ordering is unknown we get a non-convex problem, which leads to a much slower algorithm. In this paper, we propose a penalized likelihood approach that estimates DAGs when a partial ordering is known. By combining ideas from the known ordering problem, we formulate a more efficient and tractable algorithm than the case of the completely unknown ordering.
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