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Distribution Networks provide the final tier in the transfer of electricity from generators to the end consumers. Traditionally, distribution networks have been equipped with limited real-time monitoring devices and have low observability. However, there has been a recent surge in the deployment of smart meters in distribution networks for use in demand response, improved home-monitoring and other smart grid inspired topics. This paper discusses learning and estimation problems in the distribution grid using available phasor and voltage magnitude data. For a wide range of realistic operating conditions, polynomial time algorithms are proposed to learn the structure of the distribution network as well as estimate the statistics of load profiles at the constituent nodes. Further, the algorithms are extended to cases with missing data, where observations limited to a fraction of the nodes are available for structure learning. This work can be applied to improve control and optimize operations in the grid as well as understand the scope of adversarial attacks. Host: Misha Chertkov |