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We introduce a unified\nalgorithm to efficiently learn a broad class of linear and non-linear state\nspace models, including variants where the emission and transition\ndistributions are modeled by deep neural networks. Our learning algorithm\nsimultaneously learns a compiled inference network and the generative model,\nleveraging a structured variational approximation parameterized by recurrent\nneural networks to mimic the posterior distribution. We apply the learning\nalgorithm to both synthetic and real-world datasets, demonstrating its\nscalability and versatility. 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