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In this paper, we develop compositional methods for formally verifying differential privacy for algorithms whose analysis goes beyond the composition theorem. Our methods are based on the observation that differential privacy has deep connections with a generalization of probabilistic couplings, an established mathematical tool for reasoning about stochastic processes. Even when the composition theorem is not helpful, we can often prove privacy by a coupling argument. We demonstrate our methodsarXiv:1601.05047v4 fatcat:ebuijcjdzvbalcbqephgryxoyy