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We consider the problem of decentralized detection under constraints on the number of bits that can be transmitted by each sensor. In contrast to most previous work, in which the joint distribution of sensor observations is assumed to be known, we address the problem when only a set of empirical samples is available. We propose a novel algorithm using the framework of empirical risk minimization and marginalized kernels and analyze its computational and statistical properties both theoretically and empirically. We provide an efficient implementation of the algorithm and demonstrate its performance on both simulated and real data sets.