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We study the problem of learning representations that are private yet informative, i.e., provide information about intended "ally" targets while hiding sensitive "adversary" attributes. We propose Exclusion-Inclusion Generative Adversarial Network (EIGAN), a generalized private representation learning (PRL) architecture that accounts for multiple ally and adversary attributes unlike existing PRL solutions. While centrally-aggregated dataset is a prerequisite for most PRL techniques, data in real-world is often siloed across multiple distributed nodes unwilling to share the raw data because of privacy concerns. We address this practical constraint by developing D-EIGAN, the first distributed PRL method that learns representations at each node without transmitting the source data. We theoretically analyze the behavior of adversaries under the optimal EIGAN and D-EIGAN encoders and the impact of dependencies among ally and adversary tasks on the optimization objective. Our experiments on various datasets demonstrate the advantages of EIGAN in terms of performance, robustness, and scalability. In particular, EIGAN outperforms the previous state-of-the-art by a significant accuracy margin (47% improvement), and D-EIGAN's performance is consistently on par with EIGAN under different network settings.