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Abstract: With the prevalence of machine learning services, crowdsourced data containing sensitive information poses substantial privacy challenges. Existing work focusing on protecting against membership inference attacks under the rigorous framework of differential privacy are vulnerable to attribute inference attacks. In light of the current gap between theory and practice, we develop a novel theoretical framework for privacy-preservation under the attack of attribute inference. Under our framework, we propose a minimax optimization formulation to protect the given attribute and analyze its privacy guarantees against arbitrary adversaries. On the other hand, it is clear that privacy constraint may cripple utility when the protected attribute is correlated with the target variable. To this end, we also prove an information-theoretic lower bound to precisely characterize the fundamental trade-off between utility and privacy. Empirically, we extensively conduct experiments to corroborate our privacy guarantee and validate the inherent trade-offs in different privacy preservation algorithms. Our experimental results indicate that the adversarial representation learning approaches achieve the best trade-off in terms of privacy preservation and utility maximization.