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As machine learning algorithms grow in popularity and diversify to many industries, ethical and legal concerns regarding their fairness have become increasingly relevant. We explore the problem of algorithmic fairness, taking an information-theoretic view. The maximal correlation framework is introduced for expressing fairness constraints and shown to be capable of being used to derive regularizers that enforce independence and separation-based fairness criteria, which admit optimization algorithms for both discrete and continuous variables which are more computationally efficient than existing algorithms. We show that these algorithms provide smooth performance-fairness tradeoff curves and perform competitively with state-of-the-art methods on both discrete datasets (COMPAS, Adult) and continuous datasets (Communities and Crimes).