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It is now well understood that machine learning models, trained on data without due care, often exhibit unfair and discriminatory behavior against certain populations. Traditional algorithmic fairness research has mainly focused on supervised learning tasks, particularly classification. While fairness in unsupervised learning has received some attention, the literature has primarily addressed fair representation learning of continuous embeddings. In this paper, we conversely focus on unsupervised learning using probabilistic graphical models with discrete latent variables. We develop a fair stochastic variational inference technique for the discrete latent variables, which is accomplished by including a fairness penalty on the variational distribution that aims to respect the principles of intersectionality, a critical lens on fairness from the legal, social science, and humanities literature, and then optimizing the variational parameters under this penalty. We first show the utility of our method in improving equity and fairness for clustering using naïve Bayes and Gaussian mixture models on benchmark datasets. To demonstrate the generality of our approach and its potential for real-world impact, we then develop a special-purpose graphical model for criminal justice risk assessments, and use our fairness approach to prevent the inferences from encoding unfair societal biases.