  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
na\"ive 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.
