PyUoI contains implementations of Union of Intersections framework for a variety of penalized generalized linear models as well as dimensionality reductions techniques such as column subset selection and non-negative matrix factorization. In general, UoI is a statistical machine learning framework that leverages two concepts in model inference: Separating the selection and estimation problems to simultaneously achieve sparse models with low-bias and low-variance parameter estimates. Stability to perturbations in both selection and estimation. PyUoI is designed to function similarly to scikit-learn, as it often builds upon scikit-learn's implementations of the aforementioned algorithms. Further details on the UoI framework can be found in the NeurIPS paper (Bouchard et al., 2017). The development version of this package can be found on Github. Our documentation can be found here.