Predictive Multiplicity in Probabilistic Classification

For a prediction task, there may exist multiple models that perform almost equally well. This multiplicity complicates how we typically develop and deploy machine learning models. We study how multiplicity affects predictions -- i.e., predictive multiplicity -- in probabilistic classification. We introduce new measures for this setting and present optimization-based methods to compute these measures for convex empirical risk minimization problems like logistic regression. We apply our methodology to gain insight into why predictive multiplicity arises. We study the incidence and prevalence of predictive multiplicity in real-world risk assessment tasks. Our results emphasize the need to report multiplicity more widely.