Convex Regression with Interpretable Sharp Partitions

Ashley Petersen, Noah Simon, Daniela Witten.

Year: 2016, Volume: 17, Issue: 94, Pages: 1−31


We consider the problem of predicting an outcome variable on the basis of a small number of covariates, using an interpretable yet non-additive model. We propose convex regression with interpretable sharp partitions (CRISP) for this task. CRISP partitions the covariate space into blocks in a data- adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low- variance fits. We explore the properties of CRISP, and evaluate its performance in a simulation study and on a housing price data set.