We consider the problem of fitting a regression model that is both flexible and interpretable. We propose two procedures for this task: the Fused Lasso Additive Model (FLAM), which is an additive model of piecewise constant fits; and Convex Regression with Interpretable Sharp Partitions (CRISP), which extends FLAM to allow for non-additivity. Both FLAM and CRISP are the solutions to convex optimization problems that can be efficiently solved. We show that FLAM and CRISP outperform competitors, such as sparse additive models (Ravikumar et al, 2009), CART (Breiman et al, 1984), and thin plate splines (Duchon, 1977), in a range of settings. We propose unbiased estimators for the degrees of freedom of FLAM and CRISP, which allow us to characterize their complexity.
This is joint work with Ashley Petersen and Noah Simon at University of Washington.