Multidimensional Shape Constraints

Maya R. Gupta
Erez Louidor
Olexander Mangylov
Nobuyuki Morioka
Taman Narayan
ICML 2020(2020)
Google Scholar


We propose new multi-input shape constraints across four intuitive categories: complements, diminishers, dominance, and unimodality constraints. We show these shape constraints can be checked and even enforced when training machine-learned models for linear models, generalized additive models, and the nonlinear function class of multi-layer lattice models. Toy examples and real-world experiments illustrate how the different shape constraints can be used to increase interpretability and better regularize machine-learned models.