Learning Interpretable Models using Soft Integrity Constraints

Khaled Belahcene (1, 2, 3) , Nataliya Sokolovska (1, 2) , Yann Chevaleyre (4) , Jean-Daniel Zucker (5, 1)

1 INSERM - Institut National de la Santé et de la Recherche Médicale
2 SU - Sorbonne Université
3 UTC - Université de Technologie de Compiègne
4 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
5 IRD - Institut de Recherche pour le Développement

Integer models are of particular interest for applications where predictive models are supposed not only to be accurate but also interpretable to human experts. We introduce a novel penalty term called Facets whose primary goal is to favour integer weights. Our theoretical results illustrate the behaviour of the proposed penalty term: for small enough weights, the Facets matches the L1 penalty norm, and as the weights grow, it approaches the L2 regularizer. We provide the proximal operator associated with the proposed penalty term, so that the regularized empirical risk minimizer can be computed efficiently. We also introduce the Strongly Convex Facets, and discuss its theoretical properties. Our numerical results show that while achieving the state-of-the-art accuracy, optimisation of a loss function penalized by the proposed Facets penalty term leads to a model with a significant number of integer weights.

Domaines: Apprentissage [cs.LG]

Khaled Belahcene, Nataliya Sokolovska, Yann Chevaleyre, Jean-Daniel Zucker. Learning Interpretable Models using Soft Integrity Constraints. 2019. ⟨hal-02360875⟩