Hard Shape-Constrained Kernel Machines - Archive ouverte HAL Access content directly
Conference Papers Year : 2020

Hard Shape-Constrained Kernel Machines

Abstract

Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape requirements in a hard fashion is an extremely challenging problem. Classically, this task is tackled (i) in a soft way (without out-of-sample guarantees), (ii) by specialized transformation of the variables on a case-by-case basis, or (iii) by using highly restricted function classes, such as polynomials or polynomial splines. In this paper, we prove that hard affine shape constraints on function derivatives can be encoded in kernel machines which represent one of the most flexible and powerful tools in machine learning and statistics. Particularly, we present a tightened second-order cone constrained reformulation, that can be readily implemented in convex solvers. We prove performance guarantees on the solution, and demonstrate the efficiency of the approach in joint quantile regression with applications to economics and to the analysis of aircraft trajectories, among others.
Fichier principal
Vignette du fichier
neurips_2020.pdf (1.21 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02625276 , version 1 (26-05-2020)
hal-02625276 , version 2 (17-10-2020)

Identifiers

  • HAL Id : hal-02625276 , version 2

Cite

Pierre-Cyril Aubin-Frankowski, Zoltán Szabó. Hard Shape-Constrained Kernel Machines. Advances in Neural Information Processing Systems (NeurIPS-2020), Dec 2020, Vancouver (Virtual), Canada. ⟨hal-02625276v2⟩
130 View
40 Download

Share

Gmail Facebook Twitter LinkedIn More