Structured nonlinear variable selection

Gregorova, Magda (Haute école de gestion de Genève, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale ; University of Geneva, Switzerland) ; Kalousis, Alexandros (Haute école de gestion de Genève, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale ; University of Geneva, Switzerland) ; Marchand-Maillet, Stéphane (University of Geneva, Switzerland)

We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive models. We propose two new regularizers based on partial derivatives as nonlinear equivalents of group lasso and elastic net. We formulate the problem within the framework of learning in reproducing kernel Hilbert spaces and show how the variational problem can be reformulated into a more practical finite dimensional equivalent. We develop a new algorithm derived from the ADMM principles that relies solely on closed forms of the proximal operators. We explore the empirical properties of our new algorithm for Nonlinear Variable Selection based on Derivatives (NVSD) on a set of experiments and confirm favourable properties of our structured-sparsity models and the algorithm in terms of both prediction and variable selection accuracy.


Conference Type:
full paper
Faculty:
Economie et Services
School:
HEG - Genève
Institute:
CRAG - Centre de Recherche Appliquée en Gestion
Subject(s):
Informatique
Publisher:
Monterey, USA, 6-10 August 2018
Date:
2018-08
Monterey, USA
6-10 August 2018
Pagination:
10 p.
Published in:
Proceedings of Conference on Uncertainty in Artificial Intelligence (UAI)
External resources:
Appears in Collection:



 Record created 2018-10-04, last modified 2019-06-11

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