Sparse smooth additive regression models with shape constraints

M. Cuesta Santa Teresa, C. D'Ambrosio, M. Durban, V. Guerrero

Shape-constrained smooth additive regression models are a flexible and interpretable tool for modeling complex data while enforcing monotonicity or convexity. Variable selection is crucial in these models because their performance and interpretability can decrease in high-dimensional settings. We address sparsity through the best subset variable selection problem, which identifies the k most informative covariates by adding a set of constraints with binary variables to the model estimation. In our setting, shape-constrained models are estimated using a conic optimization approach. As a result, best subset selection leads to a mixed-integer conic program with semidefinite variables in the constraints, which is not tractable for off-the-shelf solvers. To address this challenge, we work with the perspective formulation and its continuous relaxation, which is tighter than in big-M formulations. We evaluate the proposed method on simulated and real datasets, obtaining promising results.

Keywords: shape-constrained regression, feature selection, mathematical optimization, B-splines

GT AMyC II: Advances in Clustering and Regression Analysis
September 4, 2026  11:10 AM
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