ParamBoost: Gradient Boosted Piecewise Cubic Polynomials
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911610827702272 |
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| author | Salvadé, Nicolas Hillel, Tim |
| author_facet | Salvadé, Nicolas Hillel, Tim |
| contents | Generalized Additive Models (GAMs) can be used to create non-linear glass-box (i.e. explicitly interpretable) models, where the predictive function is fully observable over the complete input space. However, glass-box interpretability itself does not allow for the incorporation of expert knowledge from the modeller. In this paper, we present ParamBoost, a novel GAM whose shape functions (i.e. mappings from individual input features to the output) are learnt using a Gradient Boosting algorithm that fits cubic polynomial functions at leaf nodes. ParamBoost incorporates several constraints commonly used in parametric analysis to ensure well-refined shape functions. These constraints include: (i) continuity of the shape functions and their derivatives (up to C2); (ii) monotonicity; (iii) convexity; (iv) feature interaction constraints; and (v) model specification constraints. Empirical results show that the unconstrained ParamBoost model consistently outperforms state-of-the-art GAMs across several real-world datasets. We further demonstrate that modellers can selectively impose required constraints at a modest trade-off in predictive performance, allowing the model to be fully tailored to application-specific interpretability and parametric-analysis requirements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18864 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | ParamBoost: Gradient Boosted Piecewise Cubic Polynomials Salvadé, Nicolas Hillel, Tim Machine Learning Generalized Additive Models (GAMs) can be used to create non-linear glass-box (i.e. explicitly interpretable) models, where the predictive function is fully observable over the complete input space. However, glass-box interpretability itself does not allow for the incorporation of expert knowledge from the modeller. In this paper, we present ParamBoost, a novel GAM whose shape functions (i.e. mappings from individual input features to the output) are learnt using a Gradient Boosting algorithm that fits cubic polynomial functions at leaf nodes. ParamBoost incorporates several constraints commonly used in parametric analysis to ensure well-refined shape functions. These constraints include: (i) continuity of the shape functions and their derivatives (up to C2); (ii) monotonicity; (iii) convexity; (iv) feature interaction constraints; and (v) model specification constraints. Empirical results show that the unconstrained ParamBoost model consistently outperforms state-of-the-art GAMs across several real-world datasets. We further demonstrate that modellers can selectively impose required constraints at a modest trade-off in predictive performance, allowing the model to be fully tailored to application-specific interpretability and parametric-analysis requirements. |
| title | ParamBoost: Gradient Boosted Piecewise Cubic Polynomials |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.18864 |