# ParamBoost: Gradient Boosted Piecewise Cubic Polynomials

arXiv: https://arxiv.org/abs/2604.18864 · HTML: https://mlsanity.com/paper/2604.18864/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [An Explainable Machine Learning Model for Early Detection of Parkinson's Disease using LIME on DaTscan Imagery](https://mlsanity.com/paper/2008.00238/) (2020)
- [Consistent feature attribution for tree ensembles](https://mlsanity.com/paper/1706.06060/) (2017)
- [Interpretable Machine Learning with an Ensemble of Gradient Boosting Machines](https://mlsanity.com/paper/2010.07388/) (2020)
- [Gradient Boosting With Piece-Wise Linear Regression Trees](https://mlsanity.com/paper/1802.05640/) (2018)
- [CAT: Interpretable Concept-based Taylor Additive Models](https://mlsanity.com/paper/2406.17931/) (2024)
- [Predicting Census Survey Response Rates With Parsimonious Additive Models and Structured Interactions](https://mlsanity.com/paper/2108.11328/) (2021)
- [RUMBoost: Gradient Boosted Random Utility Models](https://mlsanity.com/paper/2401.11954/) (2024)

## Abstract (arXiv)

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.