# Sparse Deep Additive Model with Interactions: Enhancing Interpretability and Predictability

arXiv: https://arxiv.org/abs/2509.23068 · HTML: https://mlsanity.com/paper/2509.23068/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 62 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Group Sparse Regularization for Deep Neural Networks](https://mlsanity.com/paper/1607.00485/) (2016)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [Explainable Neural Networks based on Additive Index Models](https://mlsanity.com/paper/1806.01933/) (2018)
- [Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection](https://mlsanity.com/paper/2209.09326/) (2022)
- [Sparse Neural Additive Model: Interpretable Deep Learning with Feature Selection via Group Sparsity](https://mlsanity.com/paper/2202.12482/) (2022)
- [Safe Pattern Pruning: An Efficient Approach for Predictive Pattern Mining](https://mlsanity.com/paper/1602.04548/) (2016)
- [Higher-order Neural Additive Models: An Interpretable Machine Learning Model with Feature Interactions](https://mlsanity.com/paper/2209.15409/) (2022)
- [Learning Discriminative Bayesian Networks from High-dimensional Continuous Neuroimaging Data](https://mlsanity.com/paper/1506.06868/) (2015)
- [Deep P-Spline: Theory, Fast Tuning, and Application](https://mlsanity.com/paper/2501.01376/) (2025)

## Abstract (arXiv)

Recent advances in deep learning highlight the need for personalized models that can learn from small samples, handle high-dimensional features, and remain interpretable. To address this, we propose the Sparse Deep Additive Model with Interactions (SDAMI), a framework that combines sparsity-driven feature selection with deep subnetworks for flexible function approximation. Central to SDAMI is the Effect Footprint principle, which posits that higher-order interactions leave detectable marginal traces on constituent variables, enabling their discovery without exhaustive search. SDAMI executes this principle through a three-stage strategy: (1) screening for footprint variables, (2) disentangling main effects from interactions via group lasso, and (3) modeling components with dedicated deep subnetworks. Theoretical analysis confirms that footprints vanish only under measure-zero symmetry conditions that are rare in practice, ensuring consistent interaction recovery. Extensive simulations demonstrate that SDAMI successfully identifies pure interactions that heredity-based baselines fundamentally miss, recovering complex effect structures with near-zero false positive rates. Together, these results position SDAMI as a principled framework for interpretable high-dimensional regression.