# Generalized Sparse Additive Models

arXiv: https://arxiv.org/abs/1903.04641 · HTML: https://mlsanity.com/paper/1903.04641/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2019.

## Built on by (most cited first, 11 of 11)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Exploring and Interacting with the Set of Good Sparse Generalized Additive Models](https://mlsanity.com/paper/2303.16047/) (2023)
- [SurvNAM: The machine learning survival model explanation](https://mlsanity.com/paper/2104.08903/) (2021)
- [Multivariate Trend Filtering for Lattice Data](https://mlsanity.com/paper/2112.14758/) (2021)
- [Learning Directed Acyclic Graphs from Partial Orderings](https://mlsanity.com/paper/2403.16031/) (2024)
- [Generalized Sparse Additive Model with Unknown Link Function](https://mlsanity.com/paper/2410.06012/) (2024)
- [Generalized Functional ANOVA: A Complete Theoretical Framework](https://mlsanity.com/paper/2605.18422/) (2026)
- [DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelation](https://mlsanity.com/paper/2205.07932/) (2022)
- [Classification by sparse generalized additive models](https://mlsanity.com/paper/2212.01792/) (2022)
- [Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach](https://mlsanity.com/paper/2306.06756/) (2023)
- [Minimax Additive Regression under Unknown Dependent Designs](https://mlsanity.com/paper/2609.39212/) (2026)

## Abstract (arXiv)

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of observations and features. We prove minimax optimal convergence bounds for this class under a weak compatibility condition. In addition, we characterize the rate of convergence when this compatibility condition is not met. Finally, we also show that the optimal penalty parameters for structure and sparsity penalties in our framework are linked, allowing cross-validation to be conducted over only a single tuning parameter. We complement our theoretical results with empirical studies comparing some existing methods within this framework.