# Sparse Partially Linear Additive Models

arXiv: https://arxiv.org/abs/1407.4729 · HTML: https://mlsanity.com/paper/1407.4729/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2014.

## Built on by (most cited first, 5 of 5)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Fast Sparse Classification for Generalized Linear and Additive Models](https://mlsanity.com/paper/2202.11389/) (2022)
- [Group selection and shrinkage: Structured sparsity for semiparametric additive models](https://mlsanity.com/paper/2105.12081/) (2021)
- [Comparables XAI: Faithful Example-based AI Explanations with Counterfactual Trace Adjustments](https://mlsanity.com/paper/2602.13784/) (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)

## Abstract (arXiv)

The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing each to have either a linear or nonlinear effect on the response. However, the choice of which features to treat as linear or nonlinear is typically assumed known. Thus, to make a GPLAM a viable approach in situations in which little is known a~priori about the features, one must overcome two primary model selection challenges: deciding which features to include in the model and determining which of these features to treat nonlinearly. We introduce the sparse partially linear additive model (SPLAM), which combines model fitting and both of these model selection challenges into a single convex optimization problem. SPLAM provides a bridge between the lasso and sparse additive models. Through a statistical oracle inequality and thorough simulation, we demonstrate that SPLAM can outperform other methods across a broad spectrum of statistical regimes, including the high-dimensional (pgg N) setting. We develop efficient algorithms that are applied to real data sets with half a million samples and over 45,000 features with excellent predictive performance.