# Fused Lasso Additive Model

arXiv: https://arxiv.org/abs/1409.5391 · HTML: https://mlsanity.com/paper/1409.5391/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2014.

## Built on by (most cited first, 7 of 7)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [MARS via LASSO](https://mlsanity.com/paper/2111.11694/) (2021)
- [Interactive Generalized Additive Model and Its Applications in Electric Load Forecasting](https://mlsanity.com/paper/2310.15662/) (2023)
- [Challenges in interpretability of additive models](https://mlsanity.com/paper/2504.10169/) (2025)
- [Modeling High-Dimensional Data with Unknown Cut Points: A Fusion Penalized Logistic Threshold Regression](https://mlsanity.com/paper/2202.08441/) (2022)
- [DDAC-SpAM: A Distributed Algorithm for Fitting High-dimensional Sparse Additive Models with Feature Division and Decorrelation](https://mlsanity.com/paper/2205.07932/) (2022)
- [FAST: An Optimization Framework for Fast Additive Segmentation in Transparent ML](https://mlsanity.com/paper/2402.12630/) (2024)

## Abstract (arXiv)

We consider the problem of predicting an outcome variable using p covariates that are measured on n independent observations, in the setting in which flexible and interpretable fits are desirable. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively-chosen knots. FLAM is the solution to a convex optimization problem, for which a simple algorithm with guaranteed convergence to the global optimum is provided. FLAM is shown to be consistent in high dimensions, and an unbiased estimator of its degrees of freedom is proposed. We evaluate the performance of FLAM in a simulation study and on two data sets.