# Boosting Causal Additive Models

arXiv: https://arxiv.org/abs/2401.06523 · HTML: https://mlsanity.com/paper/2401.06523/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 12 Jan 2024.

## Builds on (most cited first, 19 of 19)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables](https://mlsanity.com/paper/2102.07921/) (2021)
- [Score-based Causal Learning in Additive Noise Models](https://mlsanity.com/paper/1311.6359/) (2013)
- [Additive Approximations in High Dimensional Nonparametric Regression via the SALSA](https://mlsanity.com/paper/1602.00287/) (2016)
- [Learning Causal Graphs in Manufacturing Domains using Structural Equation Models](https://mlsanity.com/paper/2210.14573/) (2022)

## Abstract (arXiv)

We present a boosting-based method to learn additive Structural Equation Models (SEMs) from observational data, with a focus on the theoretical aspects of determining the causal order among variables. We introduce a family of score functions based on arbitrary regression techniques, for which we establish necessary conditions to consistently favor the true causal ordering. Our analysis reveals that boosting with early stopping meets these criteria and thus offers a consistent score function for causal orderings. To address the challenges posed by high-dimensional data sets, we adapt our approach through a component-wise gradient descent in the space of additive SEMs. Our simulation study underlines our theoretical results for lower dimensions and demonstrates that our high-dimensional adaptation is competitive with state-of-the-art methods. In addition, it exhibits robustness with respect to the choice of the hyperparameters making the procedure easy to tune.