# Causal Discovery with Generalized Linear Models through Peeling Algorithms

arXiv: https://arxiv.org/abs/2310.16698 · HTML: https://mlsanity.com/paper/2310.16698/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 52 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 11 of 11)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models](https://mlsanity.com/paper/1412.8765/) (2014)
- [Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization](https://mlsanity.com/paper/1401.5755/) (2014)
- [Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)](https://mlsanity.com/paper/1704.08783/) (2017)
- [Discovery and inference of a causal network with hidden confounding](https://mlsanity.com/paper/2309.09420/) (2023)
- [Pathwise Coordinate Optimization for Sparse Learning: Algorithm and Theory](https://mlsanity.com/paper/1412.7477/) (2014)
- [The restricted strong convexity revisited: Analysis of equivalence to error bound and quadratic growth](https://mlsanity.com/paper/1511.01635/) (2015)
- [Testing Directed Acyclic Graph via Structural, Supervised and Generative Adversarial Learning](https://mlsanity.com/paper/2106.01474/) (2021)
- [Inference for a Large Directed Acyclic Graph with Unspecified Interventions](https://mlsanity.com/paper/2110.03805/) (2021)

## Built on by (most cited first, 2 of 2)

- [On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models](https://mlsanity.com/paper/2609.17942/) (2026)
- [DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables](https://mlsanity.com/paper/2610.06086/) (2026)

## Abstract (arXiv)

This article presents a novel method for causal discovery with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data. Causal discovery often faces challenges due to unmeasured confounders that hinder the identification of causal relationships. The proposed approach addresses this issue by developing two peeling algorithms (bottom-up and top-down) to ascertain causal relationships and valid instruments. This approach first reconstructs a super-graph to represent ancestral relationships between variables, using a peeling algorithm based on nodewise GLM regressions that exploit relationships between primary and instrumental variables. Then, it estimates parent-child effects from the ancestral relationships using another peeling algorithm while deconfounding a child's model with information borrowed from its parents' models. The article offers a theoretical analysis of the proposed approach, which establishes conditions for model identifiability and provides statistical guarantees for accurately discovering parent-child relationships via the peeling algorithms. Furthermore, the article presents numerical experiments showcasing the effectiveness of our approach in comparison to state-of-the-art structure learning methods without confounders. Lastly, it demonstrates an application to Alzheimer's disease (AD), highlighting the utility of the method in constructing gene-to-gene and gene-to-disease regulatory networks involving Single Nucleotide Polymorphisms (SNPs) for healthy and AD subjects.