# Causal Discovery from Poisson Branching Structural Causal Model Using High-Order Cumulant with Path Analysis

arXiv: https://arxiv.org/abs/2403.16523 · HTML: https://mlsanity.com/paper/2403.16523/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 25 Mar 2024.

## Builds on (most cited first, 3 of 3)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)](https://mlsanity.com/paper/1704.08783/) (2017)

## Built on by (most cited first, 3 of 3)

- [CDFM: Towards a General-Purpose Causal Discovery Foundation Model](https://mlsanity.com/paper/2607.11508/) (2026)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [Causal DAG Identification for Count Data via Poisson Thinning Structural Equation Models](https://mlsanity.com/paper/2609.06098/) (2026)

## Abstract (arXiv)

Count data naturally arise in many fields, such as finance, neuroscience, and epidemiology, and discovering causal structure among count data is a crucial task in various scientific and industrial scenarios. One of the most common characteristics of count data is the inherent branching structure described by a binomial thinning operator and an independent Poisson distribution that captures both branching and noise. For instance, in a population count scenario, mortality and immigration contribute to the count, where survival follows a Bernoulli distribution, and immigration follows a Poisson distribution. However, causal discovery from such data is challenging due to the non-identifiability issue: a single causal pair is Markov equivalent, i.e., Xrightarrow Y and Yrightarrow X are distributed equivalent. Fortunately, in this work, we found that the causal order from X to its child Y is identifiable if X is a root vertex and has at least two directed paths to Y, or the ancestor of X with the most directed path to X has a directed path to Y without passing X. Specifically, we propose a Poisson Branching Structure Causal Model (PB-SCM) and perform a path analysis on PB-SCM using high-order cumulants. Theoretical results establish the connection between the path and cumulant and demonstrate that the path information can be obtained from the cumulant. With the path information, causal order is identifiable under some graphical conditions. A practical algorithm for learning causal structure under PB-SCM is proposed and the experiments demonstrate and verify the effectiveness of the proposed method.