# Identifiability of AMP chain graph models

arXiv: https://arxiv.org/abs/2106.09350 · HTML: https://mlsanity.com/paper/2106.09350/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 79 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [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)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Learning linear structural equation models in polynomial time and sample complexity](https://mlsanity.com/paper/1707.04673/) (2017)
- [A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization](https://mlsanity.com/paper/1508.04874/) (2015)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [A polynomial-time algorithm for learning nonparametric causal graphs](https://mlsanity.com/paper/2006.11970/) (2020)
- [Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexity](https://mlsanity.com/paper/1703.01196/) (2017)
- [Causal Discovery from Incomplete Data: A Deep Learning Approach](https://mlsanity.com/paper/2001.05343/) (2020)
- [Geometric Rescaling Algorithms for Submodular Function Minimization](https://mlsanity.com/paper/1707.05065/) (2017)
- [AMP Chain Graphs: Minimal Separators and Structure Learning Algorithms](https://mlsanity.com/paper/2002.10870/) (2020)
- [Marginal AMP Chain Graphs](https://mlsanity.com/paper/1305.0751/) (2013)
- [Every LWF and AMP chain graph originates from a set of causal models](https://mlsanity.com/paper/1312.2967/) (2013)
- [Alternative Markov and Causal Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1511.05835/) (2015)
- [Identification of Strong Edges in AMP Chain Graphs](https://mlsanity.com/paper/1711.09990/) (2017)

## Abstract (arXiv)

We study identifiability of Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs. For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are monotone non-decreasing in topological order. This condition extends the equal variance identifiability criterion for Bayes nets, and it can be generalized from determinants to any super-additive function on positive semidefinite matrices. When the component decomposition is unknown, we describe conditions that allow recovery of the full structure using a polynomial time algorithm based on submodular function minimization. We also conduct experiments comparing our algorithm's performance against existing baselines.