## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 11, Number 2 (2017), 5342-5374.

### Distributional equivalence and structure learning for bow-free acyclic path diagrams

Christopher Nowzohour, Marloes H. Maathuis, Robin J. Evans, and Peter Bühlmann

#### Abstract

We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and some sufficient conditions for distributional equivalence of BAPs which are used in an algorithmic approach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also present applications to real and simulated datasets using our publicly available R-package.

#### Article information

**Source**

Electron. J. Statist., Volume 11, Number 2 (2017), 5342-5374.

**Dates**

Received: October 2016

First available in Project Euclid: 28 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1514430421

**Digital Object Identifier**

doi:10.1214/17-EJS1372

**Mathematical Reviews number (MathSciNet)**

MR3743733

**Zentralblatt MATH identifier**

1384.62209

**Keywords**

Causal inference structure learning hidden variables latent variables path diagrams structural equation models distributional equivalence greedy search

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Nowzohour, Christopher; Maathuis, Marloes H.; Evans, Robin J.; Bühlmann, Peter. Distributional equivalence and structure learning for bow-free acyclic path diagrams. Electron. J. Statist. 11 (2017), no. 2, 5342--5374. doi:10.1214/17-EJS1372. https://projecteuclid.org/euclid.ejs/1514430421