# Practical Algorithms for Orientations of Partially Directed Graphical Models

arXiv: https://arxiv.org/abs/2302.14386 · HTML: https://mlsanity.com/paper/2302.14386/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 28 Feb 2023.

## Builds on (most cited first, 7 of 7)

- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Learning Causal Graphs with Small Interventions](https://mlsanity.com/paper/1511.00041/) (2015)
- [A Transformational Characterization of Equivalent Bayesian Network Structures](https://mlsanity.com/paper/1302.4938/) (2013)
- [Active Structure Learning of Causal DAGs via Directed Clique Tree](https://mlsanity.com/paper/2011.00641/) (2020)
- [An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation](https://mlsanity.com/paper/1303.5435/) (2013)
- [Minimal enumeration of all possible total effects in a Markov equivalence class](https://mlsanity.com/paper/2010.08611/) (2020)
- [Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applications](https://mlsanity.com/paper/2205.02654/) (2022)

## Built on by (most cited first, 1 of 1)

- [Lifted Causal Inference](https://mlsanity.com/paper/2606.28024/) (2026)

## Abstract (arXiv)

In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially directed acyclic graph (PDAG), which contains both directed and undirected edges indicating uncertainty of causal relations between random variables. The main focus of this paper is on the maximal orientation task, which, for a given PDAG, aims to orient the undirected edges maximally such that the resulting graph represents the same Markov equivalent DAGs as the input PDAG. This task is a subroutine used frequently in causal discovery, e. g., as the final step of the celebrated PC algorithm. Utilizing connections to the problem of finding a consistent DAG extension of a PDAG, we derive faster algorithms for computing the maximal orientation by proposing two novel approaches for extending PDAGs, both constructed with an emphasis on simplicity and practical effectiveness.