# A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

arXiv: https://arxiv.org/abs/2205.10083 · HTML: https://mlsanity.com/paper/2205.10083/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 21 of 21)

- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Learning Causal Graphs with Small Interventions](https://mlsanity.com/paper/1511.00041/) (2015)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Cost-Optimal Learning of Causal Graphs](https://mlsanity.com/paper/1703.02645/) (2017)
- [Budgeted Experiment Design for Causal Structure Learning](https://mlsanity.com/paper/1709.03625/) (2017)
- [Active Structure Learning of Causal DAGs via Directed Clique Tree](https://mlsanity.com/paper/2011.00641/) (2020)
- [Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders](https://mlsanity.com/paper/1807.03024/) (2018)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [Experimental Design for Cost-Aware Learning of Causal Graphs](https://mlsanity.com/paper/1810.11867/) (2018)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs](https://mlsanity.com/paper/2012.09679/) (2020)
- [Learning Bayesian Networks in the Presence of Structural Side Information](https://mlsanity.com/paper/2112.10884/) (2021)
- [LazyIter: A Fast Algorithm for Counting Markov Equivalent DAGs and Designing Experiments](https://mlsanity.com/paper/2006.09670/) (2020)
- [Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applications](https://mlsanity.com/paper/2205.02654/) (2022)
- [Counting and Sampling from Markov Equivalent DAGs Using Clique Trees](https://mlsanity.com/paper/1802.01239/) (2018)
- [Interventional Experiment Design for Causal Structure Learning](https://mlsanity.com/paper/1910.05651/) (2019)
- [A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Models](https://mlsanity.com/paper/1302.3600/) (2013)

## Built on by (most cited first, 7 of 7)

- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2509.21423/) (2025)
- [Interventional Causal Discovery in a Mixture of DAGs](https://mlsanity.com/paper/2406.08666/) (2024)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Design of Experiment for Discovering Directed Mixed Graph](https://mlsanity.com/paper/2509.01887/) (2025)
- [SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targets](https://mlsanity.com/paper/2605.16620/) (2026)

## Abstract (arXiv)

We study experiment design for unique identification of the causal graph of a simple SCM, where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skeleton of causal graphs with cycles may not be possible from merely the observational distribution. Furthermore, intervening on a variable in such graphs does not necessarily lead to orienting all the edges incident to it. In this paper, we propose an experiment design approach that can learn both cyclic and acyclic graphs and hence, unifies the task of experiment design for both types of graphs. We provide a lower bound on the number of experiments required to guarantee the unique identification of the causal graph in the worst case, showing that the proposed approach is order-optimal in terms of the number of experiments up to an additive logarithmic term. Moreover, we extend our result to the setting where the size of each experiment is bounded by a constant. For this case, we show that our approach is optimal in terms of the size of the largest experiment required for uniquely identifying the causal graph in the worst case.