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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

Counting and Sampling from Markov Equivalent DAGs Using Clique Trees

February 1, 2023

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Authors

AmirEmad Ghassami

University of Illinois at Urbana-Champaign


Saber Salehkaleybar

Sharif University of Technology


Negar Kiyavash

University of Illinois at Urbana-Champaign


Kun Zhang

Carnegie Mellon University


DOI:

10.1609/aaai.v33i01.33013664


Abstract:

A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equivalence, based on conditional independence relations among the variables. Therefore, the number of DAGs equivalent to the ground truth DAG is an indicator of the causal complexity of the underlying structure–roughly speaking, it shows how many interventions or how much additional information is further needed to recover the underlying DAG. In this paper, we propose a new technique for counting the number of DAGs in a Markov equivalence class. Our approach is based on the clique tree representation of chordal graphs. We show that in the case of bounded degree graphs, the proposed algorithm is polynomial time. We further demonstrate that this technique can be utilized for uniform sampling from a Markov equivalence class, which provides a stochastic way to enumerate DAGs in the equivalence class and may be needed for finding the best DAG or for causal inference given the equivalence class as input. We also extend our counting and sampling method to the case where prior knowledge about the underlying DAG is available, and present applications of this extension in causal experiment design and estimating the causal effect of joint interventions.

Topics: AAAI

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HOW TO CITE:

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang Counting and Sampling from Markov Equivalent DAGs Using Clique Trees Proceedings of the AAAI Conference on Artificial Intelligence (2019) 3664-3671.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang Counting and Sampling from Markov Equivalent DAGs Using Clique Trees AAAI 2019, 3664-3671.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang (2019). Counting and Sampling from Markov Equivalent DAGs Using Clique Trees. Proceedings of the AAAI Conference on Artificial Intelligence, 3664-3671.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang. Counting and Sampling from Markov Equivalent DAGs Using Clique Trees. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.3664-3671.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang. 2019. Counting and Sampling from Markov Equivalent DAGs Using Clique Trees. "Proceedings of the AAAI Conference on Artificial Intelligence". 3664-3671.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang. (2019) "Counting and Sampling from Markov Equivalent DAGs Using Clique Trees", Proceedings of the AAAI Conference on Artificial Intelligence, p.3664-3671

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang, "Counting and Sampling from Markov Equivalent DAGs Using Clique Trees", AAAI, p.3664-3671, 2019.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang. "Counting and Sampling from Markov Equivalent DAGs Using Clique Trees". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.3664-3671.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang. "Counting and Sampling from Markov Equivalent DAGs Using Clique Trees". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 3664-3671.

AmirEmad Ghassami||Saber Salehkaleybar||Negar Kiyavash||Kun Zhang. Counting and Sampling from Markov Equivalent DAGs Using Clique Trees. AAAI[Internet]. 2019[cited 2023]; 3664-3671.


ISSN: 2374-3468


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