Counting and Sampling Markov Equivalent Directed Acyclic Graphs

Talvitie, Topi; Koivisto, Mikko

doi:10.1609/aaai.v33i01.33017984

Cited by 18 publications

(26 citation statements)

References 10 publications

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“…We gave an exact algorithm that is able to compute the posterior of causal effects for data sets of realistic size, with up to around 20 variables. This scaling is similar to the scaling of other exact exponential algorithms for BMA over structures in graphical models, a topic of active research (see, e.g., Koivisto and Sood 2004;Tian and He 2009;Tian, He, and Ram 2010;Parviainen and Koivisto 2011;Chen and Tian 2014;Kangas, Niinimäki, and Koivisto 2015;Talvitie and Koivisto 2019). With a small modification to our approach for computing parent set posteriors, we obtained a variant that is currently the fastest known algorithm for computing ancestor relation posterior probabilities (Chen, Meng, and Tian 2015).…”

Section: Discussionsupporting

confidence: 68%

A Bayesian Approach for Estimating Causal Effects from Observational Data

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Talvitie

Hyttinen

et al. 2020

AAAI

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We present a novel Bayesian method for the challenging task of estimating causal effects from passively observed data when the underlying causal DAG structure is unknown. To rigorously capture the inherent uncertainty associated with the estimate, our method builds a Bayesian posterior distribution of the linear causal effect, by integrating Bayesian linear regression and averaging over DAGs. For computing the exact posterior for all cause-effect variable pairs, we give an algorithm that runs in time O(3d d) for d variables, being feasible up to 20 variables. We also give a variant that computes the posterior probabilities of all pairwise ancestor relations within the same time complexity, significantly improving the fastest previous algorithm. In simulations, our Bayesian method outperforms previous methods in estimation accuracy, especially for small sample sizes. We further show that our method for effect estimation is well-adapted for detecting strong causal effects markedly deviating from zero, while our variant for computing posteriors of ancestor relations is the method of choice for detecting the mere existence of a causal relation. Finally, we apply our method on observational flow cytometry data, detecting several causal relations that concur with previous findings from experimental data.

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Section: Discussionsupporting

confidence: 68%

A Bayesian Approach for Estimating Causal Effects from Observational Data

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Talvitie

Hyttinen

et al. 2020

AAAI

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“…is the number of MAOs when we add m dominating vertices. • Dynamic Programming in Tree Decomposition: The algorithm by Talvitie and Koivisto (2019) based on dynamic programming on the clique-tree with time-complexity in O(2 k k!k 2 n) parameterised by the treewidth k. We implemented 2 AnonMAO using C++, and for the other algorithms, we used the C++ implementations of Talvitie and Koivisto (2019). All the implementations use only one thread of execution and compute the result exactly.…”

Section: Resultsmentioning

confidence: 99%

“…Talvitie and Koivisto (2019) observed that each UCCG considered in the RootPicking algorithm is an induced subgraph of the original UCCG. By memoizing the results, they reduced the time complexity toÕ(2 n ) and also achieved speedups in practice (Talvitie and Koivisto 2019). He and Yu (2016) extended the RootPicking algorithm to better handle dense graphs.…”

Section: Return Solmentioning

confidence: 99%

“…The problems of counting and sampling DAGs in a Markov equivalence class are particularly central in the area of these exploration problems, because approaches to the other problems typically reduce to them (Radhakrishnan, Solus, and Uhler 2017;. For this reason, various algorithms for sampling and counting DAGs in a Markov equivalence class have been proposed (Talvitie and Koivisto 2019;He, Jia, and Yu 2015;Ghassami et al 2019;He and Yu 2016;Bernstein and Tetali 2017).…”

Section: Introductionmentioning

confidence: 99%

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Title

Ganian

Hamm

Talvitie

2020

AAAI

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We consider the problem of counting the number of DAGs which are Markov-equivalent, i.e., which encode the same conditional independencies between random variables. The problem has been studied, among others, in the context of causal discovery, and it is known that it reduces to counting the number of so-called moral acyclic orientations of certain undirected graphs, notably chordal graphs.Our main empirical contribution is a new algorithm which outperforms previously known exact algorithms for the considered problem by a significant margin. On the theoretical side, we show that our algorithm is guaranteed to run in polynomial time on a broad class of chordal graphs, including interval graphs.

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“…Chordal graphs arise in practical applications from a wide variety of fields, such as database management, computer vision, and Bayesian networks. Counting Markov equivalent DAGs in chordal graphs plays an important role in structural learning of Bayesian networks (Ghassami et al 2019;Talvitie and Koivisto 2019). Generating chordal graphs uniformly at random is necessary for testing the performance of those algorithms.…”

Section: Introductionmentioning

confidence: 99%

Sampling Random Chordal Graphs by MCMC (Student Abstract)

Sun

Bezáková

2020

AAAI

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Chordal graphs are a widely studied graph class, with applications in several areas of computer science, including structural learning of Bayesian networks. Many problems that are hard on general graphs become solvable on chordal graphs. The random generation of instances of chordal graphs for testing these algorithms is often required. Nevertheless, there are only few known algorithms that generate random chordal graphs, and, as far as we know, none of them generate chordal graphs uniformly at random (where each chordal graph appears with equal probability). In this paper we propose a Markov chain Monte Carlo (MCMC) method to sample connected chordal graphs uniformly at random. Additionally, we propose a Markov chain that generates connected chordal graphs with a bounded treewidth uniformly at random. Bounding the treewidth parameter (which bounds the largest clique) has direct implications on the running time of various algorithms on chordal graphs. For each of the proposed Markov chains we prove that they are ergodic and therefore converge to the uniform distribution. Finally, as initial evidence that the Markov chains have the potential to mix rapidly, we prove that the chain on graphs with bounded treewidth mixes rapidly for trees (chordal graphs with treewidth bound of one).

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Counting and Sampling Markov Equivalent Directed Acyclic Graphs

Cited by 18 publications

References 10 publications

A Bayesian Approach for Estimating Causal Effects from Observational Data

A Bayesian Approach for Estimating Causal Effects from Observational Data

Title

Sampling Random Chordal Graphs by MCMC (Student Abstract)

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