Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs

Wienöbst, Marcel; Bannach, Max; Liśkiewicz, Maciej

doi:10.1609/aaai.v35i13.17448

Cited by 7 publications

(22 citation statements)

References 16 publications

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“…While the algorithms for computing maximal orientations used in practice resort to directly applying the Meek rules, the best theoretical methods are based on two other important primitives of causal analysis: (i) the consistent extension of a PDAG to a DAG and (ii) computing the CPDAG representation of the graphs Markov equivalent to a given DAG. This was already mentioned by Chickering (1995) and generalized to instances with background knowledge by Wienöbst et al (2021). Using the clever algorithm of Chickering (1995), the second task (ii) can be solved in linear time.…”

Section: Introductionmentioning

confidence: 95%

“…As discussed above, algorithms for extending PDAGs play a key role in the maximal orientation task. While, from a theoretical point of view, previous results suggest that it is likely not possible to further improve the asymptotic run time of extendability algorithms, as Wienöbst et al (2021) gave a conditional O(n 3 ) lower bound for combinatorial algorithms, from a practical perspective, the current algorithms are either extremely simple, as Dor-Tarsi's approach, or very sophisticated with considerable practical overhead, as the methods proposed by Wienöbst et al (2021). In this work, we are searching for a middle ground and give two novel approaches to extend PDAGs, with the main focus lying on simplicity and effectiveness.…”

Section: Two New Simple Algorithms For Extendabilitymentioning

confidence: 99%

“…The primary significance of the MPDAG model, including completed PDAGs (CPDAGs, also called essential graphs) (Andersson et al, 1997) is that it represents Markov equivalent DAGs in an elegant and convenient way. It is commonly used for solving many important problems as, e.g., counting and sampling Markov equivalent DAGs (He et al, 2015;Wienöbst et al, 2021), estimating causal effects (Maathuis et al, 2009;van der Zander and Liśkiewicz, 2016;Perković et al, 2017), or learning causal models (Chickering, 2002), where CPDAGs represent the states of the search space. Consequently, orienting a given PDAG maximally, is a frequently used primitive in causal inference and discovery, perhaps most prominently arising in constraint-based causal structure learning, as, e. g., the final step in the PC algorithm (Spirtes et al, 2000;Kalisch and Bühlman, 2007) and its modifications.…”

Section: Introductionmentioning

confidence: 99%

“…This approach is used in the GES algorithm (Chickering, 2002) and in a modified way in the GIES algorithm (Hauser and Bühlmann, 2012), the latter however having the same worst-case complexity as the direct application of the Meek rules discussed above. More recently, Wienöbst et al (2021) generalized both approaches, while maintaining the optimal time complexity of O(n 3 ), to maximally orient a PDAG to an MPDAG.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, we aim to illustrate the strengths of using consistent DAG extensions in the computation of the maximal orientation of a PDAG. While this approach has been proposed theoretically in (Chickering, 1995;Wienöbst et al, 2021), it has only been used in special cases and has not found widespread application in practice, evidenced by the fact that most software packages such as pcalg (Kalisch et al, 2012) and causaldag (Squires, 2018) rely on algorithms, which apply the Meek rules directly. Utilizing consistent DAG extensions instead, yields a better worst-case complexity and is superior in practice as we demonstrate in our experiments.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Practical Algorithms for Orientations of Partially Directed Graphical Models

Luttermann¹,

Wienöbst²,

Liśkiewicz³

2023

Preprint

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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.

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Section: Introductionmentioning

confidence: 95%

Section: Two New Simple Algorithms For Extendabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Practical Algorithms for Orientations of Partially Directed Graphical Models

Luttermann¹,

Wienöbst²,

Liśkiewicz³

2023

Preprint

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Causal Discovery of Dynamic Models for Predicting Human Spatial Interactions

et al. 2022

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Identifying the main features and learning the causal relationships of a dynamic system from timeseries of sensor data are key problems in many real-world robot applications. In this paper, we propose an extension of a state-of-the-art causal discovery method, PCMCI, embedding an additional feature-selection module based on transfer entropy. Starting from a prefixed set of variables, the new algorithm reconstructs the causal model of the observed system by considering only its main features and neglecting those deemed unnecessary for understanding the evolution of the system. We first validate the method on a toy problem and on synthetic data of brain network, for which the ground-truth models are available, and then on a real-world robotics scenario using a large-scale time-series dataset of human trajectories. The experiments demonstrate that our solution outperforms the previous state-of-the-art technique in terms of accuracy and computational efficiency, allowing better and faster causal discovery of meaningful models from robot sensor data.

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Causal Structure Learning: A Combinatorial Perspective

Squires

Uhler

2022

Found Comput Math

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In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs and various generalizations which allow for some variables to be unobserved in the available data. We devote special attention to two fundamental combinatorial aspects of causal structure learning. First, we discuss the structure of the search space over causal graphs. Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can be refined by adding interventional data.

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Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs

Cited by 7 publications

References 16 publications

Practical Algorithms for Orientations of Partially Directed Graphical Models

Practical Algorithms for Orientations of Partially Directed Graphical Models

Causal Discovery of Dynamic Models for Predicting Human Spatial Interactions

Causal Structure Learning: A Combinatorial Perspective

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