Recent Advances in Counting and Sampling Markov Equivalent DAGs

Wienöbst, Marcel; Bannach, Max; Liśkiewicz, Maciej

doi:10.1007/978-3-030-87626-5_20

Cited by 5 publications

(6 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both algorithms are easy to implement and very fast in practice (outperforming previous approaches by a large margin in experimental evaluations (Wienöbst et al, 2021b)). We complement our theoretical findings with optimized implementations in C ++ and Julia to facilitate the application to real-world problems.…”

Section: Our Contributionmentioning

confidence: 98%

“…The computation of C G (K) can be performed efficiently through adaptions of wellknown graph traversal algorithms used most prominently in chordality testing. While in (Wienöbst et al, 2021b) specifically the so-called Lexicographic BFS algorithm has been used to compute C G (K), we now propose a more general framework which allows "plugging in" various linear-time chordality testing algorithms.…”

Section: Basics Of the Clique-picking Algorithmmentioning

confidence: 99%

“…The implementation of line 4 is trickier. In (Wienöbst et al, 2021b) Here, we propose a surprisingly simple Monte Carlo algorithm for the implementation of line 4 based on rejection sampling. Due to the combinatorial structure of counting function φ, we are able bound the expected number of draws in this rejection sampling routine by a constant.…”

Section: Uniform Sampling Of Markov Equivalent Dagsmentioning

confidence: 99%

“…As there are, to the best of our knowledge, no other implementations of exact sampling from an MEC, we will confine ourselves to showing that (i) the overhead of the preprocessing for sampling compared to the "standard" Clique-Picking algorithm is negligible and (ii) that sampling after preprocessing is extremely fast. We compare implementations of the algorithms in Julia and generated chordal graphs as described in (Wienöbst et al, 2021b), namely using the subtree intersection method (Seker et al, 2017) with density parameter k = log n (the expected number of neighbors per vertex is proportional to this parameter) and the algorithm by Scheinerman (1988) for sampling random interval graphs (interval graphs form a subclass of chordal graphs). For each input graph, we performed the counting algorithm without and with preprocessing.…”

Section: Uniform Sampling Of Markov Equivalent Dagsmentioning

confidence: 99%

See 3 more Smart Citations

Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applications

Wienöbst¹,

Bannach²,

Liśkiewicz³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Counting and sampling directed acyclic graphs from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper we show that these tasks can be performed in polynomial time, solving a long-standing open problem in this area. Our algorithms are effective and easily implementable. As we show in experiments, these breakthroughs make thought-to-be-infeasible strategies in active learning of causal structures and causal effect identification with regard to a Markov equivalence class practically applicable.

show abstract

Section: Our Contributionmentioning

confidence: 98%

Section: Basics Of the Clique-picking Algorithmmentioning

confidence: 99%

Section: Uniform Sampling Of Markov Equivalent Dagsmentioning

confidence: 99%

Section: Uniform Sampling Of Markov Equivalent Dagsmentioning

confidence: 99%

See 2 more Smart Citations

Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applications

Wienöbst¹,

Bannach²,

Liśkiewicz³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The first problem -computing the number of DAGs within a given MEC, or computationally equivalently, sampling uniformly from the MEC -is important for a number of experimental design algorithms [56], which use Monte-Carlo approximations to compute expectations over the MEC and pick interventions with good average-case behavior. A recent advance [174] provides a polynomialtime algorithm for this task based on a representation of the equivalence class via clique trees, improving over previous algorithms with exponential worst-case runtime [72,14,161,57,6,52].…”

Section: Combinatorial Aspects Of Markov Equivalencementioning

confidence: 99%

Causal Structure Learning: a Combinatorial Perspective

Squires¹,

Uhler²

2022

Preprint

View full text Add to dashboard Cite

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 (DAGs) 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.

show abstract