Active Structure Learning of Causal DAGs via Directed Clique Tree

Squires, Chandler; Magliacane, Sara; Greenewald, Kristjan; Katz, Dmitriy; Kocaoğlu, Murat; Shanmugam, Karthikeyan

doi:10.48550/arxiv.2011.00641

Cited by 5 publications

(32 citation statements)

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“…To the best of our knowledge, this is the rst work that addresses the problem of tight (up to a constant factor) universal lower bounds. We note that the best known universal lower bounds (Squires et al, 2020) so far are not tight and provide concrete examples of graph families that illustrate this in Section 3.2.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, learning algorithms based only on the observed joint distribution (Glymour et al, 2019) cannot direct these remaining edges. As a result, algorithms which use additional interventional distributions were developed (Squires et al (2020) and references therein). In addition to the joint distribution, these algorithms also assume access to interventional distributions generated as a result of randomizing some target vertices in the original CBN (a process called intervention) and thereby breaking their dependence on any of their ancestors.…”

Section: Introductionmentioning

confidence: 99%

“…Interventions, especially on a large set of nodes, however, can be expensive to perform (Kocaoglu et al, 2017). In this respect, the setting of atomic interventions, where each intervention is on a single node, is already very interesting and nding the smallest number of atomic interventions that can orient the MEC is well studied (Squires et al, 2020). A long line of work, including those cited above, has considered in various settings the problem of designing methods for nding the smallest set of atomic interventions that would fully orient all edges of a given MEC.…”

Section: Introductionmentioning

confidence: 99%

“…Universal Lower Bounds: While several works have reported lower bounds (on minimum number of atomic interventions required to orient an MEC) in di erent settings, a very satisfying solution concept for such lower bounds, called universal lower bounds, was proposed by Squires et al (2020). A universal lower bound of 𝐿 atomic interventions for orienting a given MEC means that if a set of atomic interventions is of size less than 𝐿, then for every ground-truth DAG 𝐷 in the MEC, the set 𝑆 will fail to fully orient the MEC.…”

Section: Introductionmentioning

confidence: 99%

“…The goal is to nd a universal lower bound such that for any DAG 𝐷 in the MEC, the smallest set of atomic interventions that can orient the MEC into 𝐷 has size bounded above by a constant factor of the universal lower bound. Similar to Squires et al (2020), we work in the setting of causally su cient models, i.e. there are no hidden confounders, selection bias or feedback.…”

Section: Introductionmentioning

confidence: 99%

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Universal Lower Bound for Learning Causal DAGs with Atomic Interventions

Porwal¹,

Srivastava²,

Sinha³

2021

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A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected edges have to be oriented using interventions, which can be very expensive to perform in applications. Thus, the problem of minimizing the number of interventions needed to fully orient the MEC has received a lot of recent attention, and is also the focus of this work. We prove two main results. The rst is a new universal lower bound on the number of atomic interventions that any algorithm (whether active or passive) would need to perform in order to orient a given MEC. Our second result shows that this bound is, in fact, within a factor of two of the size of the smallest set of atomic interventions that can orient the MEC. Our lower bound is provably better than previously known lower bounds. The proof of our lower bound is based on the new notion of clique-block shared-parents (CBSP) orderings, which are topological orderings of DAGs without v-structures and satisfy certain special properties. Further, using simulations on synthetic graphs and by giving examples of special graph families, we show that our bound is often signi cantly better.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Universal Lower Bound for Learning Causal DAGs with Atomic Interventions

Porwal¹,

Srivastava²,

Sinha³

2021

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Quantum algorithm for Feynman loop integrals

Ramírez-Uribe,

Rentería-Olivo,

Rodrigo

et al. 2021

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We present the first flagship application of a quantum algorithm to Feynman loop integrals. The two onshell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. Since the number of causal states to be identified is nearly half of the total number of states in most cases, an efficient modification of Grover's algorithm is introduced, requiring only O(1) iterations. The output of the quantum algorithm in the IBM quantum simulator is used to bootstrap the causal representation in the loop-tree duality of representative multiloop topologies. The algorithm may also find application and interest in graph theory to solve problems involving directed acyclic graphs.

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Causal Bandits with Unknown Graph Structure

Lu¹,

Meisami²,

Tewari³

2021

Preprint

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In causal bandit problems, the action set consists of interventions on variables of a causal graph. Several researchers have recently studied such bandit problems and pointed out their practical applications. However, all existing works rely on a restrictive and impractical assumption that the learner is given full knowledge of the causal graph structure upfront. In this paper, we develop novel causal bandit algorithms without knowing the causal graph. Our algorithms work well for causal trees, causal forests and a general class of causal graphs. The regret guarantees of our algorithms greatly improve upon those of standard multi-armed bandit (MAB) algorithms under mild conditions. Lastly, we prove our mild conditions are necessary: without them one cannot do better than standard MAB bandit algorithms.

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Active Structure Learning of Causal DAGs via Directed Clique Tree

Cited by 5 publications

References 0 publications

Universal Lower Bound for Learning Causal DAGs with Atomic Interventions

Universal Lower Bound for Learning Causal DAGs with Atomic Interventions

Quantum algorithm for Feynman loop integrals

Causal Bandits with Unknown Graph Structure

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