Order-Independent Structure Learning of Multivariate Regression Chain Graphs

Javidian, Mohammad Ali; Valtorta, Marco; Jamshidi, Pooyan

doi:10.1007/978-3-030-35514-2_24

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…PC like algorithm for MVR CGs in (Sonntag, 2014;Sonntag and Peña, 2012), Decompositionbased algorithm for MVR CGs in (Javidian and Valtorta, 2019).…”

Section: Conclusion and Summarymentioning

confidence: 99%

On the Properties of MVR Chain Graphs

Javidian¹,

Valtorta²

2018

Preprint

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Depending on the interpretation of the type of edges, a chain graph can represent different relations between variables and thereby independence models. Three interpretations, known by the acronyms LWF, MVR, and AMP, are prevalent. We review Markov properties for MVR chain graphs and propose an alternative local Markov property for them. Except for pairwise Markov properties, we show that for MVR chain graphs all Markov properties in the literature are equivalent for semigraphoids. We derive a new factorization formula for MVR chain graphs which is more explicit than and different from the proposed factorizations for MVR chain graphs in the literature. Finally, we provide a summary table comparing different features of LWF, AMP, and MVR chain graphs.

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“…PC like algorithm for MVR CGs in (Sonntag, 2014;Sonntag and Peña, 2012), Decompositionbased algorithm for MVR CGs in (Javidian and Valtorta, 2019).…”

Section: Conclusion and Summarymentioning

confidence: 99%

On the Properties of MVR Chain Graphs

Javidian¹,

Valtorta²

2018

Preprint

Self Cite

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“…Due to the difficulty of finding valid scoring functions, CGs structure learning uses the constraint-based method, which employs conditional independence tests to infer the relationship among variables. Similarly, most of the structure learning methods of AMP CGs and MVR CGs also use constraint-based methods (Javidian, Valtorta, & Jamshidi, 2020a;Wang & Bhattacharyya, 2022;Javidian, 2019).…”

Section: Introductionmentioning

confidence: 99%

Block Domain Knowledge-Driven Learning of Chain Graphs Structure

Yang,

Cao

2024

jair

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As the interdependence between arbitrary objects in the real world grows, it becomes gradually important to use chain graphs containing directed and undirected edges to learn the structure among objects. However, independence among some variables corresponds to multiple structures and the direction of edges among variables cannot be uniquely determined. This limitation restricts existing chain graphs structure learning algorithms to only learning their Markov equivalence class. To alleviate this limitation, we de ne the block domain knowledge and propose a block domain knowledge-driven learning chain graphs structure algorithm (KDLCG). The KDLCG algorithm learns the adjacencies and spouses of all variables, which are utilized to directly construct the skeleton and orient the edges of the complexes, thereby learning the Markov equivalence class of the chain graphs. Subsequently, the KDLCG algorithm then updates some edges with Meek rules, guided by block domain knowledge. Finally, the KDLCG algorithm directs some edges by estimating causal effects between two variables, driven by block domain knowledge. Meanwhile, we conduct theoretical analysis to prove the correctness of our algorithm and compare it with the LCD algorithm and MBLWF algorithm on synthetic and real-world datasets. The experimental results validate the effectiveness of our algorithm.

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