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Directed Acyclic Graph Reconstruction Leveraging Prior Partial Ordering Information

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Machine Learning, Optimization, and Data Science (LOD 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11943))

Abstract

Reconstructing directed acyclic graphs (DAGs) from observed data constitutes an important machine learning task. It has important applications in systems biology and functional genomics. However, it is a challenging learning problem, due to the need to consider all possible orderings of the network nodes and score the resulting network structures based on the available data. The resulting computational complexity for enumerating all possible orderings is exponential in the size of the network. A large number of methods based on various modeling formalisms have been developed to address this problem, primarily focusing on developing fast algorithms to reduce computational time. On many instances, partial topological information may be available for subsets of the nodes; for example, in biology one has information about transcription factors that regulate (precede) other genes, or such information can be obtained from perturbation/silencing experiments for subsets of DAG nodes (genes).

We develop a framework for estimating DAGs from observational data under the assumption that the nodes are partitioned into sets and a complete topological ordering exists amongst them. The proposed approach combines (i) (penalized) regression to estimate edges between nodes across different sets, with (ii) the popular PC-algorithm that identifies the skeleton of the graph within each set. In the final step, we combine the results from the previous two steps to screen out redundant edges. We illustrate the performance of the proposed approach on topologies extracted from the DREAM3 competition. The numerical results showcase the usefulness of the additional partial topological ordering information for this challenging learning problem.

Supported by grants NIH 1U01CA23548701 and 5R01GM11402904 to G. Michailidis.

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Author information

Authors and Affiliations

  1. Informatics Institute, University of Florida, Gainesville, USA

    Pei-Li Wang & George Michailidis

  2. Department of Statistics, University of Florida, Gainesville, USA

    George Michailidis

Authors
  1. Pei-Li Wang
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  2. George Michailidis
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Corresponding author

Correspondence to George Michailidis .

Editor information

Editors and Affiliations

  1. University of Cambridge, Cambridge, UK

    Giuseppe Nicosia

  2. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  3. Harvard University, Cambridge, MA, USA

    Renato Umeton

  4. Università di Catania, Catania, Catania, Italy

    Giovanni Giuffrida

  5. Almawave, Rome, Roma, Italy

    Vincenzo Sciacca

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Wang, PL., Michailidis, G. (2019). Directed Acyclic Graph Reconstruction Leveraging Prior Partial Ordering Information. In: Nicosia, G., Pardalos, P., Umeton, R., Giuffrida, G., Sciacca, V. (eds) Machine Learning, Optimization, and Data Science. LOD 2019. Lecture Notes in Computer Science(), vol 11943. Springer, Cham. https://doi.org/10.1007/978-3-030-37599-7_38

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  • DOI: https://doi.org/10.1007/978-3-030-37599-7_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-37598-0

  • Online ISBN: 978-3-030-37599-7

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