Identifying a Probabilistic Boolean Threshold Network from Samples

Avraham A. Melkman, Xiaoqing Cheng, Wai Ki Ching, Tatsuya Akutsu

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


This paper studies the problem of exactly identifying the structure of a probabilistic Boolean network (PBN) from a given set of samples, where PBNs are probabilistic extensions of Boolean networks. Cheng et al. studied the problem while focusing on PBNs consisting of pairs of AND/OR functions. This paper considers PBNs consisting of Boolean threshold functions while focusing on those threshold functions that have unit coefficients. The treatment of Boolean threshold functions, and triplets and n-tuplets of such functions, necessitates a deepening of the theoretical analyses. It is shown that wide classes of PBNs with such threshold functions can be exactly identified from samples under reasonable constraints, which include: 1) PBNs in which any number of threshold functions can be assigned provided that all have the same number of input variables and 2) PBNs consisting of pairs of threshold functions with different numbers of input variables. It is also shown that the problem of deciding the equivalence of two Boolean threshold functions is solvable in pseudopolynomial time but remains co-NP complete.

Original languageEnglish
Pages (from-to)869-881
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number4
StatePublished - 1 Apr 2018


  • Network inference
  • probabilistic Boolean networks (PBNs)
  • threshold functions
  • threshold networks

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

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