TY - JOUR

T1 - Identification of the Structure of a Probabilistic Boolean Network from Samples Including Frequencies of Outcomes

AU - Akutsu, Tatsuya

AU - Melkman, Avraham A.

N1 - Funding Information:
Manuscript received March 13, 2018; revised September 14, 2018; accepted November 28, 2018. Date of publication December 24, 2018; date of current version July 17, 2019. The work of T. Akutsu was supported by Japan Society for the Promotion of Science, Japan, under Grant 26540125. (Corresponding author: Tatsuya Akutsu.) T. Akutsu is with the Bioinformatics Center, Institute for Chemical Research, Kyoto University, Kyoto 611-0011, Japan (e-mail: takutsu@kuicr.kyoto-u.ac.jp).
Publisher Copyright:
© 2012 IEEE.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - We study the problem of identifying the structure of a probabilistic Boolean network (PBN), a probabilistic model of biological networks, from a given set of samples. This problem can be regarded as an identification of a set of Boolean functions from samples. Existing studies on the identification of the structure of a PBN only use information on the occurrences of samples. In this paper, we also make use of the frequencies of occurrences of subtuples, information that is obtainable from the samples. We show that under this model, it is possible to identify a PBN from among a class of PBNs, for much broader classes of PBNs. In particular, we prove that, under a reasonable assumption, the structure of a PBN can be identified from among the class of PBNs that have at most three functions assigned to each node, but that identification may be impossible if four or more functions are assigned to each node. We also analyze the sample complexity for exactly identifying the structure of a PBN, and present an efficient algorithm for the identification of a PBN consisting of threshold functions from samples.

AB - We study the problem of identifying the structure of a probabilistic Boolean network (PBN), a probabilistic model of biological networks, from a given set of samples. This problem can be regarded as an identification of a set of Boolean functions from samples. Existing studies on the identification of the structure of a PBN only use information on the occurrences of samples. In this paper, we also make use of the frequencies of occurrences of subtuples, information that is obtainable from the samples. We show that under this model, it is possible to identify a PBN from among a class of PBNs, for much broader classes of PBNs. In particular, we prove that, under a reasonable assumption, the structure of a PBN can be identified from among the class of PBNs that have at most three functions assigned to each node, but that identification may be impossible if four or more functions are assigned to each node. We also analyze the sample complexity for exactly identifying the structure of a PBN, and present an efficient algorithm for the identification of a PBN consisting of threshold functions from samples.

KW - Boolean functions

KW - probabilistic Boolean networks (PBNs)

KW - sample complexity

KW - threshold functions

UR - http://www.scopus.com/inward/record.url?scp=85059026968&partnerID=8YFLogxK

U2 - 10.1109/TNNLS.2018.2884454

DO - 10.1109/TNNLS.2018.2884454

M3 - Article

AN - SCOPUS:85059026968

SN - 2162-237X

VL - 30

SP - 2383

EP - 2396

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

IS - 8

M1 - 8587124

ER -