Learning Hidden Graphs From Samples

Several real-world problems, like molecular biology and chemical reactions, have hidden graphs, and we need to learn the hidden graph using edge-detecting samples. In this problem, the learner receives examples explaining whether a set of vertices induces an edge of the hidden graph. This article ex...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 45; no. 10; pp. 11993 - 12003
Main Authors: Abniki, Ahmad, Beigy, Hamid
Format: Journal Article
Language:English
Published: United States IEEE 01.10.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptation models
Apexes
Chemical reactions
Complexity theory
Electron tubes
Empirical risk minimization algorithm
graph learning
Graph theory
Graphs
hidden graphs
Learning
Molecular biology
Monte Carlo methods
nonuniform learning
probably approximately correct learning
Risk management
structural risk minimization algorithm
Topology
Training
Trees (mathematics)
VC-dimension
Vertex sets
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
Online Access:Get full text
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Summary:Several real-world problems, like molecular biology and chemical reactions, have hidden graphs, and we need to learn the hidden graph using edge-detecting samples. In this problem, the learner receives examples explaining whether a set of vertices induces an edge of the hidden graph. This article examines the learnability of this problem using the PAC and Agnostic PAC learning models. By computing the VC-dimension of hypothesis spaces of hidden graphs, hidden trees, hidden connected graphs, and hidden planar graphs through edge-detecting samples, we also find the sample complexity of learning these spaces. We study the learnability of this space of hidden graphs in two cases, namely for known and unknown vertex sets. We show that the class of hidden graphs is uniformly learnable when the vertex set is known. Furthermore, we prove that the family of hidden graphs is not uniformly learnable but is nonuniformly learnable when the vertex set is unknown.
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2023.3283784