Modeling PU learning using probabilistic logic programming

The goal of learning from positive and unlabeled (PU) examples is to learn a classifier that predicts the posterior class probability. The challenge is that the available labels in the data are determined by (1) the true class, and (2) the labeling mechanism that selects which positive examples get...

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Published in:Machine learning Vol. 113; no. 3; pp. 1351 - 1372
Main Authors: Verreet, Victor, De Raedt, Luc, Bekker, Jessa
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2024
Springer Nature B.V
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ISSN:0885-6125, 1573-0565, 1573-0565
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Abstract The goal of learning from positive and unlabeled (PU) examples is to learn a classifier that predicts the posterior class probability. The challenge is that the available labels in the data are determined by (1) the true class, and (2) the labeling mechanism that selects which positive examples get labeled, where often certain examples have a higher probability to be selected than others. Incorrectly assuming an unbiased labeling mechanism leads to learning a biased classifier. Yet, this is what most existing methods do. A handful of methods makes more realistic assumptions, but they are either so general that it is impossible to distinguish between the effects of the true classification and of the labeling mechanism, or too restrictive to correctly model the real situation, or require knowledge that is typically unavailable. This paper studies how to formulate and integrate more realistic assumptions for learning better classifiers, by exploiting the strengths of probabilistic logic programming (PLP). Concretely, (1) we propose PU ProbLog: a PLP-based general method that allows to (partially) model the labeling mechanism. (2) We show that our method generalizes existing methods, in the sense that it can model the same assumptions. (3) Thanks to the use of PLP, our method supports also PU learning in relational domains. (4) Our empirical analysis shows that partially modeling the labeling bias, improves the learned classifiers.
AbstractList The goal of learning from positive and unlabeled (PU) examples is to learn a classifier that predicts the posterior class probability. The challenge is that the available labels in the data are determined by (1) the true class, and (2) the labeling mechanism that selects which positive examples get labeled, where often certain examples have a higher probability to be selected than others. Incorrectly assuming an unbiased labeling mechanism leads to learning a biased classifier. Yet, this is what most existing methods do. A handful of methods makes more realistic assumptions, but they are either so general that it is impossible to distinguish between the effects of the true classification and of the labeling mechanism, or too restrictive to correctly model the real situation, or require knowledge that is typically unavailable. This paper studies how to formulate and integrate more realistic assumptions for learning better classifiers, by exploiting the strengths of probabilistic logic programming (PLP). Concretely, (1) we propose PU ProbLog: a PLP-based general method that allows to (partially) model the labeling mechanism. (2) We show that our method generalizes existing methods, in the sense that it can model the same assumptions. (3) Thanks to the use of PLP, our method supports also PU learning in relational domains. (4) Our empirical analysis shows that partially modeling the labeling bias, improves the learned classifiers.
Author De Raedt, Luc
Bekker, Jessa
Verreet, Victor
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Cites_doi 10.1609/aaai.v32i1.11715
10.1007/s10994-020-05877-5
10.1109/TPAMI.2021.3061456
10.1016/S0004-3702(98)00034-4
10.1609/aaai.v36i4.20332
10.1007/s10994-015-5481-4
10.1109/IEEECONF44664.2019.9048765
10.1145/1401890.1401920
10.1007/978-3-319-78090-0_2
10.1609/aaai.v36i6.20624
10.7551/mitpress/4298.003.0069
10.1007/978-3-031-01333-1_30
10.1145/2939672.2939744
10.1007/978-3-642-23780-5_47
10.1017/S1471068414000076
10.1609/aaai.v28i1.9072
10.1016/j.patrec.2013.06.010
10.1137/1.9781611977172.3
10.1609/aaai.v34i04.5848
10.1109/ICDM.2003.1250918
10.1007/978-3-030-46147-8_5
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Weak supervision
Positive unlabeled learning
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References G Blanchard (6461_CR5) 2010; 11
6461_CR21
6461_CR22
6461_CR23
6461_CR24
6461_CR29
6461_CR25
6461_CR26
6461_CR27
6461_CR28
T Khot (6461_CR20) 2015; 100
6461_CR3
6461_CR2
D Fierens (6461_CR10) 2015; 15
6461_CR1
H Blockeel (6461_CR7) 1998; 101
6461_CR11
6461_CR12
6461_CR9
6461_CR13
6461_CR8
6461_CR6
6461_CR30
6461_CR31
6461_CR18
6461_CR19
6461_CR14
6461_CR15
6461_CR16
6461_CR17
J Bekker (6461_CR4) 2020; 109
References_xml – ident: 6461_CR1
  doi: 10.1609/aaai.v32i1.11715
– volume: 109
  start-page: 719
  issue: 4
  year: 2020
  ident: 6461_CR4
  publication-title: Machine Learning
  doi: 10.1007/s10994-020-05877-5
– ident: 6461_CR13
  doi: 10.1109/TPAMI.2021.3061456
– volume: 101
  start-page: 285
  issue: 1–2
  year: 1998
  ident: 6461_CR7
  publication-title: Artificial Intelligence
  doi: 10.1016/S0004-3702(98)00034-4
– ident: 6461_CR29
  doi: 10.1609/aaai.v36i4.20332
– ident: 6461_CR18
– volume: 100
  start-page: 75
  issue: 1
  year: 2015
  ident: 6461_CR20
  publication-title: Machine Learning
  doi: 10.1007/s10994-015-5481-4
– ident: 6461_CR30
– ident: 6461_CR17
  doi: 10.1109/IEEECONF44664.2019.9048765
– ident: 6461_CR9
  doi: 10.1145/1401890.1401920
– ident: 6461_CR3
  doi: 10.1007/978-3-319-78090-0_2
– ident: 6461_CR27
– ident: 6461_CR11
  doi: 10.1609/aaai.v36i6.20624
– ident: 6461_CR21
– ident: 6461_CR23
– ident: 6461_CR28
  doi: 10.7551/mitpress/4298.003.0069
– ident: 6461_CR31
  doi: 10.1007/978-3-031-01333-1_30
– ident: 6461_CR8
  doi: 10.1145/2939672.2939744
– ident: 6461_CR14
  doi: 10.1007/978-3-642-23780-5_47
– volume: 15
  start-page: 358
  year: 2015
  ident: 6461_CR10
  publication-title: Theory and Practice of Logic Programming
  doi: 10.1017/S1471068414000076
– ident: 6461_CR19
  doi: 10.1609/aaai.v28i1.9072
– volume: 11
  start-page: 2973
  year: 2010
  ident: 6461_CR5
  publication-title: Journal of Machine Learning Research
– ident: 6461_CR15
– ident: 6461_CR6
– ident: 6461_CR25
  doi: 10.1016/j.patrec.2013.06.010
– ident: 6461_CR12
  doi: 10.1137/1.9781611977172.3
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  doi: 10.1609/aaai.v34i04.5848
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  doi: 10.1109/ICDM.2003.1250918
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SubjectTerms Artificial Intelligence
Classifiers
Computer Science
Control
Empirical analysis
Labeling
Labels
Learning
Logic programming
Machine Learning
Mechatronics
Modeling
Modelling
Natural Language Processing (NLP)
Positive unlabeled learning
Probabilistic logic programming
Robotics
Simulation and Modeling
Special Issue on Learning and Reasoning 2022
Statistical analysis
Unidentifiability
Weak supervision
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