Adapting Linear Discriminant Analysis to the Paradigm of Learning from Label Proportions

Research areas:

• Methodology - Machine learning

Year:

2016

Type of Publication:

In Proceedings

Authors:

• Pérez-Ortiz, María
• Gutiérrez, Pedro Antonio
• Carbonero-Ruz, Mariano
• Hervás-Martínez, César

Book title:

2016 IEEE Symposium Series on Computational Intelligence (IEEE SSCI 2016)

Pages:

1-7

Organization:

Athens, Greece

Month:

6th-9th December

ISBN:

978-1-5090-4241-8

BibTex:

@conference{162016, author = "Mar{\'i}a P{\'e}rez-Ortiz and Pedro Antonio Guti{\'e}rrez and Mariano Carbonero-Ruz and C{\'e}sar Herv{\'a}s-Mart{\'i}nez", abstract = "Learning from label proportions denotes the learning paradigm where training data is provided in groups (or {\&}#039;bags{\&}#039;), and only the label proportion of each bag is available. The objective is to learn a model to predict the class label of an individual instance, which differentiates this paradigm from the one of multi-instance learning. This learning setting presents very different applications in political science, marketing, healthcare and, in general, all fields concerning anonymous data. Two different iterative strategies are proposed in this paper to deal with this type of problems, both based on the optimisation of the class membership of the patterns using the pattern distribution per bag and the label proportions. To do so, linear discriminant analysis is reformulated to deal with non-crisp class memberships. A thorough set of experiments is conducted to test: 1) the performance gap between these approaches and the fully supervised setting, 2) the potential advantages of optimising class memberships by our proposals, and 3) the influence of factors such as the bag size and the number of classes of the problem in the performance. The results of these experiments are promising, but further research should be encouraged for studying more complex data configurations.", booktitle = "2016 IEEE Symposium Series on Computational Intelligence (IEEE SSCI 2016)", doi = "10.1109/SSCI.2016.7850150", isbn = "978-1-5090-4241-8", month = "6th-9th December", organization = "Athens, Greece", pages = "1--7", publisher = "IEEE Press", title = "{A}dapting {L}inear {D}iscriminant {A}nalysis to the {P}aradigm of {L}earning from {L}abel {P}roportions", url = "doi.org/10.1109/SSCI.2016.7850150", year = "2016", }

Abstract:

Learning from label proportions denotes the learning paradigm where training data is provided in groups (or 'bags'), and only the label proportion of each bag is available. The objective is to learn a model to predict the class label of an individual instance, which differentiates this paradigm from the one of multi-instance learning. This learning setting presents very different applications in political science, marketing, healthcare and, in general, all fields concerning anonymous data. Two different iterative strategies are proposed in this paper to deal with this type of problems, both based on the optimisation of the class membership of the patterns using the pattern distribution per bag and the label proportions. To do so, linear discriminant analysis is reformulated to deal with non-crisp class memberships. A thorough set of experiments is conducted to test: 1) the performance gap between these approaches and the fully supervised setting, 2) the potential advantages of optimising class memberships by our proposals, and 3) the influence of factors such as the bag size and the number of classes of the problem in the performance. The results of these experiments are promising, but further research should be encouraged for studying more complex data configurations.