<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Positive unlabeled (PU) learning is an important problem motivated by the occurrence of this type of partial observability in many applications. The present paper reconsiders recent advances in parametric modeling of PU data based on empirical likelihood maximization and argues that they can be significantly improved. The proposed approach is based on the fact that the likelihood for the logistic fit and an unknown labeling frequency can be expressed as the sum of a convex and a concave function, which is explicitly given. This allows methods such as the concave-convex procedure (CCCP) or its variant, the disciplined convex-concave procedure (DCCP), to be applied. We show by analyzing real data sets that, by using the DCCP to solve the optimization problem, we obtain significant improvements in the posterior probability and the label frequency estimation over the best available competitors.</p>
</abstract>

Positive unlabeled (PU) learning is an important problem motivated by the occurrence of this type of partial observability in many applications. The present paper reconsiders recent advances in parametric modeling of PU data based on empirical likelihood maximization and argues that they can be significantly improved. The proposed approach is based on the fact that the likelihood for the logistic fit and an unknown labeling frequency can be expressed as the sum of a convex and a concave function, which is explicitly given. This allows methods such as the concave-convex procedure (CCCP) or its variant, the disciplined convex-concave procedure (DCCP), to be applied. We show by analyzing real data sets that, by using the DCCP to solve the optimization problem, we obtain significant improvements in the posterior probability and the label frequency estimation over the best available competitors.

Revisiting Strategies for Fitting Logistic Regression for Positive and Unlabeled Data

Faculty of Mathematics and Information Sciences

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Positive unlabeled (PU) learning is an important problem motivated by the occurrence of this type of partial observability in many applications. The present...

Revisiting Strategies for Fitting Logistic Regression for Positive and Unlabeled Data

Data publikacji: 04 lip 2022

Zakres stron: 299 - 309

Otrzymano: 05 lis 2021

Przyjęty: 10 lut 2022

DOI: https://doi.org/10.34768/amcs-2022-0022

Słowa kluczowe
positive and unlabeled learning, empirical risk, logistic regression, concave-convex optimization

© 2022 Adam Wawrzeńczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Revisiting Strategies for Fitting Logistic Regression for Positive and Unlabeled Data

Data publikacji: 04 lip 2022

Zakres stron: 299 - 309

Otrzymano: 05 lis 2021

Przyjęty: 10 lut 2022

DOI: https://doi.org/10.34768/amcs-2022-0022

Słowa kluczowepositive and unlabeled learning, empirical risk, logistic regression, concave-convex optimization

© 2022 Adam Wawrzeńczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Słowa kluczowe
positive and unlabeled learning, empirical risk, logistic regression, concave-convex optimization