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

<p>We consider the positive-unlabelled multi-label scenario in which multiple target variables are not observed directly. Instead, we observe surrogate variables indicating whether or not the target variables are labelled. The presence of a label means that the corresponding variable is positive. The absence of the label means that the variable can be either positive or negative. We analyze embedded feature selection methods based on two weighted penalized empirical risk minimization frameworks. In the first approach, we introduce weights of observations. The idea is to assign larger weights to observations for which there is a consistency between the values of the true target variable and the corresponding surrogate variable. In the second approach, we consider a weighted empirical risk function which corresponds to the risk function for the true unobserved target variables. The weights in both the methods depend on the unknown propensity score functions, whose estimation is a challenging problem. We propose to use very simple bounds for the propensity score, which leads to relatively simple forms of weights. In the experiments we analyze the predictive power of the methods considered for different labelling schemes.</p>
</abstract>

We consider the positive-unlabelled multi-label scenario in which multiple target variables are not observed directly. Instead, we observe surrogate variables indicating whether or not the target variables are labelled. The presence of a label means that the corresponding variable is positive. The absence of the label means that the variable can be either positive or negative. We analyze embedded feature selection methods based on two weighted penalized empirical risk minimization frameworks. In the first approach, we introduce weights of observations. The idea is to assign larger weights to observations for which there is a consistency between the values of the true target variable and the corresponding surrogate variable. In the second approach, we consider a weighted empirical risk function which corresponds to the risk function for the true unobserved target variables. The weights in both the methods depend on the unknown propensity score functions, whose estimation is a challenging problem. We propose to use very simple bounds for the propensity score, which leads to relatively simple forms of weights. In the experiments we analyze the predictive power of the methods considered for different labelling schemes.

Joint Feature Selection and Classification for Positive Unlabelled Multi–Label Data Using Weighted Penalized Empirical Risk Minimization

Faculty of Mathematics and Information Science

International Journal of Applied Mathematics and Computer Science

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

We consider the positive-unlabelled multi-label scenario in which multiple target variables are not observed directly. Instead, we observe surrogate variables...

Joint Feature Selection and Classification for Positive Unlabelled Multi–Label Data Using Weighted Penalized Empirical Risk Minimization

Published Online: Jul 04, 2022

Page range: 311 - 322

Received: Oct 14, 2021

Accepted: Jan 25, 2022

DOI: https://doi.org/10.34768/amcs-2022-0023

Keywords
positive and unlabelled data, multi-label classification, feature selection, empirical risk minimization

© 2022 Paweł Teisseyre, published by Sciendo

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

Joint Feature Selection and Classification for Positive Unlabelled Multi–Label Data Using Weighted Penalized Empirical Risk Minimization

Published Online: Jul 04, 2022

Page range: 311 - 322

Received: Oct 14, 2021

Accepted: Jan 25, 2022

DOI: https://doi.org/10.34768/amcs-2022-0023

Keywordspositive and unlabelled data, multi-label classification, feature selection, empirical risk minimization

© 2022 Paweł Teisseyre, published by Sciendo

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

Keywords
positive and unlabelled data, multi-label classification, feature selection, empirical risk minimization