# mk:incos14

### Summary

*Evolving Fair Linear Regression for the Representation of Human-Drawn Regression Lines*. Mario Köppen, Kaori Yoshida and Kei Ohnishi. In 2014 International Conference on Intelligent Networking and Collaborative Systems (INCoS 2014), pages 296-303. IEEE, September 2014.

### Abstract

Here we study a generalization of linear regression to the case of maximal elements of a general fairness relation. The regression then is based on balancing the distances to the data points. The studied relations are lexicographic minimum, maxmin fairness, proportional fairness, and majorities, all in a complementary version to represent minimality. A new combination of proportional fairness and majority is introduced as well. Experiments are performed on human subjects solving the visual task to draw a line fitting to given data points, and by use of evolutionary computation (here by Differential Evolution) the weights of a fair linear regression are adjusted to the human-provided results. The fact that this gives a more precise approximation than (weighted) linear regression hints on the inclusion of the balance among the distances to the given data points in the human decision making process.

### Bibtex entry

`@INPROCEEDINGS { mk:incos14,`

ABSTRACT = { Here we study a generalization of linear regression to the case of maximal elements of a general fairness relation. The regression then is based on balancing the distances to the data points. The studied relations are lexicographic minimum, maxmin fairness, proportional fairness, and majorities, all in a complementary version to represent minimality. A new combination of proportional fairness and majority is introduced as well. Experiments are performed on human subjects solving the visual task to draw a line fitting to given data points, and by use of evolutionary computation (here by Differential Evolution) the weights of a fair linear regression are adjusted to the human-provided results. The fact that this gives a more precise approximation than (weighted) linear regression hints on the inclusion of the balance among the distances to the given data points in the human decision making process. },

AUTHOR = { Mario Köppen and Kaori Yoshida and Kei Ohnishi },

BOOKTITLE = { 2014 International Conference on Intelligent Networking and Collaborative Systems (INCoS 2014) },

ADDED = { 2014-10-16 07:01:39 +0000 },

MODIFIED = { 2014-10-16 07:04:58 +0000 },

DOI = { 10.INCoS?.2014.89 },

MONTH = { September },

ORGANIZATION = { IEEE },

PAGES = { 296-303 },

PDF = { incos14.pdf },

TITLE = { Evolving Fair Linear Regression for the Representation of Human-Drawn Regression Lines },

YEAR = { 2014 },

}