## Abstract

Efficiency criteria for conformal prediction, such as observed fuzziness (i.e., the sum of p-values associated with false labels), are commonly used to evaluate the performance of given conformal predictors. Here, we investigate whether it is possible to exploit efficiency criteria to learn classifiers, both conformal predictors and point classifiers, by using such criteria as training objective functions.

The proposed idea is implemented for the problem of binary classification of hand-written digits. By choosing a 1-dimensional model class (with one real-valued free parameter), we can solve the optimization problems through an (approximate) exhaustive search over (a discrete version of) the parameter space. Our empirical results suggest that conformal predictors trained by minimizing their observed fuzziness perform better than conformal predictors trained in the traditional way by minimizing the prediction error of the corresponding point classifier. They also have reasonable performance in terms of their prediction error on the test set.

The proposed idea is implemented for the problem of binary classification of hand-written digits. By choosing a 1-dimensional model class (with one real-valued free parameter), we can solve the optimization problems through an (approximate) exhaustive search over (a discrete version of) the parameter space. Our empirical results suggest that conformal predictors trained by minimizing their observed fuzziness perform better than conformal predictors trained in the traditional way by minimizing the prediction error of the corresponding point classifier. They also have reasonable performance in terms of their prediction error on the test set.

Original language | English |
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Title of host publication | Proceedings of Machine Learning Research |

Editors | Alex Gammerman, Vladimir Vovk, Zhiyuan Luo, Evgueni Smirnov, Giovanni Cherubin |

Pages | 55-64 |

Number of pages | 10 |

Volume | 128 |

Publication status | Published - Sept 2020 |

## Keywords

- classification
- criterion of efficiency
- inductive conformal prediction
- observed fuzziness