### Abstract

Class imbalance situations, where one class is rare compared to the other, arise frequently in machine learning applications. It is well known that the usual misclassification error is ill-suited for measuring performance in such settings. A wide range of performance measures have been proposed for this problem. However, despite the large number of studies on this problem, little is understood about the statistical consistency of the algorithms proposed with respect to the performance measures of interest. In this paper, we study consistency with respect to one such performance measure, namely the arithmetic mean of the true positive and true negative rates (AM), and establish that some practically popular approaches, such as applying an empirically determined threshold to a suitable class probability estimate or performing an empirically balanced form of risk minimization, are in fact consistent with respect to the AM (under mild conditions on the underlying distribution). Experimental results confirm our consistency theorems.

Original language | English |
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Title of host publication | 30th International Conference on Machine Learning, ICML 2013 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 1640-1648 |

Number of pages | 9 |

Edition | PART 2 |

Publication status | Published - 2013 |

Externally published | Yes |

Event | 30th International Conference on Machine Learning, ICML 2013 - Atlanta, GA Duration: 16 Jun 2013 → 21 Jun 2013 |

### Other

Other | 30th International Conference on Machine Learning, ICML 2013 |
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City | Atlanta, GA |

Period | 16/6/13 → 21/6/13 |

### Fingerprint

### ASJC Scopus subject areas

- Human-Computer Interaction
- Sociology and Political Science

### Cite this

*30th International Conference on Machine Learning, ICML 2013*(PART 2 ed., pp. 1640-1648). International Machine Learning Society (IMLS).

**On the statistical consistency of algorithms for binary classification under class imbalance.** / Menon, Aditya Krishna; Narasimhan, Harikrishna; Agarwal, Shivani; Chawla, Sanjay.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*30th International Conference on Machine Learning, ICML 2013.*PART 2 edn, International Machine Learning Society (IMLS), pp. 1640-1648, 30th International Conference on Machine Learning, ICML 2013, Atlanta, GA, 16/6/13.

}

TY - GEN

T1 - On the statistical consistency of algorithms for binary classification under class imbalance

AU - Menon, Aditya Krishna

AU - Narasimhan, Harikrishna

AU - Agarwal, Shivani

AU - Chawla, Sanjay

PY - 2013

Y1 - 2013

N2 - Class imbalance situations, where one class is rare compared to the other, arise frequently in machine learning applications. It is well known that the usual misclassification error is ill-suited for measuring performance in such settings. A wide range of performance measures have been proposed for this problem. However, despite the large number of studies on this problem, little is understood about the statistical consistency of the algorithms proposed with respect to the performance measures of interest. In this paper, we study consistency with respect to one such performance measure, namely the arithmetic mean of the true positive and true negative rates (AM), and establish that some practically popular approaches, such as applying an empirically determined threshold to a suitable class probability estimate or performing an empirically balanced form of risk minimization, are in fact consistent with respect to the AM (under mild conditions on the underlying distribution). Experimental results confirm our consistency theorems.

AB - Class imbalance situations, where one class is rare compared to the other, arise frequently in machine learning applications. It is well known that the usual misclassification error is ill-suited for measuring performance in such settings. A wide range of performance measures have been proposed for this problem. However, despite the large number of studies on this problem, little is understood about the statistical consistency of the algorithms proposed with respect to the performance measures of interest. In this paper, we study consistency with respect to one such performance measure, namely the arithmetic mean of the true positive and true negative rates (AM), and establish that some practically popular approaches, such as applying an empirically determined threshold to a suitable class probability estimate or performing an empirically balanced form of risk minimization, are in fact consistent with respect to the AM (under mild conditions on the underlying distribution). Experimental results confirm our consistency theorems.

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M3 - Conference contribution

SP - 1640

EP - 1648

BT - 30th International Conference on Machine Learning, ICML 2013

PB - International Machine Learning Society (IMLS)

ER -