Infinitely Imbalanced Logistic Regression

  • Authors:
  • Art B. Owen

  • Affiliations:
  • -

  • Venue:
  • The Journal of Machine Learning Research
  • Year:
  • 2007

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Abstract

In binary classification problems it is common for the two classes to be imbalanced: one case is very rare compared to the other. In this paper we consider the infinitely imbalanced case where one class has a finite sample size and the other class's sample size grows without bound. For logistic regression, the infinitely imbalanced case often has a useful solution. Under mild conditions, the intercept diverges as expected, but the rest of the coefficient vector approaches a non trivial and useful limit. That limit can be expressed in terms of exponential tilting and is the minimum of a convex objective function. The limiting form of logistic regression suggests a computational shortcut for fraud detection problems.