When a Constant Classifier is as Good as Any Linear Classifier |
| |
| Authors: | Steven P Ellis |
| |
| Institution: | 1. NYSPI at Columbia University , New York , New York , USA spe4@columbia.edu |
| |
| Abstract: | A classifier is constant if it classifies all examples into just one class. Call a training data set “(linearly) indiscriminate” if a constant classifier minimizes, among all linear classifiers, the misclassification rate on the training data set. General sufficient conditions are presented for the probability of getting an indiscriminate data set to be positive. Similarly, general sufficient conditions are also presented for the probability of getting an indiscriminate data set to be 0. A small simulation study examines how our results are reflected in the behavior of logistic regression. |
| |
| Keywords: | Classification Logistic regression Misclassification rate |
|
|
