Anomaly Detection with Discrete Minimax Classifier for Imbalanced Dataset or Uncertain Class Proportions

Supervised classification is becoming a useful tool in condition monitoring. For example, from a set of measured features (temperature, vibration, etc.), we might be interested in predicting machine failures. Given some costs of class misclassifications and a set of labeled learning samples, this task aims to fit a decision rule by minimizing the empirical risk of misclassifications. However, learning a classifier when the class proportions of the training set are uncertain, and might differ from the unknown state of nature, may increase the misclassification risk when classifying some test samples. This drawback can also occur when dealing with imbalanced datasets, which is common in condition monitoring. To make a decision rule robust with respect to the class proportions, a solution is to learn a decision rule which minimizes the maximum class-conditional risk. Such a decision rule is called a minimax classifier. This paper studies the minimax classifier for classifying discrete or discretized features between several classes. Our algorithm is applied to a real condition monitoring database.