Feature extraction for universal hypothesis testing via rank-constrained optimization

We consider the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large, motivated by the application in anomaly detection. We investigate a feature-based technique called mismatched universal test for this purpose. Its finite-observation performance can be much better than the (optimal) Hoeffding test, and good performance depends crucially on the choice of features. We propose a feature extraction technique with performance guarantees. This talk is an overview of our research on the mismatched universal test and the feature extraction technique.