Out-of-Distribution Detection using BiGAN and MDL

We consider the following problem: we have a large dataset of normal data available. We are now given a new, possibly quite small, set of data, and we are to decide if these are normal data, or if they are indicating a new phenomenon. This is a novelty detection or out-of-distribution detection problem. An example is in medicine, where the normal data is for people with no known disease, and the new dataset people with symptoms. Other examples could be in security. We solve this problem by training a bidirectional generative adversarial network (BiGAN) on the normal data and using a Gaussian graphical model to model the output. We then use universal source coding, or minimum description length (MDL) on the output to decide if it is a new distribution, in an implementation of Kolmogorov and Martin-L\"{o}f randomness. We apply the methodology to both MNIST data and a real-world electrocardiogram (ECG) dataset of healthy and patients with Kawasaki disease, and show better performance in terms of the ROC curve than similar methods.