  A new method for outlier detection and generation is introduced by lifting
data into the space of probability distributions which are not analytically
expressible, but from which samples can be drawn using a neural generator.
Given a mixture of unknown latent inlier and outlier distributions, a
Wasserstein double autoencoder is used to both detect and generate inliers and
outliers. The proposed method, named WALDO (Wasserstein Autoencoder for
Learning the Distribution of Outliers), is evaluated on classical data sets
including MNIST, CIFAR10 and KDD99 for detection accuracy and robustness. We
give an example of outlier detection on a real retail sales data set and an
example of outlier generation for simulating intrusion attacks. However we
foresee many application scenarios where WALDO can be used. To the best of our
knowledge this is the first work that studies both outlier detection and
generation together.
