  We present a detailed study on Variational Autoencoders (VAEs) for anomalous
jet tagging at the Large Hadron Collider. By taking in low-level jet
constituents' information, and training with background QCD jets in an
unsupervised manner, the VAE is able to encode important information for
reconstructing jets, while learning an expressive posterior distribution in the
latent space. When using the VAE as an anomaly detector, we present different
approaches to detect anomalies: directly comparing in the input space or,
instead, working in the latent space. In order to facilitate general search
approaches such as bump-hunt, mass-decorrelated VAEs based on distance
correlation regularization are also studied. We find that the naive
mass-decorrelated VAEs fail at maintaining proper detection performance, by
assigning higher probabilities to some anomalous samples. To build a performant
mass-decorrelated anomalous jet tagger, we propose the Outlier Exposed VAE
(OE-VAE), for which some outlier samples are introduced in the training process
to guide the learned information. OE-VAEs are employed to achieve two goals at
the same time: increasing sensitivity of outlier detection and decorrelating
jet mass from the anomaly score. We succeed in reaching excellent results from
both aspects. Code implementation of this work can be found at
https://github.com/taolicheng/VAE-Jet
