  We propose a new model-agnostic search strategy for physics beyond the
standard model (BSM) at the LHC, based on a novel application of neural density
estimation to anomaly detection. Our approach, which we call Classifying
Anomalies THrough Outer Density Estimation (CATHODE), assumes the BSM signal is
localized in a signal region (defined e.g. using invariant mass). By training a
conditional density estimator on a collection of additional features outside
the signal region, interpolating it into the signal region, and sampling from
it, we produce a collection of events that follow the background model. We can
then train a classifier to distinguish the data from the events sampled from
the background model, thereby approaching the optimal anomaly detector. Using
the LHC Olympics R&D dataset, we demonstrate that CATHODE nearly saturates the
best possible performance, and significantly outperforms other approaches that
aim to enhance the bump hunt (CWoLa Hunting and ANODE). Finally, we demonstrate
that CATHODE is very robust against correlations between the features and
maintains nearly-optimal performance even in this more challenging setting.
