  We propose a new machine-learning-based anomaly detection strategy for
comparing data with a background-only reference (a form of weak supervision).
The sensitivity of previous strategies degrades significantly when the signal
is too rare or there are many unhelpful features. Our Prior-Assisted Weak
Supervision (PAWS) method incorporates information from a class of signal
models in order to significantly enhance the search sensitivity of weakly
supervised approaches. As long as the true signal is in the pre-specified
class, PAWS matches the sensitivity of a dedicated, fully supervised method
without specifying the exact parameters ahead of time. On the benchmark LHC
Olympics anomaly detection dataset, our mix of semi-supervised and weakly
supervised learning is able to extend the sensitivity over previous methods by
a factor of 10 in cross section. Furthermore, if we add irrelevant (noise)
dimensions to the inputs, classical methods degrade by another factor of 10 in
cross section while PAWS remains insensitive to noise. This new approach could
be applied in a number of scenarios and pushes the frontier of sensitivity
between completely model-agnostic approaches and fully model-specific searches.
