  Anomaly detection (AD) is a crucial task in machine learning with various
applications, such as detecting emerging diseases, identifying financial
frauds, and detecting fake news. However, obtaining complete, accurate, and
precise labels for AD tasks can be expensive and challenging due to the cost
and difficulties in data annotation. To address this issue, researchers have
developed AD methods that can work with incomplete, inexact, and inaccurate
supervision, collectively summarized as weakly supervised anomaly detection
(WSAD) methods. In this study, we present the first comprehensive survey of
WSAD methods by categorizing them into the above three weak supervision
settings across four data modalities (i.e., tabular, graph, time-series, and
image/video data). For each setting, we provide formal definitions, key
algorithms, and potential future directions. To support future research, we
conduct experiments on a selected setting and release the source code, along
with a collection of WSAD methods and data.
