  In recommendation systems, items are likely to be exposed to various users
and we would like to learn about the familiarity of a new user with an existing
item. This can be formulated as an anomaly detection (AD) problem
distinguishing between "common users" (nominal) and "fresh users" (anomalous).
Considering the sheer volume of items and the sparsity of user-item paired
data, independently applying conventional single-task detection methods on each
item quickly becomes difficult, while correlations between items are ignored.
To address this multi-task anomaly detection problem, we propose collaborative
anomaly detection (CAD) to jointly learn all tasks with an embedding encoding
correlations among tasks. We explore CAD with conditional density estimation
and conditional likelihood ratio estimation. We found that: $i$) estimating a
likelihood ratio enjoys more efficient learning and yields better results than
density estimation. $ii$) It is beneficial to select a small number of tasks in
advance to learn a task embedding model, and then use it to warm-start all task
embeddings. Consequently, these embeddings can capture correlations between
tasks and generalize to new correlated tasks.
