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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.