Paper:
Deep approaches to anomaly detection have recently shown promising results over shallow methods on large and complex datasets. Typically anomaly detection is treated as an unsupervised learning problem. In practice however, one may have-in addition to a large set of unlabeled samples-access to a small pool of labeled samples, e.g. a subset verified by some domain expert as being normal or anomalous. Semi-supervised approaches to anomaly detection aim to utilize such labeled samples, but most proposed methods are limited to merely including labeled normal samples. Only a few methods take advantage of labeled anomalies, with existing deep approaches being domain-specific. In this work we present Deep SAD, an end-to-end deep methodology for general semi-supervised anomaly detection. Using an information-theoretic perspective on anomaly detection, we derive a loss motivated by the idea that the entropy of the latent distribution for normal data should be lower than the entropy of the anomalous distribution. We demonstrate in extensive experiments on MNIST, Fashion-MNIST, and CIFAR-10, along with other anomaly detection benchmark datasets, that our method is on par or outperforms shallow, hybrid, and deep competitors, yielding appreciable performance improvements even when provided with only little labeled data.

Review:
[Summary]
The paper proposes an abnormal detection (AD) framework under general settings where 1) unlabeled data, 2) labeled positive (normal) data, and 3) labeled negative (abnormal) data are available (with the last two optional), denoted as semi-supervised AD. Starting from the assumption that abnormal data are sampled from background unpredicted distribution, rather than “cluster” assumption, it is argued that conventional discriminative formulation is not applicable. Motivated by the recent deep AD methods (e.g., deep SVDD), the paper proposes to approach semi-supervised AD from the information theoretic perspective where 1) mutual information between raw data and learnt representation should be maximized (infomax principle), 2) entropy of labeled positive data should be minimized (“compactness” constraint), and 3) enrtropy of labeled negative data should be maximized to reflect the uncertainty assumption of anomaly. The solution is implemented by the encoder of a pre-trained autoencoder that is further fine tuned to enforce entropy assumption on all types of training data. Extensive experiments on benchmarks suggests promising results on the proposed framework versus other state-of-the-arts.
[Comments]
The paper is well written and easy to follow (the presentation is especially pleasant to read). The problem is well defined and of interest to the community under fairly general and practical conditions. Despite the fact that the implementation is only marginally tweaked from previous work (deep SVDD), the theoretical motivation, nevertheless, is sound and well justified, and the empirical evaluation is extensive to reveal the behaviors of the proposed method. It would be better if complexity analysis can also be provided for all concerning methods. Overall, the value of the paper is worth circulation in the community. 
[Area to improve]
The manuscript could be further improved by exploring the training process more. In the current format, the solution follows the strategy of deep SVDD that learns the model in two separate stages: pre-training the autoencoder, and then fitting the encoder to enforce compactness and entropy minimization/maximization. What if these are implemented in an end-to-end fashion? Will this help to achieve a better result?