Paper:
Many anomaly detection methods exist that perform well on low-dimensional problems however there is a notable lack of effective methods for highdimensional spaces, such as images. Inspired by recent successes in deep learning we propose a novel approach to anomaly detection using generative adversarial networks. Given a sample under consideration, our method is based on searching for a good representation of that sample in the latent space of the generator; if such a representation is not found, the sample is deemed anomalous. We achieve stateof-the-art performance on standard image benchmark datasets and visual inspection of the most anomalous samples reveals that our method does indeed return anomalies.

Review:
In the paper, the authors proposed using GAN for anomaly detection.
In the method, we first train generator g_\theta from a dataset consisting of only healthy data points.
For evaluating whether the data point x is anomalous or not, we search for a latent representation z such that x \approx g_\theta(z).
If such a representation z could be found, x is deemed to be healthy, and anomalous otherwise.
For searching z, the authors proposed a gradient-descent based method that iteratively update z.
Moreover, the authors proposed updating the parameter \theta of the generator g_\theta.
The authors claimed that this parameter update is one of the novelty of their method, making it different from the method of Schlegl et al. (2017).
In the experiments, the authors showed that the proposed method attained the best AUC on MNIST and CIFAR-10.
In my first reading of the paper, I felt that the baselines in the experiments are too primitive.
Specifically, for KDE and OC-SVM, a naive PCA is used to reduce the data dimension.
Nowadays, there are several publicly available CNNs that are trained on large image datasets such as ImageNet.
Then, one can use such CNNs as feature extractor, that will give better low dimensional expression of the data than the naive PCA.
I believe that the performances of KDE and OC-SVM can be improved by using such feature extractors.
Additionally, I found that some well-known anomaly detection methods are excluded from the comparison.
In Emmott et al. (2013), which the authors referred as a related work, it was reported that Isolation Forest and Ensemble of GMMs performed well on several datasets (better than KDE and OC-SVM).
It would be essential to add these methods as baselines to be compared with the proposed method.
Overall, I think the experimental results are far from satisfactory.
### Response to Revision ###
It is interesting to see that the features extracted from AlexNet are not helpful for anomaly detection.
It would be interesting to see whether features extracted from middle layers are helpful or they are still useless.
I greatly appreciate the authors for their extensive experiments as a response to my comments.
However, I have decided to keep my score unchanged, as the additional experiments have shown that the performance of the proposed method is not significantly better than the other methods.
In particular, in MNIST, GMM performed better.