The capability of reliably detecting out-of-distribution samples is one of the key factors in deploying a good classifier, as the test distribution always does not match with the training distribution in most real-world applications. In this work, we propose a deep generative classifier which is effective to detect out-of-distribution samples as well as classify in-distribution samples, by integrating the concept of Gaussian discriminant analysis into deep neural networks. Unlike the discriminative (or softmax) classifier that only focuses on the decision boundary partitioning its latent space into multiple regions, our generative classifier aims to explicitly model class-conditional distributions as separable Gaussian distributions. Thereby, we can define the confidence score by the distance between a test sample and the center of each distribution. Our empirical evaluation on multi-class images and tabular data demonstrate that the generative classifier achieves the best performances in distinguishing out-of-distribution samples, and also it can be generalized well for various types of deep neural networks.
Summary:
Unlike the softmax classifier, the authors considered the generative classifier based on Gaussian discriminative analysis and showed that such deep generative classifiers can be useful for detecting out-of-distribution samples. For various benchmark tasks, the proposed method outperforms baselines based on the softmax classifier.  
Detailed comments:
The novelty of this paper is not significant due to the following reasons:
1. The main message (i.e. the concept of the deep generative classifier can be useful for detecting out-of-distribution samples) is not really new because it has been explored before [Lee' 18]. Even though this paper considers training a deep generative classifier directly unlike [Lee' 18], the proposed method looks like a simple variant of [Lee' 18].
2. Missing baselines for training the deep generative classifier: training the deep generative classifier directly has been studied by [Guerriero' 18] and [Pang' 18] but the authors did not compare the proposed training method with such baselines. Because of that, it is hard to say that contributions from proposing a training method are significant. 
Questions:
1. Could the authors consider a case without an identity covariance assumption? Most training methods for deep generative classifier assumes the identity covariance matrix because optimizing the log determinant is not easy. So, it would be interesting if the authors can handle this issue. 
2. Even though the authors assume the identity covariance matrix, the covariance matrix of pre-trained features can not be an identity matrix. Could the authors report the performance of Mahalanobis detector using the proposed deep generative classifier? 
[Lee' 18] Lee, K., Lee, K., Lee, H. and Shin, J., 2018. A simple unified framework for detecting out-of-distribution samples and adversarial attacks. In Advances in Neural Information Processing Systems (pp. 7167-7177).
[Guerriero' 18] Samantha Guerriero, Barbara Caputo, Thomas Mensink, DeepNCM: Deep Nearest Class Mean Classifiers, ICLR workshop 2018.
[Pang' 18] Pang, T., Du, C. and Zhu, J.,  Max-mahalanobis linear discriminant analysis networks. In ICML, 2018.