Paper:
With the recently rapid development in deep learning, deep neural networks have been widely adopted in many real-life applications. However, deep neural networks are also known to have very little control over its uncertainty for test examples, which potentially causes very harmful and annoying consequences in practical scenarios. In this paper, we are particularly interested in designing a higher-order uncertainty metric for deep neural networks and investigate its performance on the out-of-distribution detection task proposed by Hendrycks & Gimpel (2016). Our method first assumes there exists an underlying higher-order distribution P(z), which generated label-wise distribution P(y) over classes on the K-dimension simplex, and then approximate such higher-order distribution via parameterized posterior function p θ (z|x) under variational inference framework, finally we use the entropy of learned posterior distribution p θ (z|x) as uncertainty measure to detect out-of-distribution examples. However, we identify the overwhelming over-concentration issue in such a framework, which greatly hinders the detection performance. Therefore, we further design a log-smoothing function to alleviate such issue to greatly increase the robustness of the proposed entropy-based uncertainty measure. Through comprehensive experiments on various datasets and architectures, our proposed variational Dirichlet framework with entropy-based uncertainty measure is consistently observed to yield significant improvements over many baseline systems.

Review:
This paper proposes a new framework for out-of-distribution detection, based on variational inference and a prior Dirichlet distribution. The Dirichlet distribution is presented, and the way it is used withing the method is discussed (i.e. clipping, scaling, etc). Experiments on several datasets and comparison with the state of the art is reported and extensively discussed.
The motivation of the proposed approach is clear, and I agree with the attempt to regularize the network output. The choice of the Dirichlet distribution is quite natural, as each of its samples are the prior weights of a multinomial distribution. However, some other choices are less clear (clipping, scaling, decision, and the use of a non-informative prior). The overall inference procedure appears to be advantageous in the many experiments that the authors report (several datasets, and several baselines).
The first thought that came to my mind, is that out-of-distribution detection is to classification what outlier detection is to regression. Therefore, relevant and recent work on the topic deserves to be cited, for instance:
S. Lathuiliere, P. Mesejo, X. Alameda-Pineda and R. Horaud, DeepGUM: Learning Deep Robust Regression with a Gaussian-Uniform Mixture Model, In ECCV, 2018.
One thing that I found quite strange at first sight is the choice of clipping the parameters of the Dirichlet distribution. It is said that this is done in order to choose an appropriate prior distribution. However, the choice is not very well motivated, because what "appropriate" means is not discussed. So why do you clip to 1? What would happen if some of the alpha's go over 1? Is it a numerical problem, a modeling problem, a convergence issue?
I would also like the authors to comment on the use of a non-informative Dirichlet distribution within the KL-divergence. The KL divergence measures the deviation between the approximate a posteriori distribution and the true one. If one selects the non-informative Dirichlet distribution, this is not only a brutal approximation of the true posterior, but most importantly a distribution that does not depend on x, and that therefore cannot be truly called posterior.
It is also strange to take a decision based on the maximum alpha. On the contrary, the smallest alpha should be taken, since it is the one that concentrates more probability mass to the associated corner in the simplex.
Regarding the scaling function, it is difficult to grasp its motivation and effects. It is annouced that the aim of the smoothing function is to smooth the concentration parameters alpha. But in what sense? Why do they need to be smoothed? Is this done to avoid numerical/convergence problems? Is this a key part of the model? The same stands, by the way, for the form of the input perturbation.
The experiments are plenty, and I appreciated the sanity check done after introducing the datasets. However, I did not manage to understand why some methods appear in some tables and not in other (for example "Semantic"). I also have the feeling that the authors could have chosen CIFAR-100 in Table 2, since most of the metrics reported are quite high (the problems are not much challenging).
Regarding the parameter eta, I would say that its discussion right after Table 3 is not long enough. Specially, given the high sensitivity of this parameter, as reported in the Table of Figure 4. What is the overall interpretation of this sensitivity?
From a quantitative perspective, the results are impressive, since the propose methods systematically outperforms the baselines (at least the ones reported). However, since these baselines are not the same in all experiments, CIFAR-100 is not used, and the discussion of the results could be richer, I conclude that the experimental section is not too strong.
In addition to all my comments, I would say that the authors chose to exceed the standard limit of 8 pages. Even if this is allowed, the extra pages should be justified. I am affraid that there are many choices not well motivated, and that the discussion of the results is not informative enough. I am therefore not inclined to accept the paper as it is.