State-of-the-art Unsupervised Domain Adaptation (UDA) methods learn transferable features by minimizing the feature distribution discrepancy between the source and target domains. Different from these methods which do not model the feature distributions explicitly, in this paper, we explore explicit feature distribution modeling for UDA. In particular, we propose Distribution Matching Prototypical Network (DMPN) to model the deep features from each domain as Gaussian mixture distributions. With explicit feature distribution modeling, we can easily measure the discrepancy between the two domains. In DMPN, we propose two new domain discrepancy losses with probabilistic interpretations. The first one minimizes the distances between the corresponding Gaussian component means of the source and target data. The second one minimizes the pseudo negative log likelihood of generating the target features from source feature distribution. To learn both discriminative and domain invariant features, DMPN is trained by minimizing the classification loss on the labeled source data and the domain discrepancy losses together. Extensive experiments are conducted over two UDA tasks. Our approach yields a large margin in the Digits Image transfer task over state-of-the-art approaches. More remarkably, DMPN obtains a mean accuracy of 81.4% on VisDA 2017 dataset. The hyper-parameter sensitivity analysis shows that our approach is robust w.r.t hyper-parameter changes.
<Paper summary>
The authors proposed Distribution Matching Prototypical Network (DMPN) for unsupervised domain adaptation. DMPN extracts features from the input data and models them as Gaussian mixture distributions. By explicitly modeling the distributions that the features follow, the discrepancy between the distribution of source data and that of target data can be easily evaluated. DMPN is trained by jointly minimizing two kinds of loss, which are classification loss on the source data and domain discrepancy loss that is calculated via the explicit models. Experimental results on two popular benchmark datasets validate the advantage of DMPN over other state-of-the-art methods. 
<Review summary>
The proposed method seems simple but empirically performs well. The paper is well written and easy to follow, so we can maybe easily implement it. However, I have several concerns mainly about the details and theories of the proposed method, which makes my score a bit lower than the border line. Given clarifications in an author response, I would be willing to increase the score.
<Details>
* Strength
 + The motivation of using ProtoNet for domain adaptation seems reasonable.
 + The proposed method performs well in the experiments.
 + The paper, especially the experiment section, is well written and easy to follow.
* Weakness and concerns
 - Several points on the proposed loss (GCMM and PDM) are not sufficiently discussed.
  -- Why do we need two kinds of loss? These losses seem to play almost same role. Since PDM loss corresponds to target-side log likelihood regularization term (Eq. (3)), I wonder if we really need GCMM loss. 
  -- Since the authors explicitly model the feature distributions by Gaussian mixtures (GMs), it might be possible to calculate a standard divergence between source and target data distributions by using the parameters of GMs. Compared with such a straightforward approach, the proposed method seems to be ad-hoc and is not theoretically validated. What term of divergence (or distance) does it minimize?
  -- When a certain class does not appear in pseudo-labeled target data, how can we calculate GCMM loss? (specifically, \mu^{et}_c)
  -- Are Eq. (3) and Eq. (6) correct? These are defined as total loss, not average, over each domain. It means that the scale of the coefficients for these terms changes according to the number of training data, but the sensitivity analysis in Fig. 2 does not show such effect.
  -- Since the proposed losses heavily depend on the pseudo labels on the target data, it should be important to carefully set a proper threshold for the confidence. Is the proposed method sensitive against the change of this threshold? If so, how can we tune it?
  -- How can we know p(c) in advance?
 - The theory shown in 3.5 is not sufficiently validated. 
  -- The authors state ````we minimize the first term through minimizing the domain discrepancy losses," but it is not sufficiently supported, because the relationship between the proposed losses and H-delta-H divergence is not clear. 
 - I am concerned about whether the proposed method works well with harder datasets such as Office-Home dataset, because each class data are modeled by a simple Gaussian distribution in the proposed method. 
* Minor concerns that do not have an impact on the score
 - Using both f^s_i and F(x^s_i; \theta) is confusing.
 - Typo in Eq. (7): PMD -> PDM