Paper:
Unsupervised knowledge transfer has a great potential to improve the generalizability of deep models to novel domains. Yet the current literature assumes that the label distribution is domain-invariant and only aligns the feature distributions or vice versa. In this paper, we explore the task of Generalized Domain Adaptation: How to transfer knowledge across different domains in the presence of both shift in the feature and label distribution? We propose a feature and label distribution CO-ALignment (COAL) model to tackle this problem. Our model leverages prototype-based conditional alignment and label distribution estimation to alleviate the negative effect of the the types of domain shift respectively. We demonstrate experimentally that when both types of shift exist in the data, COAL leads to state-of-the-art performance on several cross-domain benchmarks.

Review:
This paper proposes domain adverarial approaches modified to address covariate shift 
even in the case of shifting label distributions. The paper is interesting and the authors
are looking at an important problem, but the paper suffers several major misconceptions
and the exposition is full of errors.  
The paper proposes a method called “self training” to “estimate and align” the  target label distribution
and a “prototype-based method” for conditional alignment.
The paper purports to introduce a new problem: “generalized domain adaptation”
but actually this is just covariate shift. 
They confuse the term “label shift” and the colloquial “shifting label distribution”.
Moreover when they describe the method formally they fail 
to even state the covariate shift assumption (that p(y|x) = q(y|x) ).
Absent this statement, the problem is unfdamentally underspecified.
They have stated only that p(y) \neq q(y) and that p(x|y) \neq q(x|y).
Thus the claimed contribution is to solve an impossible (more accurately, underspecified problem).
The proposed method leverages a “similarity classifier”
The thing that the authors call a similarity-based classifier
isn’t well explained. It looks like an ad-hoc variation on a standard
softmax prediction layer. 
Here, not that similarity means similarity between x and the label weights w,
not similarity between examples and each other.
Moreover this classifier is trained as a classifier using a 
standard cross-entropy objective on the target domain.
The paper lacks any formal justification for what this is offering
that we do not get from a standard classifier.
The next component of the model is "Prototype-based Conditional Alignment by Minimax Entropy”
and it is also confusingly explained.
The paper attempts to make some reference to the theory of Shai Ben David
which has been badly misapplied in the deep domain papers
(see discussion by Johannson et al 2019 and Wu et al 2019).
Strangely, the authors misattribute the theory to Zhao 2019.
There are some nice ideas in the paper and the experimental results 
(flaws in domain adaptation benchmarks notwithstanding)
appear to be promising.
However the paper is written too confusingly, is outright wrong in many places
and runs the risk of badly misleading readers over even the most basic of definitions.
I encourage the authors to give the paper a gut rewrite
and do not believe that it can be published while resembling its current form.
“only aligns the covariate shift”
>>> 	Be more formal, not clear what it means to “align the shift”
	Moreover, note that owing to lack of shared support , it’s not clear 
	what precisely the current methods (domain-adversarial) do
	or according to what principles they work.
“the covariate shift needs to be minimized”
>>> 	This is not a coherent way of describing the problem.
	The covariate shift is a property of the data.
	You cannot “minimize the shift”
“label shift (p(y) ̸= q(y))”
>>> 	Actually this is a “shfit in label distribution”. 
	Note that you can have a shift in label distribution 
	even under the covariate shift assumption.
	Label shift is the reverse assumption that p(x|y) = q(x|y).
“minimizing the label shift”
>>>	Again, this doesn’t make sense. The practitioner doesn’t get to choose the data
	that they will face at test time. The “shift” refers to the data. 
"Specifically, we assume p(x|y) ̸= q(x|y) and p(y) ̸= q(y)”
>>>	The problem described in this paper is called Generalized Domain Adaptation”
	but actually it is just “covariate shift” this is not a new problem. 
	The use of new terminology for old problems and misapplication of old terminology,
	e.g. “label shift” make this paper a potential danger to readers 
	who then will be confused in their subsequent interactions with 
	the wider literature on distribution shift.
“These methods have achieved state-of-the- art performance on several domain adaptation benchmarks“
>>>	It’s worth pointing out that benchmark SOTA is a dubious way to assess performance out of sample.
	The point is that in supervised learning you get to know that your target is the same as your source,
	so it’s ok to have a whole community smash the validation set and then see if we push the leaderboard on test data
	With domain adaption, the relevant sample size is the number of shifts, no the number of images.
	Having the community pound on 2-3 shifts tells us virtually nothing.
"our approach diminishes covariate and label shift”
>>>	Again this is not the accurate way to describe what you do.
	You attempt to salvage classifier performance under these shifts,
	you cannot “diminish the shift”. 
“Recently, Azizzadenesheli et al. (2019b) propose a regularized algorithm to correct shifts in the label distribution by estimating the importance weights using labeled source data and unlabeled target data. Lipton et al. (2018b) introduce a test distribution estimator to detect and correct for label shift.”
>>>	This is not exactly the right characterization of the related work.
	The method proposed by Lipton 2018 is precisely what 
	Azzizadeneshelli 2019 build upon (by adding a regularizer) 
“Conventional domain adaptation approaches … only align marginal feature distribution”
>>>	Again, the authors speak about “aligning the marginal feature distribution”,
	but this is confusing, Representations are aligned, not features.
	
“This motivates us to align the conditional feature distribution, i.e. p(x|y) and q(x|y)”
>>>	Again these are not things that can be “aligned”. They are properties of the data.
	The entire paper needs to be re-written to be semantically coherent.