Generalized Domain Adaptation with Covariate and Label Shift CO-ALignment
Authors: Shuhan Tan
Xingchao Peng
Kate Saenko
Venue:  (2020)
Keywords: Domain Adaptation
Label Shift
Covariate Shift

Abstract: 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 covariate or vice versa. In this paper, we explore the task of Generalized Domain Adaptation (GDA): How to transfer knowledge across different domains in the presence of both covariate and label shift? We propose a covariate and label distribution CO-ALignment (COAL) model to tackle this problem. Our model leverages prototype-based conditional alignment and label distribution estimation to diminish the covariate and label shifts, 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.

Under review as a conference paper at ICLR 2020
DOMAIN ADAPTATION WITH FEATURE AND LABEL DISTRIBUTION CO-ALIGNMENT
Anonymous authors Paper under double-blind review
ABSTRACT
Unsupervised knowledge transfer has great potential to improve the generaliz- ability of deep models novel domains. Yet the current literature assumes that the label distribution is domain-invarian and only aligns the feature distributions or vice versa. In this paper, we explore the task of Generalized Domain Adap- tation: 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 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-arr performance several cross-domain benchmarks.
INTRODUCTION
The success of deep learning models is highly dependent the assumption that the training and testing data are i.id and sampled from the same distribution. In reality, they are typically collected from different but related domains, leading to phenomenon known as domain shift (Quionero- Candela et al. 2009). To bridge the domain gap. Unsupervised Domain Adaptation (UDA) transfers the knowledge learned from a labeled source domain to an unlabeled target domain by statistical distribution aligmment (Long et al. 2015 Tzeng et al. 2014a) or adversarial alignment (Tzeng et al.) 2017 Ganin & Lempitsky 2015a Saito al.) 2018). Though recent UDA work has made great progress, it has mostly failed to address the case of Shift in Label Distribution, i.e,, a changing prior over the labels. Denote the input data as x and output labels as y, and let the source and target domain be characterized by probability distributions p and respectively. The majority of methods assume that the conditional label distribution is invariant (p(ylz) = 4(vlz)), and only the Shift in Feature Distribution (SFD) (p(x) * q(x)) needs to be tackled, neglecting any potential Shift in Label Distribution (SLD) (p(y) * q(y)). However, recent theoretical work (Zhao et al. 2019a) has demonstrated that tackling SLD is crucial solving the domain adaptation problem. SLD also occurs in real applications; for example, an autonomous driving system should be able to handle changing frequencies of pedestrians and cars when adapting from rural to downtown area.
In this paper, we propose Generalized Domain Adaptation (GDA), a more challenging but practical domain adaptation setting where the conditional Shift in Feature Distribution and Shift in Label Distribution are required to be minimized simultaneously. Specifically, in addition to the Covariate Shift assumption (p(x) A q(x), p(y)=)) = g(ylaz)) further assume p( (y) + q(>) yy) and p(y) + q(y). The main challenges of GDA are: (1) SLD exists between the source and target domain, which hampers the effectiveness of mainstream domain adaptation methods that only minimize SFD, (2) aligning the conditional feature distributions (p(zl1y), ((xly)) ) is difficult in the presence of SL.D, and (3) when the data one or both of the domains are unequally distributed across different categories, it is difficult to train unbiased classifier. An overview of GDA is shown in Figure !
Mainstream unsupervised domain adaptation aligns the marginal feature distributions of two do- mains by methods that include minimizing the Maximum Mean Discrepancy (Long et al. 2015 Tzeng et al., 2014a), aligning high-order moments (Zellinger et al. 2017 Peng et al.] 2019a), or adversarial training (Tzeng et al.] 2017; Ganin & Lempitsky| 2015a). These methods have achieved state-of-the the-art performance on several domain adaptation benchmarks (Saenko et al. 2010 Venkateswara et al. 2017 Peng et al. 2017) which have significant SFD but limited SLD.

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Self-nraining
Conditional A Aignment
Shift in Feature Distribution
G Generalized Domain Shift
Ours
Previous M Methods
Classifier Unlabeled Target Samples
Source Samples
Shift in Label Distribution
Pseudo-labeled Target Samples
We propose the GDA setting, where consider SFD and SLD simultancously. To tackle this problem, we propose use self-training estimate and align the target label distribution, and use a prototype- based method for conditional alignment. this way, we can better align the feature distribution of each category. Due to label shift, previous methods that learn marginal domain-invariant features will incorrectly align samples from different categories, leading negative transfer.
Figure 1:
These models are limited when applicd to the GDA task as they only align the feature distri- bution, ignoring the real issue of SLD which exists in many real-world applications. Another line of works (Lipton et al., 2018a (Azizzaennesheli et al.] 2019a) assume that only SLD ex- ists (p(y) # q(V)) between two domains and the conditional feature distribution is invariant (p(xlly) = (z)l)) These methods have achieved good performance when the data in both do- mains are sampled from the same data distributions but under different label distributions. However, these models cannot handle the GDA task as the label distribution is not well aligned. Taking steps towards minimizing the SFD and SLD simultaneously, several works (Zhang et al.) 2013 Gong et al., 2016; Wu et al. 2019) provide theoretical analysis with additional constraints on distribu- tions p and g. such as linearity assumption between p(zrly) and q(> y) (Zhang et al. 2013)), which does not necessarily hold in many real applications. In addition, no practical algorithm which can solve real-world cross-domain problems has been proposed by these papers.
We postulate that it is essential to align the conditional feature distributions as well as the label distri- butions to tackle the GDA task. In this work, we address GDA with SFD and SLD CO-ALigmment (COAL). Specifically, our approach diminishes the negative effect of SFD and SLD with prototype- based conditional distribution alignment and label distribution estimation, respectively. First, to reduce the SFD in the context of SLD, it is essential to align the conditional rather than marginal feature distributions, to avoid the negative transfer effects which are caused by matching marginal feature distributions, according
theoretical proof from Zhao et al. (2019a) (illustrated in Fig- ure Z). To this end, we propose a prototype-based method to align the conditional feature distribu- tions of the two domains. The source prototypes are computed by learning a similarity- bbsed clas- sifier and the target prototypes are estimated by a minimax entropy algorithm (Saito et al. 2019b). Second, we align the label distributions in the context of SFD by estimating the target label dis- tribution. We incorporate feature distribution and label distribution alignment into an end-to-end deep learning framework, as illustrated in Figure [ Comprehensive experiments on standard cross- domain recognition benchmarks demonstrate that COAL achieves significant improvements over the state-of-the the-rrr methods on the task of GDA.
The main contributions of this paper are highlighted as follows: (1) to the best of our knowledge, we provide the first practical solution and set of benchmarks for joint SFD and SLD in deep learn- ing: (2) we develop end-to-end CO-ALignment (COAL) framework which leverages conditional prototype-basee alignment to solve the problem caused by SFD and label distribution estimation to solve the problem caused by the SLD; and (3) we deliver extensive experiments and analysis to show the effectiveness of COAL, and importantly, we empirically demonstrate that state-of-the-an methods fail align conditional feature distribution in the presence of label distribution.
RELATED WORK
Unsupervised Domain Adaptation Domain adaptation aims transfer the knowledge learned from one or more source domains to a target domain. Recently, many unsupervised domain adapta- tion methods have been proposed. These methods be taxonomically divided into three cate- gories (Wang& & Deng 2018). The first category is the discrepancy- based approach, which leverages different measures to align the marginal feature distributions between source and target domains.
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Step A
Step
LE ys.
| Pr
ar gmax
Xj
F
C
Softmax
xz.
F
Softmax
-
top-k?
m
Gradient
-H(P)
Reverse
F
= Feature Extractor
Classifier
H
Entropy
Leg = Cross Entropy Loss
Gradient Path
Figure 2: Overview of the proposed COAL model. Our model is trained iteratively between two steps. In step A, we forward the target samples through our model to generate the pseudo labels and mask. In step we train our models by self-training with the pseudo labels and mask to align the label distributions, and prototype-buse basse conditional aligument with the minimax entropy.
Commonly used measures include Maximum Mean Discrepancy (MMD) (Long al., 2017: Tzeng
et al. 2014b), H-divergence (Ben-David et al. 2010). Kullback-Lerbler (KL) divergence (Zhuang
al. 20130, and Wasserstein distance (Lee & Raginsky 2017 Shen al. 2017). The second cat-
egory is the adversarial based approach (Tzzng et al.) 2017; Liu & Tuzel 2016 Peng et al. 2019b)
which uses a domain discriminator to encourage domain confusion via an adversarial objective. The third category is the ecconstruction-base approach. Data are reconstructed in the new domain by an encoder-decoder (Bousmalis et al.] 2016)) Ghifary et al. 2016) or a GAN discriminator, such dual-GAN (Yi et al., (201)), Gycle-GAN (Zhu et al. 2017). disco-GAN (Kim et al.) (017)), and CyCADA (Hofiman et al.) 2018). However, these methods mainly consider aligning the marginal distributions to decrease feature shift, neglecting label shift. To the best of our knowledge, the first the propose an end-to-end deep model to tackle both feature and label shift between the source and target domains.
Learning with Label Shift Despite its wide applicability, learning under label shift remains under- explored. Existing works tackle this challenge by importance reweighting target distribution estimation. Specifically, Zhang et al. (2013) exploit importance reweighting to enhance knowledge transfer under label shift. Recently, Lipton al. (2018b) introduce a test distribution estimator to detect and correct for label shift. Based on it, Azizzadnneshell et al. (2019b) propose regularized algorithm better estimate the target label distribution. These methods assume that the source and target domains share the same generative distributions and only differ in the marginal label distribution. In this work, we explore transfer learning between domains under domain and label shifts. In this direction, Zhhoo et al. (2019b) introduce theoretical analysis to show that only learning domain-invariant Teatures is not sufficient solve domain adaptation task since the label priors not aligned. In related work, Wu et al. (2019) propose asymmetricalll-rrllace distribution alignment to overcomes the limitations of standard domain adaptation algorithms which aims to extract domain-invariant representations. Panareda Busto & Gall (2017) propose open set domain adaptation where the categories in the training domain and testing domain are not fully overlapped. Cao et (2018)) introduce partial domain adaptation where the categories in the target domain are a subset of those in the source domain.
Domain adaptation with self-training Self-training methods utilize pseudo-labels to compensate for the lack of categorical information in the target domain. The intuition is to assign pseudo-labels unlabeled samples based on the predictions of one or more classifiers. [ong al. (2013) jointly align the marginal and conditional distributions using an MMD loss with pseudo-label refinement. Saito et al. (2017) leverage an asymmetric tri-training strategy to assign pseudo-labels to the unla- beled target domain. Xie et al.] (2018) propose to assign pseudo-labels to all target samples and use them to achieve semantic alignment across domains. Zhang et al. (2018) progressively enlarge the training data with pseudo-labeled target samples assigned by the classifier from the previous training epoch and retrain the model with the enlarged training set. Recently, Chen et al. (2019)) propose to progressively label the target samples and align the prototypes of source domain and target domain to achieve domain alignment. However, to the best of our knowledge, self-training has not been applied for DA with label shift.
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3 CO-ALIGNMENT OF FEATURE AND LABEL DISTRIBUTION
In domain adaptation with shift in the feature and label distribution, are given source domain Ds {(x]] v1 = with N₂ labeled examples, and target domain Dy (()) with Ne unlabeled examples. We assume that p(aly) # (xlly) and p(y) * ((y). We aim to construct a end-to-end deep neural network which is able to transfer the knowledge learned from Ds DT,
and train a classifier y = ((x) which can minimize task risk er( = ((())))))((())) 4 v).
Previous works either focus on aligning the marginal feature distributions (Long et al. 2015 Tzeng et al. 2017) or aligning the label distributions (Lipton et al. 2018b). These approaches are not able to fully tackle the domain adaptation with shift in the feature and label distribution as they only align one of the two marginal distributions. In this work, we tackle GDA with prototype mrosetype-based conditional alignment and label distribution estimation.
3.1 PROTOTYPE-BASED CONDITIONAL ALIGNMENT OF FEATURE DISTRIBUTION
The mainstream idea in covariate-shift oriented methods is to learn -nnaarinn features by aligning the marginal feature distributions, which was proved to be inferior in the presence of label shift (Zhao et al., 2019a). Instead, we propose align the conditional feature distributions. To this end, we leverage a similrity-basee bastiy classifier to estimate p(z yy) and minimax entropy algorithm to align it with (x>ly). We achieve conditional feature distribution alignment by aligning the source and target prototypes in an adversarial process.
Similarity- based Classifier The architecture of our COAL model contains feature extractor F and a similarity- -ased classifier C. Similarity- or prototype-base based classifiers perform well in few- shot learning settings (Chen et al., 2019b), which motivates us to adopt them since in label-shift settings some categories can have low frequencies. Specifically, C' is composed of a weight matrix W E Rdxx and a temperature parameter T, where d is the dimension of feature generated by F, and e is the total number of classes. Denote W as [W1, W2...., wel. this matrix can be seen d-dimension vectors, one for each category. For each input feature F (x)). we compute its similarity with the izh weight vector as 8; F(#)w, Then, we compute the probability of the sample being labeled as class by h,(x) ( F(z)w, T[]
[[]][]]] ), normalizing over all the classes Finally, can compute
the prototype-based classification loss for Ds with standard cross-entropy loss:
Lsc fee (h(z),))
(1)
The intuition behind this loss is that the higher the confidence of sample x being classified as class i, the closer the embedding of x is to w, Hence, when optimizing Equation [] we are reducing the intra-class variation by pushing the embedding of each sample x closer to its corresponding weight vector in W. In this way, W; can be seen as representative data point (prototype) for p(zly = i).
bassed Conditional Alignment by Minimax Entropy Due to the lack of categorical information in the target domain, it is infeasible to utilize Equation D to obtain target prototypes. Instead, we propose to tackle this problem by 1) moving each source prototype to closer to its nearby target samples, and 2) clustering target samples around this moved prototype. Inspired by Saito et al. (2019a). we propose to achieve these two objectives jointly by entropy minimax learning. Specifically, for each sample x² E Dr fed into the network, we can compute the entropy of the classifier's 's output by
H = -
ha(x)) log ha(x).
Larger H indicates the target samples are similar to all the weight vectors (prototypes) of C. We achieve conditional feature distributions alignment by aligning the source and target prototypes in an adversarial process: (I) we train C' to maximize Ht aiming to move the prototypes from the source samples towards the neighboring target samples; (2) we train F to minimize H, aiming to make the embedding of target samples closer to their nearby prototypes. By training with these two objectives as min-max game between C' and F, we can align source and target prototypes. Practically, we add gradient-reverse layer (Ganin & Lempitsky 2015a) between C and F to flip the sign of gradient.
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Algorithm 1: Conditional Feature Alignment with Decision Boundary Refinement
Input: F. C. Ds, Dr, Niter, Nepochs No, Output: F,C
kg
train F and C with Ds using Equation | for i O,..., Nopoch do
Step A:
compute Dj = {( Vi. m.) m with & as in Section 3.2
Step B:
for -......,Neee do
randomly sample mini-batch train and C with Equation
{ of 2 e Ds. (at), v. , Dr
k min(k (k- + kistep: kinax)
3.2 LABEL. DISTRIBUTION ESTIMATION WITH SELF-TRAINING
As the source label distribution ply) is different from that of the target (V)), is not guaranteed that the classifier C' which has low risk on Ds will have low error on the target domain. Intuitively, the classifier is trained with imbalanced source data, the decision boundary will be dominated by the most frequent categories in the training data, leading to a "biased" classifier. When the classifier is applied to target domain with different label distribution, its accuracy will degrade as it is highly biased. To tackle this problem, we employ the self-training method to estimate the target label distribution and refine the decision boundary. In addition, we leverage balanced sampling of the source data to further diminish the effect of label shift.
Self-training In order to refine the decision boundary, we propose estimate the target label distri- bution with self-training (Zou et al. (2018). We will assign pseudo labels ÿ to all the target samples according to the output the classifier C. As we have aligned the conditional feature distributions (p(xly) and gxxly)), we assume that the pseudo label distribution ς(ū) is the approximation of the real label distribution q(y) for the target domain.
For each category, we select top-k percent of the target samples with the highest confidence scores belonging to that category. We utilize the highest probability in h(()) as the classifier's confidence on sample æ. Specifically, for each pseudo-labeled sample (x., 5), we set its selection mask m = hxx) among the top-k percent of all the target samples with the same pseduo-label, otherwise m = 0. Denote the pseudo-labeled target set as Dy = {(x,, of. m.) J. we leverage the data and pseudo labels from Dr to train the classifier C, aiming to refine the decision boundary with target label distribution. The total loss function for classification is:
LSt
Lsc (e,. (h(x)) 1) m
Coe
where ÿ indicates the pseudo labels and m indicates selection masks. In our approach, we choose the top-k percent of the highest confidence target samples within each category, instead of univer- sally. This is crucial to estimate the real target label distribution, otherwise, the easy-to-transfer citegory(ies) will dominate DT, leading to inaccurate estimation of the target label distribution.
Balanced Sampling of Source Data In addition estimating the target label distribution, we pro- pose a balanced sampling process to enhance label shift alignment. When coping with label shift, the label distribution of the source domain could be highly unbalanced. classifier trained on un- balanced categories will make bighly- predictions for the samples from the target domain (He) Garcial 2009). This effect also hinders the self-training process discussed above, as the label dis- tribution estimation will also be biased. To tackle these problems, we apply balanced mini-batch sampler to generate training data from the source domain and ensure that each source mini-batch contains roughly the same number of samples for each category.
3.3 TRAINING PROCESS
In this section, we combine the above ideas into an end-to-end training process. Given input samples from source domain Dş and target domain Dr, first initialize our network F and C. with only
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labeled data Ds. Then, iterate between the assignment of pseudo labels and adaptive learning until convergence or reaching the maximum number iterations. An overview of this process can be seen in Algorithm [ The overall training objective is as follows:
Ö = arg min LST - aHl
C
f arg min LST aHl
3.4 THEORETICAL INSIGHTS
Conditional Feature Alignment According to Zhao et al. (2019b), the target error in domain adap- tation bounded by three terms: source error, 2) the discrepancy between the marginal distribu- tions and 3) the distance between the source and target optimal labeling functions. Denote h E H as the hypothesis, eg(.) and (-(-) as the expected error of labeling function on source and target domain, and fs and fr as the optimal labeling functions in the source and target domain. Then, we have:
(5) where dæ denote the discrepancy of the marginal distributions (Zhao et al. 2019b). The bound demonstrates that the optimal labeling functions fs and fr need to generalize well in both domains, such that the term min min(cs(ft (Cs(f)). (fs)) can be bounded. Conventional domain adaptation ap- proaches which only align marginal feature distribution cannot guarantee that min(es(Fr et (fs) is minimized. This motivates us to align the conditional feature distribution, i.e. p(ælyy) and q(>ly)- Our model COALestimates and aligns the source and target prototypes align p(xly) and (zal)).
er(h) Es(h) + (Ds, Dr) + min(es((fr,,
Decision Boundary Refinement Theorem 4.3 in Zhao et al. (2019b) indicates that the target error (r) can be minimized if we only align the feature distributions and neglect the shift in label distribution. Denote d the Jensen-Shannon(SS. distance between two distributions, Zhao et al. (2019h) propose:
+T(()))))))))) (())
(6)
This theorem demonstrates that when the divergence between label distributions d (p(y), g(v)) is significant, minimizing the divergence between marginal distributions d.s((p()) q(x)) and the
source task error (h) will enlarge the target task error eT(h). Motivated by this, we propose to align the empirical label distributions with self-training algorithm.
4 EXPERIMENTS
We evaluate our CO- 1O-ALigmment (COAL) model with three popular benchmarks, i.e., Digits, Office- Home (Venkateswara et 2017) and DomainNet (Peng al.] 2019a). Sample images of these datasets can be found in Figure 3a As Digits and Office-Home dataset contains limited SLD, we artificially create considerable SLD by random sub-sampling the data for each category.
4.1 SETUP
Sub-sampling Protocol. create significant SLD between source and target domains, we sub- sample the current datasets with Reversely protocol. this setting, both the source and target domains have unbalanced label distribution, while the label distribution of the source domain is reversed version of that of the target domain. An illustration of this setting can be found in Figure ().. We refer our reader to supplementary material for more details!
Source and Unbalanced Target (RS-UT)
Digits We select four digits datasets: MNIST (LCCun et al. 1998). USPS (Hull 1994). SVHN Netzer al. 2011) and Synthetic Digits (SYN) (Ganin & Lempitsky 2015b). In this work, investigate four domain adaptation tasks: MNIST + USPS, USPS + MNIST, SVHN MNIST, and SYN MNIST.
Office- Home /Venkateswara et al. 2017) is a dataset collected in office and home environment with 65 object classes and four domains: Real World (Rw), Clipart (CI), Product (Pr), Art (Ar). Since

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bacqpeck
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Digits
Office-Home
DomainNet
(a) Sample images of the datasets we use in our experiments.
(NST
USPS(UT)
sketch
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(b) Artificial SLD
(c) Natural SLD
Figure 3: (a): Image examples from Digits, Office-Home (Venkateswara al. 2017), and Domain- Net Peng et al. (2019a). (b): illustrations of Reversely-unbaalnceed Source (RS) and Unbalanced
Target (UT) distribution MNIST USSP task. (c): Natural SLD of DomainNet.
Methods
MNIST-USSP UNIST
SVHN-MNIST
SYN -MNIST
AVG
Source Only
75.31
87.92.10.74
50.25.1.811
85.74.10.99
74.81
F-DANN
1..19:11.61
81.62.+2.38
45.65
82.07-11.65
70.48
JAN
75.75
78.82-10.93
53.21
1..64
70.86
BBSE
75.01+33.68
78.84 10.73
49.01=2.002
85.69-0.71
72.14
BSP
7..9
89.74=0.77
50.61
17.30=1.200
72.41
PADA
73.66110.15
78.59=10.23
54.1311.661
85.06=10.60
72.86
MCD
77.1815.65
85.3414.07
53.52.14.23
76.37:1.48
73.10
DAN
19.12+1.34
87.15+1.771
53.63+1.80
80.89+2.000
75.20
DANN
77.28+2..13
91.88+00.74
17.16+1.83
77.60
75.98
COAL (Ours)
88.12.10.37
93.04.11.67
65.67.11.29
90.60
84.33
Table 1: Per-class mean accuracy Digits with RS-UT label shifts. Our model achieves 84.33% average accuracy across four experimental settings, outperforming other basclines.
the "Art" domain too small to sample an imbalanced subset, we focus on the remaining domains and explore all the six adaptation scenarios.
DomainNet (Peng et al. 2019a) a large-scale testbed for domain adaptation, which contains six domains with about 0.6 million images distributed among 345 classes. Since some domains and classes contains many outliers, we select 40 commonly-seen classes from four domains: Real (R), Clipart (C), Painting (P), Sketch (S). Different from two datasets above, the SLD in DomainNet is significant enough, as illustrated in Figure 3 Moreover, the images are directly collected from image search engine and they are in consistence with the natural label distribution in the real world.
Baselines We compare covarite and SLD CO-ALignment (COAL) with state-of-the-art domain adaptation methods that mainly aligns feature distribution: Deep Adaptation Network (DAN) (Long et al. 2015), Joint Adaptation Network (JAN) (Long et al., 2017), Domain Adversarial Neural Net- work (DANN) (Ganin Lempitsky (015a)). Batch Spectral Penalization (BSP) (Chen al. 2019c),
f-divergence Domain Adversarial Neural Network (F-DANN) (Wu et al.) 2019). Maximum Classi- fier Discrepancy (MCD) (Saito et al. 2018). We also compare our model with methods that aligns the marginal label distribution: Partial Adversarial Domain Adaptation (PADA) (Cao et al. 2018a). Black Box Shift Estimation (BBSE) (Lipton al. 2018b).
Implementation Details. We implement all our experiments in Pytorct platform. For the Digits dataset, we adopt the network architecture proposed by Saito et al. (2018). 3. We adopt SGD with the momentum of 0.9 and learning rate of 0.01 for the linear classifier and 0.001 for all other layers. The batch size is set as 32 for samples from each domain. For the other two datasets, we utilize ResNet-
https://pytorch...

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Methods
-P
Rw->CI
Pr-+Rw
Pr-+CI
CI->Rw
C1->Pr
AVG
Source Only
69.77
38.35
67.31
35.84
53.31
52.27
52.81
BSP
72.80
23.82
66.19
20.05
32.59
30.36
40.97
PADA
60.77
32.28
57.09
26.76
40.71
38.34
42.66
BBSE
61.10
33.27
62.66
31.15
39.70
38.08
44.33
MCD
66.03
33.17
62.95
29.99
44.47
39.01
45.94
DAN
69.35
40.84
66.93
34,66
53.55
52.09
52,90
F-DANN
68.56
40.57
67.32
37.33
55.84
53.67
53.88
JAN
67.20
43.60
68.87
39.21
57.98
48.57
54,24
DANN
71.62
46.51
68.40
38.07
58.83
58.05
56.91
COAT. (Ours)
73.65
42.58
73.26
40.61
59.22
57.33
58,40
Table 2: Per-class mean accuracy on Office-Home dataset with RS-UT label shifts. achieve 58.40% average accuracy across six GDA tasks, outperforming other baselines.
Our model
Methods
R-C R
P
R
S
C R
C-P
C S
P P P- P S
S-R
S C
+P
AVG
Source Only
58.84
67.89
53.08
76.70
53.55
53.06
84.39
55.55
60.19
74.62
54.60
57.78
62.52
BBSE
55.38
63.62
47.44
64.58
42.18
42.36
81.55
49.04
54.10
68.54
48.
46.07
55.25
PADA
65.91
67.13
58.43
74.69
53.09
52.86
79.84
59.33
57.87
76.52
66.97
61.08
64.48
DAN
64.36
70.65
58.44
79.44
56.78
60.05
84.56
61.62
62.21
79.69
65.01
62.04
67.07
MCD
61.97
69.33
79.78
79.78
56.61
53.66
83.38
58.31
60.98
81.74
56.27
66.78
67.38
FDANN
66.15
71.80
61.53
81.85
60.06
61.22
84,46
66.81
62.84
81.38
69.62
66.50
69.52
JAN
65.57
73.58
67.61
85,02
64.96
67.17
87.06
67.92
66.10
84.54
72.77
67.51
72.48
BSP
67.29
73.47
69.31
86.50
67.52
70.90
86.83
70.33
68.75
84.34
72.40
71.47
74.09
DANN
63.37
73.56
72.63
86.47
65.73
70.58
86.94
73.19
70.15
85.73
75.16
70.04
74.46
COAL (Ours)
73.85
74.82
70.50
85.68
70.86
71.29
87.71
69.90
67.28
83.82
73.21
70.53 74.96
Table 3: Per-class mean accuracy on DomainNet dataset with natural label shifts. Our method achieve 74.96% average accuracy across the 12 experiments. We observe that our model has signif- icant performance boost on several tasks, such R-C, and C-P. Note that DomainNet contains about 0.6 million images, it is non-trivial to have even percent performance boost.
50 (He et al. 2015 our backbone network, and replace the last fully-connected layer with randomly initialized N-way classifier layer (for N categories). We also use SGD with momentum of 0.9 while setting the learning rate to be 0.001 for linear layers and 0.0001 for all the other layers. The batch size is set as 16 each domain. set the a in Equation A set kg = kstep = 5, kmax= 50 as the parameters for self-training selection policy. For all the compared methods, decide their hyper parereearreserss on the validation set of Painting - Clipart task in DomainNet.
Evaluation metric. When the target domain is highly unbalanced, conventional overall average accuracy that treats every class uniformly not an appropriate performance metric (He & Garcial 2008). Therefore, results. Formally, we denote 5; .....7 as the accuracy for class i, where (i.i)) represents the number of class samples labeled class j. and n, ビÿ=1 ((jjj) represents the number of samples class Then, the per-class mean accuracy is computed as S - S,
follow Dong et al. (2019)
the per-class mean accuracy in main
4.2 RESULTS
We first show the experimental results of our model and the compared baselines on Digits dataset in Table [] The covariate shift between the source and target domains is related small on Digits dataset. For fair comparison, we leverage the same backbones for all the models. From the results, we can make the following observations. (1) Our model achieves 84.33% average accuracy across four experimental setting, outperforming the best-performing baselines by 8.4%! (2) Within the eight selected baselines, only DAN and DANN have marginal improvement (less than 2%) over the source-only baseline. The other six compared methods encounter the negative transfer (Pan & Yang, (0100) issue and perform worse than the source-only basclines. These results demonstrate that aligning only the marginal feature distributions tackle GDA task. In contrast, our model co-aligns the conditional feature distributions and label distributions and outperforms the baselines by large margin.
only the label distributions not fully
Next, we show the experimental results on more challenging real-image datasets, i.e. Office-Home and DomainNet, in Table and Table respectively. In Office-Home experiments, our model
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(a) Source Only
(b) DAN
(c) DANN
(d) COAL (Ours)
(c) Source Only
(f) DAN
(g) DANN
(h) COAL (Ours)
Figure 4: Feature visualization: t-SNE plot for source features, DAN features, DANN features, and COAL features on GDA task Real + Clipart. Figure (a)-(d): features from each class. Different colors denote different categories. Figure (e)-(h): features from each domain. Blue and red points represents features from the source domain and target domain, respectively.
achieves 58.40% average accuracy across the six GDA tasks, outperforming other compared base- lines. Our model has 5.59% improvement from the source-only result. We also notice that the BSP, PADA, BBSE and MCD models perform worse than the source-only baselines, which is in consis- tent with the results on Digits dataset. The empirical results on Office-Home dataset demonstrate the effectiveness of co-alignment of conditional covariate shift and SLD.
DomainNet experiments, our model get 74.96% average accuracy across the 12 experiments, outperforming the compared baselines. Note we have carefully tuned the hyper-parameters for the compared domain adaptation methods. Without the hyper-parameters tuning, i.e. directly applying the model released by the authors, these models perform worse than the source-only baselines. In addition, our model improves the performance of source-only models by 12.4%.
4.3 ANALYSIS
Ablation Study. Our COAL method has mainly two objectives: 1) alignment of conditional feature distribution and 2) alignment of label distribution. To show the importance of these two objectives in GDA, we show the performance of our method without each of these objectives respectively on multiple tasks. The results in Table showed the importance of both objectives. For example, for task USPS + MNIST, we remove the conditional feature distribution alignment objective, the accuracy of our model will drop by 2.55%. Similarly, if we remove the label distribution alignment objective, the accuracy will drop by 2.9%. These results demonstrate that both the alignment of conditional feature distribution and label distribution are important GDA task.
Feature Visualization. In this section, we plot the learned features with t-SNE (van der Maaten & Hinton 2008) in Figure 4 We investigate the Real Clipart task in DomainNet experiment with ResNet-50 backbones. From (a)-(d), we can observe that our method has better ability to cluster each sample towards its class centroid. This confirms the effectiveness of the entropy minimization in Equation 4 From (e)-(h), we observe that our method can better align source and target features in each category, while other methods either leave the feature distributions unaligned, or incorrectly aligned samples in different categories. These results further show the importance of prototype- based conditional feature alignment for generalized domain adaptation task.
Effect of Source Balanced Sampler. Source balanced samplers described in Section 3.2 can help us tackle the bias-classifier problem caused by the imbalanced data distribution source do- main. A significant performance boost can be observed after applying the balanced sampler for our COAL model, as well as the compared baselines. In this section, we specifically show the effect of using source balanced samplers. We show in Table 5 the performance of several methods with and without source balanced samplers on 5 adaptation tasks from multiple datasets. We observe that for 22 of the total 25 tasks (5 models on adaptation tasks), using source balanced samplers

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Under review as a conference paper at ICLR 2020
Methods
U-+M
M-+U
Syn->M M Cl->Rw Pr-+Rw R->C
P->C
P->
AVG
w/o self-training
85.22
85.94
55.17
58.38
69.39
71.92
62.86
77.45
70.79
w/o conditional alignment
85,57
92.28
63.34
59.41
72.11
71.34
68.50
87.14
74.96
COAL (full model)
88.12
93.04
65.67
59.81
73.46
73.65
69.90
87.71
76.42
Table 4: Ablation study of different objectives in our method. We randomly select 8 sets of exper-
iments to perform the ablation study. The results demonstrate that the prototype-basee conditional alignment and self- trfinin are both critical for GDA.
USPS-MMIIST with
SVHN-MNIST with
Pr-+CI
Cl-Rw
R-S
Methods
wio
wib
W/o
with
Wio
with
wio
with
SourceOnly
71.35
74.98
50.35
50.25
34.99
35.84
50.64
53.31
50.16
53.08
DAN
79.37
22.05
34.66
45.18
64.78
DANN
42.77
77.48
27. 66
56.35
35,17
38.07
47.19
58.05
68.92
72.63
MCD
20.15
79.59
44.83
51.91
33.06
29.99
49.57
44.47
58.50
79.78
COAL
87,50
88.12
60.12
65.67
34.03
40.61
57.67
59.22
59.23
70.50
Table 5: The performance of five models w. or w/o. source balanced sampler. We observe a significant performance boost when the source balanced sampler is applied, both for our model and the compared baselines, demonstrating the effectiveness of source balanced sampler to GDA task.
will improve the domain adaptation performance. Furthermore, in USPS + MNIST and SVHN - MNIST, source balance samplers can prevent the baseline methods from negative transfer. These results show the effectiveness of having a source balanced sampler when tackling GDA task.
Different Degrees of SLD. In Section 4 we only inves- tigated the performance of each method under certain kind of SL.D in each dataset, ie., RS-UTT. In this section, we investigate the effect of different degrees of SL.D on the performance of domain adaptation methods. Specif-
90
Accuracy
85
ically, we create 4 interval degrees of SLD between the BS-BT (Blanced Source and Blanced Target) and RS-UT setting. To this end, we compute the proportions of each category by linear interpolation between its proportions in BS-BT and RS-UT. We denote BS-BT and RS-UTT as 0% and 100% degree of SLDD respectively, and create datasets with SLDs of 20%, 40%, 60% and 80% on the linear in- terpolation. For fair comparison, all the datasets have the same total amount of samples. With these datasets, we evaluated the performances of different methods on the USPS + MNIST task of Digits. The results in Figure [5] show that the performances of previous domain adapta- tion methods will be significantly affected by SLD. For to different degrees of SLD.
DAN
DANN
80
MCD
Ours
0%
20%
40%
60%
80%
100%
Label Shift
Figure 5: Performance on UNPSTT task with different degrees of SLD. 0% and 100% denote the BS-BT and RS-UT settings respectively. Others are the linear interpo- lations of BS-BT and RS-UTT. The results demonstrate that our model are more robust
example, the accuracy of MCD drastically drops from 91.45% to 77.18%. In contrast, the perfor- mance our method is much more stable, which ranges between 93.42% and 88.12%. It shows that our method are robust to different degrees of SLD.
CONCLUSION
In this paper, we first propose a generalized domain adaptation (GDA) learning schema and demon- strate the importance of GDA in practical scenarios. Then we deliver theoretically analysis to demonstrate that aligning conditional feature distributions (p(xly), g(rlg)) and aligning the label distributions (p(v).q(v) are essential for GDA. Towards tackling GDA task, we have proposed con- ditional feature distribution and label distribution CO-ALignment (COAL) approach, which lever- ages prototype-bused conditional alignment and self-training method. Empirically, we demonstrate features by aligning the marginal distri-
that previous UDA models which learn butions fail to tackle GDA task, due the presence of shift in the label distribution. An extensive empirical evaluation on GDA benchmarks demonstrate the efficacy of the proposed model against several state-of -otthe-arttttttt domain adaptation algorithms.
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A ADDITIONAL RESULTS
We have shown in the paper the performance of different domain adaptation methods when condi- tional covariant shift and label shift exist simultaneously. To analysis the influence of label shift in unsupervised domain adaptation, in this appendix we also include the results on datasets without label shift. To this end, we also created datasets with the Balanced Source Balanced Target (BS-BT) setting. Specifically, under BS-BT every class has the same number of samples. We use this set- ting sub-sample the BS-BT datasets from Digits and Office-Home For fair comparison with the results in Section 4 we constrain that the total amount of samples of each domain is the same in BS-BT and RS-UT. We show the results in Table T and
Methods
USPST
MNIST-USPP
SVHN-MNIST
SynD-+SVH
AVG
Source Only
71.49-0.08
84.73.11.34
56,95.1.552
86.33.10.56
76.00
FDANN
72.13 1.88
87.30
34.16.1
80.77-:1.45
67.41
BBSE
79.42-3.044
74.07
53.73:1..19
87.14-1..88
71.65
PADA
73.07=0.13
81.39-
56.82:10097
85.88=00.3
74.70
JAN
87.69=0.51
93.93=0.34
56.00=4.30
82.65=3.02
77.53
DAN
83.09=2.10
86.16=0.449
63.42:12.08
86.48-10.97
78.69
BSP
1373
89.21=1444
63.31+22443
93.24:0.53
81.92
DANN
83.92 1.19
90.29-0.94
68.96+33.73
93.43-+0.36
84.23
MCD
97.53 0.04
96.86=0.60
88,47-11.96
96.82-+0.32
94.92
COAL (Ours)
92687=0.60
95.40=10.59
82.01 2.33
96.39-1..2
91.27
Table 1: Class-balanced accuracy on Digit dataset with BS-BT label shifts
Methods
Rw->Pr
Rw->CI
Pr->Rw
Pr->CI
Cl->Rw
Cl-+Pr
AVG
Source Only
72.91
39.21
69.84
38.16
56.06
54.08
55.04
PADA
64,44
33.89
59.21
30.35
41.92
41.19
45.17
BBSE
64,25
34.85
63.56
34.19
40.57
38.57
46.00
BSP
72.85
50,29
69.35
25.20
34.31
31.92
47.32
MCD
68.76
37.14
66.78
36.31
51.77
48.50
51.54
DAN
71.67
38.35
67.42
36.07
55.48
53.25
53.71
FDANN
71.20
39.11
67.30
33.86
60.85
53.64
54.33
JAN
66.69
42,28
69.61
38.65
59.42
57.19
55.64
DANN
74.70
47.10
70.07
39.35
60.56
54.88
57.78
COAL
77.44
47.42
71.23
42.87
63.46
61.24
60.61
Table 2: Class-balanced accuracy on Office-Home dataset with BS-BT label shifts
We can observe that conventional methods that focus on covariate shift can achieve decent improve- ment over the Source Only bascline in BS-BT setting. For example, MCD largely improving the performance when there is no label shift between the source and target domain. However, as we observed in Table of our paper, MCD is actually having negative transfer effect when applied to the more general GDA setting. This comparison demonstrates the importance of considering both covariate and label shift in our generalized setting. Please note that the results in this section are produced by models with parameeess tuned unbalanced DomainNet.
B CREATION DETAILS FOR LABEL SHIFT
In order to create unbalanced label distribution in each dataset, inspired by Liu et al. (2019). we follow the Paredo distribution set different proportions for each category. By using this distribu- tion. we can create tailed label distribution, which is frequently seen in real applications and benchmarks (Van Horn al. 2018 Peng al. 2019a).

---

Under review as a conference paper at ICLR 2020
The shape of Paredo distribution (Reed 2001) is controlled by parameter Because different datasets have different amount of samples, to avoid making some classes in the unbalanced dataset to have too few samples, for Digits dataset, and a = 100 for Office-Home dataset.
different parameter for each dataset. Specifically, set
We further assign each computed proportion each category by following the descending order of the original class index. Specifically, in the target domain RS-UT, we assign the kts, largest propotion to class A 1, with class index starting from O. For Digits, directly as the digit it represents. For Office-Home, we set the class index in alphabetical ascending order.
the index of each class
C IMPLEMENTATION DETAILS FOR COMPARED METHODS
In our experiments, we use the authors' official implementations for DAN Long al. 2015)) and JAN (Long et al. 2017), PADA (Cao et al. 2018b), MCD (Saito et al. 2018). and BSP (Chen et al., 2019c). For DANN (Ganin Lempitsky 2015a). BBSE (Lipton et 2018b) and FDANN (Wu et al. 2019), we implement their method by ourselves.
We tune the hyper- perempaaeetess of each method on Painting -> Clipart task in DomainNet. Specifi- cally, for PADA, BSP, DAN, JAN and DANN we tune the weight of the marginal feature alignment loss. We empirically find that these method achieve better performance when we set a to be 10 times lower than default. Intuitively, it means that we can achieve better performance under gener- alized domain shift setting if we relax the strength marginal feature alignment. For MCD we tune the number of feature generator updating times
D DETAILED INFORMATION FOR DATASETS
We provide detailed information for datasets in Table
Digits
Splits USPS
MNIST
SVHN
SYN
Total
Train
12,144
1,550 459
10,395 3,554
107,005 2,114
118,950
Test
2,181
8,308
Office-Homm
Splits Total
Real World
Product
Clipart
Total
1,253
2,045
1,017
4,315
DomainNet
Splits
Real
Painting
Clipart
Sketch
Total
Train Test
16,141 6,943
6,727 2,909
3,707 1,616
5,537 2,399
32,112
13,867
Table Detailed information datasets
2


Reviews:
[{"review_id": "r1gBdreAKH", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper deals with covariate and label shift in common\nevaluated on some standard benchmark data.\nThe paper is scientific sound and appears to be in good shape,\njust a few comments:\n- how is your label shift different to concept drift in supervised learning?\n  --> if this is basically the same I would expect that you can use,mention methods from there\n- the plots with t-SNE are obviously colorful but do not provide a lot of information - they should\n  be removed - I do not see a benefit\n- it is very common that all these methods (like yours) are provided on some kind of image\n  data ... is there a particular reason / limitation?\n- I would like to see additional experiments on similar text data -> reuters\n- self-training is a concept from semi-supervised learning and not particular well supported\n  in the community - how do you make sure that the result remain valid\n- how do you make sure that the adaptation of the labels, the covariate shift and the classifier training\n  are not in facting cheating the result to an optimum within the optimized cost function?\n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "Hyxpo0_N9r", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "In this work, the authors proposed a method to address the covariate shift and label shift problems simultaneously. In detail, the prototype-based conditional alignment and self-training based label distribution estimation is utilized. Empirically evaluation is conducted on three datasets to show the superiority of the proposed method. However, the work suffers the following weaknesses:\n \n1). The main concern of this work is its shift assumption. In the language of dataset shift, the joint distribution p(x, y) can decompose into two different manners, which are p(y|x)p(x) and p(x|y)p(y). Covariate shift is defined as p(x) not equals to q(x), while the conditional output distribution is invariant p(x|y) = q(x|y), where p(.) and q(.) are distribution for source and target domains. Label shift is defined as p(y) not equals to q(y), while the conditional input distribution p(y|x) = q(y|x). The work assumes that p(x|y) not equals to q(x|y) meanwhile p(x) not equals to q(y). It means to minimize the joint distribution p(x, y), which is well motivated. However, it does not solve the two abovementioned shifts simultaneously here. Instead, it aims to minimize the marginal distribution and conditional distribution in the anticausal direction. See more definitions in the papers “When training and test sets are different: characterizing learning transfer” and “On causal and anticausal learning.”\n \n2). The novelty of the paper is limited. While the authors claim that it is the first time to approach it in the proposed manner, the problem of both p(y) and p(x|y) change is not new. For instance, in the paper “Domain adaptation under the target and conditional shift,” the case of distribution shift correction also does not assume the same conditional distribution and marginal distribution for the source domain and the target domain. Also, the fulfill of conditional alignment is used the formulation and architecture of the work “Semi-supervised Domain Adaptation via Minimax Entropy,” except that there is no labeled target data in the target domain (see Eq.(1)). Besides, the notation f in Fig. 2 is missing the description of Section 3.           \n \n3).  Although the prototype-based method does help in minimizing the problem of p(x|y) not equals to q(x|y), using the minimax entropy domain adaptation in an unsupervised setting is problematic. Without a few labeled target data points, it is challenging to learn the discriminative features for the target domain. If positives and negatives (suppose it is a binary classification) are severely overlapped in the target domain,  the learned prototypes could be not consistent with those in the source domain. In other words, the prototypes might not indicate the same classes for source and target. Another issue is that the proposed model cannot solve the problem given in the assumption. In detail, the assumption is p(x, y) not equals to q(x, y), using the shared feature function F(.) and classifier C(.) for the source and the target cannot obtain domain-invariant feature and adaptive target predictor at the same time.\n \n4). There is an issue in the label distribution by self-training. As the authors claimed, balanced sampling could diminish the effect of the label shift. However, there is no substantial theoretical evidence on this. Intuitively, the balanced sampling only ignores the original marginal distribution of the target domain. The authors should provide more explanation on it. Meanwhile, the sampling couldn’t work when there is a large number of categories. For self-training, it seems no mechanism to alleviate the label shift. Besides, the iterative learning manner heavily depends on the initialization of self-training, i.e., the top-k samples might not represent the marginal distribution.\n \n5). For the theoretical insights, first of all, Eq.(5) is given in “A theory of learning from different domains,” Shai Ben-David et al., Machine Learning, 2010. Second, there is a mistake in Eq.(6). The second term on the right of the inequality is not JS divergence of distributions over x. Instead, it is JS divergence of those after transformation of x, z (see the subsection An information-theoretic lower bound, Zhao et al. 2019b).  Also, the descriptions of the insights are not correct.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory."}, "extra_text": {}}, {"review_id": "BJlagbmAKS", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "\n\n\nThis paper proposes domain adverarial approaches modified to address covariate shift \neven in the case of shifting label distributions. The paper is interesting and the authors\nare looking at an important problem, but the paper suffers several major misconceptions\nand the exposition is full of errors.  \n\nThe paper proposes a method called “self training” to “estimate and align” the  target label distribution\nand a “prototype-based method” for conditional alignment.\n\nThe paper purports to introduce a new problem: “generalized domain adaptation”\nbut actually this is just covariate shift. \nThey confuse the term “label shift” and the colloquial “shifting label distribution”.\nMoreover when they describe the method formally they fail \nto even state the covariate shift assumption (that p(y|x) = q(y|x) ).\nAbsent this statement, the problem is unfdamentally underspecified.\nThey have stated only that p(y) \\neq q(y) and that p(x|y) \\neq q(x|y).\nThus the claimed contribution is to solve an impossible (more accurately, underspecified problem).\n\nThe proposed method leverages a “similarity classifier”\nThe thing that the authors call a similarity-based classifier\nisn’t well explained. It looks like an ad-hoc variation on a standard\nsoftmax prediction layer. \nHere, not that similarity means similarity between x and the label weights w,\nnot similarity between examples and each other.\nMoreover this classifier is trained as a classifier using a \nstandard cross-entropy objective on the target domain.\nThe paper lacks any formal justification for what this is offering\nthat we do not get from a standard classifier.\n\nThe next component of the model is \"Prototype-based Conditional Alignment by Minimax Entropy”\nand it is also confusingly explained.\n\nThe paper attempts to make some reference to the theory of Shai Ben David\nwhich has been badly misapplied in the deep domain papers\n(see discussion by Johannson et al 2019 and Wu et al 2019).\nStrangely, the authors misattribute the theory to Zhao 2019.\n\n\nThere are some nice ideas in the paper and the experimental results \n(flaws in domain adaptation benchmarks notwithstanding)\nappear to be promising.\n\nHowever the paper is written too confusingly, is outright wrong in many places\nand runs the risk of badly misleading readers over even the most basic of definitions.\nI encourage the authors to give the paper a gut rewrite\nand do not believe that it can be published while resembling its current form.\n\n“only aligns the covariate shift”\n>>> \tBe more formal, not clear what it means to “align the shift”\n\tMoreover, note that owing to lack of shared support , it’s not clear \n\twhat precisely the current methods (domain-adversarial) do\n\tor according to what principles they work.\n\n\n“the covariate shift needs to be minimized”\n>>> \tThis is not a coherent way of describing the problem.\n\tThe covariate shift is a property of the data.\n\tYou cannot “minimize the shift”\n\n“label shift (p(y) ̸= q(y))”\n>>> \tActually this is a “shfit in label distribution”. \n\tNote that you can have a shift in label distribution \n\teven under the covariate shift assumption.\n\tLabel shift is the reverse assumption that p(x|y) = q(x|y).\n\n\n“minimizing the label shift”\n>>>\tAgain, this doesn’t make sense. The practitioner doesn’t get to choose the data\n\tthat they will face at test time. The “shift” refers to the data. \n\n\n\"Specifically, we assume p(x|y) ̸= q(x|y) and p(y) ̸= q(y)”\n>>>\tThe problem described in this paper is called Generalized Domain Adaptation”\n\tbut actually it is just “covariate shift” this is not a new problem. \n\tThe use of new terminology for old problems and misapplication of old terminology,\n\te.g. “label shift” make this paper a potential danger to readers \n\twho then will be confused in their subsequent interactions with \n\tthe wider literature on distribution shift.\n\n“These methods have achieved state-of-the- art performance on several domain adaptation benchmarks“\n>>>\tIt’s worth pointing out that benchmark SOTA is a dubious way to assess performance out of sample.\n\tThe point is that in supervised learning you get to know that your target is the same as your source,\n\tso it’s ok to have a whole community smash the validation set and then see if we push the leaderboard on test data\n\tWith domain adaption, the relevant sample size is the number of shifts, no the number of images.\n\tHaving the community pound on 2-3 shifts tells us virtually nothing.\n\n\n\"our approach diminishes covariate and label shift”\n>>>\tAgain this is not the accurate way to describe what you do.\n\tYou attempt to salvage classifier performance under these shifts,\n\tyou cannot “diminish the shift”. \n\n“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.”\n>>>\tThis is not exactly the right characterization of the related work.\n\tThe method proposed by Lipton 2018 is precisely what \n\tAzzizadeneshelli 2019 build upon (by adding a regularizer) \n\n“Conventional domain adaptation approaches … only align marginal feature distribution”\n>>>\tAgain, the authors speak about “aligning the marginal feature distribution”,\n\tbut this is confusing, Representations are aligned, not features.\n\t\n\n“This motivates us to align the conditional feature distribution, i.e. p(x|y) and q(x|y)”\n>>>\tAgain these are not things that can be “aligned”. They are properties of the data.\n\tThe entire paper needs to be re-written to be semantically coherent.", "extra_scores": {"experience_assessment": "I have published in this field for several years.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposes a method to address the covariate shift and label shift problems simultaneously. 

The paper is an interesting attempt towards an important problem. However, Reviewers and AC commonly believe that the current version is not acceptable due to several major misconceptions and misleading presentations. In particular:
- The novelty of the paper is not very significant.
- The main concern of this work is that its shift assumption is not well justified.
- The proposed method may be problematic by using the minimax entropy and self-training with resampling.
- The presentation has many errors that require a full rewrite.

Hence I recommend rejection.
Decision: Reject