Generative Model Based Noise Robust Training for Unsupervised Domain Adaptation
Authors: Zhongying Deng
Da Li
Junjun He
Yi-Zhe Song
Tao Xiang
Venue: Submitted to ICLR 2023 (2023)
Keywords: Unsupervised Domain Adaptation
Generative Models
Feature Augmentation
Generative and Discriminative Consistency

Abstract: Target domain pseudo-labeling has shown effectiveness in unsupervised domain adaptation (UDA). However, pseudo-labels of unlabeled target domain data are inevitably noisy due to the distribution shift between source and target domains. In this paper, we propose a generative model-based noise-robust training method (GeMo-NoRT), serving for domain shift elimination and label noise robustness simultaneously. GeMo-NoRT incorporates a distribution-based class-wise feature augmentation (D-CFA) and a generative-discriminative classifier consistency (GDC), both based on the class-wise target distributions modeled by generative models. D-CFA minimizes the domain gap by augmenting the source data with distribution-sampled target features, and trains a noise-robust discriminative classifier by using target domain knowledge from the generative models. GDC regards all the class-wise generative models as a generative classifier and enforces a consistency regularization between the generative and discriminative classifiers. It exploits an ensemble of target knowledge from all the generative models to train a noise-robust discriminative classifier, and eventually gets theoretically linked to the Ben-David domain adaptation theorem for reducing domain gap. Extensive experiments on Office-Home, PACS, and Digit-Five show that our GeMo-NoRT achieves state of the art under single-source and multi-source UDA settings.

Under review as a conference paper at ICLR 2023
GENERATIVE MODEL BASED NOISE ROBUST TRAIN- ING FOR UNSUPERVISED DOMAIN ADAPTATION
Anonymous authors Paper under double-blind review
ABSTRACT
Target domain pseudo-labelling has shown effectiveness in unsupervised do- main adaptation (UDA). However, pseudo-labels of unlabeled target domain data are inevitably noisy due to the distribution shift between source and tar- get domains. This paper proposes a generative model-based noise-robust train- ing method (GeMo-NoRT), which eliminates domain shift while mitigating label noise. GeMo-NoRT incorporates a distribution- baaed class-wise wise feature augmen- tation (D-CFA) and based on the class-wise target distributions modelled by generative models. D- CFA minimizes the domain gap by augmenting the source data with distribution- sampled target features, and trains a noise-robust discriminative classifier by using target domain knowledge from the generative models. GDC regards all the class- wise generative models as generative classifiers and enforces consistency regu- larization between the generative and discriminative classifiers. It exploits an en- semble of target knowledge from all the generative models to train noise-robust discriminative classifier and eventually gets theoretically linked to the Ben-David domain adaptation theorem for reducing the domain gap. Extensive experiments on Office-Home PACS, and Digit-Five show that our GeMo-NoRT achieves state- of-the-art under single-source and multi-source UDA settings.
classifier consistency (GDC), both
INTRODUCTION
Convolutional neural networks (CNNs) trained by large amounts of training data have achieved remarkable success on variety of computer vision tasks (Simonyan & Zisserman, 2014 Szegedy
et al. 2015 He et al. 2016; Long et al.) 2015a He et al. (019). However, when a tealetr CNN model is deployed a new environment, its performance usually degrades drastically. This is because the test data (of the target domain) is typically from a different distribution from the training data (of source domains). Such distribution mismatch also known as domain gap. A popular solution to tackling the domain gap issue is unsupervised domain adaptation (UDA) (Gretton al. 2012
Long et al.] 2015b; 2016 Tzeng et al. 2014; Balaji et al., 2019 Xu et al.) 2018).
UDA can be divided into two main sub-settings: single-source domain adaptation (SSDA) and multi- source domain adaptation (MSDA), according to the number of source domains. Early works have mainly focused on the single-source scenarios (Gretton et al.) Long al. 2015b Ganin al. 2016 Tzeng et al., 2017). Nevertheless, in real-world applications, the source domain data can be collected from various deployment environments, leading to multiple source setting. MSDA thus has been receiving more attention recently. Most UDA methods, including both SSDA and MSDA, tried to reduce domain gap by domain distribution alignment (Zhao et al., 2018 Xu et al. 2018 Peng et al.] 2019 Li et al. (021c). Latest methods (Wang et al.] 2020 Li et al.) 2021a) further utilized class information for class-wise alignment, with pseudo-labels used for unlabeled target data. These methods have shown effectiveness for UDA. However, due to the domain gap, model trained on the source domains cannot correctly classify all the target instances, leading to target domain pseudo-labels inevitably being noisy. If these noisy labels are directly used supervision, their negative impact can be amplified or accumulated through iterations. This can even lead to the training corrupted. The noise accumulation problem thus must be addressed.
An intuitive solution to noise accumulation is to reduce domain gap. This can indeed reduce label noise. However, in practice, the domain gap cannot be thoroughly eliminated, the label noise can

---

Under review as a conference paper at ICLR 2023
Class A
Match
+
Match
Class B
Mixed with target features
Mixed with source features
(a) D-CFA
(b) GDC
Target features of different classes
Sampled target features
Source features
A Mixed features
Distribution target features
Decision boundary of generative classifier
Distribution of mixed features
Decision boundary of discriminative classifier
Illustration for our GeMo-NoRT. The GeMo-NoRT includes (a) Distribution Based Class- wise Feature Augmentation (D-CFA) and (b) Generative and Discriminative Consistency (GDC). (a) The D-CFA uses the mixed feature (the orange triangle) to replace the original misclassified feature (i.e., the red star that should be classified to class B but with a wrong pseudo-label of class A) for classifier training. The mixed feature is obtained by mixing the original feature and the feature sampled from the target distribution of class A. In this way, the mixed feature is closer to class A, thus likelier to have correct label of class A. Such mixed feature and pseudo-label A can better match each other to train a better classifier. In the next iteration, the classifier is free to assign a new pseudo-label (e.g. class B) the original feature to stop noise accumulation. When labeled source instance is mixed with sampled features, the mixed features serve as intermediate features between source and target domains to bridge the domain gap in each class. (b) The GDC is a consistency regularization on the target domain data by matching the predictions of the discriminative classifier to these of the generative classifier. This regularization exploits an ensemble of target knowledge from all the generative models to train a noise-robust and domain- adaptive discriminative classifier.
Figure 1:
still exist. As such, is necessary to train label noise-robust model for UDA. We address the noise- robust training from the perspective of probability: to reduce the negative impact of a noisy instance, we can maximize the joint probability of its feature f and pscudo-label ÿ. i.e., p(f. 9). which can be achieved by max p( (()) (see Eq. Eq. 4 essentially assumes that the pseudo-labela are intact but the features are corrupted. So we can generate the data (i.e., features) conditioned on pseudo-labels, or we can fix the pseudo label and maximize the probability of the feature given the pseudo-labes ÿ. i.e. p(f))). Practically, we porrect'/auggent the feature of noisy instance to force it to better match the pseudo-label ÿ. This differs from other noise correction methods which assume the features are intact but the labels are corrupted. To sum up, the keys to address UDA are: 1) reducing domain gap and 2) solving the probability maximization problem.
This paper proposes a generative model based noise robust training (GeMo-NoRT) method to alle- viate the pseudo label noise (by solving the probability maximization problem) and meanwhile to reduce the domain gap for UDA. The key idea is to leverage generative model, modeling the class- diseriminative classifier.
wise target distribution, to help train noise-robust and Specifically, GeMo-NoRT learns a generative model to enable a target distribution based class-wise feature augmentation (D-CFA) and ing as feature-level and classifier-leve regularization respectively.
diseriaivedddceriiinaivee classifier consistency (GDC), serv-
D-CFA learns the target-domain class-wise feature distributions using generative models like nor- malizing flows (Durkan et al. (2019). Then, the source domain data will be augmented by the features sampled from target-domain distribution such that the domain gap can be reduced. For the pseudo- labeled target domain data, our D-CFA also provides a simple yet effective approximate solution to the probability maximization problem to alleviate noise accumulation. As shown in Figure D. we transform/augment the original feature I by mixing it with the 'genuine' features (sampled from target-domain distribution) of the class ý. The augmented feature now likelier from the class ğ thus increases the joint probability. Note that the citrribution-saaplle features can be regarded as 'genuine' features of the class ý because the class-wiss distribution models the whole population in class, making the class label of sampled features highly reliable. This ensures that almost extra label noise is introduced by the sampled features, which is critical for alleviating noise accumulation.
GDC is consistency regularization the target domain data by matching the predictions of the discriminative classifier to these of the generative classifier (see Figure [[p). where the generative classifier is all the off- generative models used as whole for class-wise probability pre-
2

---

Under review as a conference paper at ICLR 2023
diction. GDC aims minimize the prediction disagreement to improve the model robustness to label noise as Yu et al. 2019). More interestingly, our GDC is also theoretically insightful accord- ing to the famous David domain adaptation theorem [Ben-Davit et al.] 2010). Maximizing the generative-diseriinnas
classifier consistency naturally minimizes the hypothesis discrepancy HAH, thus improving the target domain performance. Eventually, our D-CFA and GDC serving as two different regularizations improve UDA on various UDA benchmarks.
Our contributions are: (1) we as the first attempt propose leverage normalizing flow-based genera- tive modeling together with CNN-based discriminative modeling to improve UDA. (2) Our proposed framework (GeMo-Noffe Mooo incorporates a D-CFA and GDC for training a noise-robust discrimina- tive classifier and meanwhile reducing the domain gap, (3) Our GeMo-NoRT achieves new state of the art on three popular UDA datasets, including PACS, Digit-Five, and Office-Home.
2 RELATED WORK
Single-Sourg Source Domain Adaptation (SSDA) aims to transfer knowledge from a labeled source domain an unlabeled target domain. The challenge in this task is the domain gap caused by the distribution mismatch between the source and target domains. To reduce domain gap, most works force a feature
extractor to extract domain- -agaaiii features for feature distribution alignment. The feature align-
ment can be achieved by minimizing maximum mcan discrepancy (MMD) (Gretton et al. 2012
Long et al. 2015b) or optimal transport (Bhushan Damodaran et al. 2018 Balaji et al.) [2019) or by
confusing domain classifier (Ganin et al. [016)] I zeng et al. (017), 7). Recent works (Na et al. 2021
Wu al. 2020) also attempt to bridge domain gap by mixing two images from different domains to
generate intermediate domains. Most related to our work is feature augmentation method, TSA (Li
al. 2021b). TSA adopts Gaussian distribution to model the domain difference each class so that cross-domain semantic augmentation can be performed to bridge the domain gap. Instead, normalizing flow (NFlow) to better model the class-wise distribution itself rather than the domain difference, and further propose a consistency regularization on the generative classifier (i.e., all the NFlow models as whole) and the discriminative one to address noise accumulation.
Multi-Source Domain Adaptation (MSDA) tackles more general scenario where multiple source domains are available. This brings different kinds of source-target domain gaps, thus more chal- lenging. Most MSDA methods still resort to feature distribution aligmment by 1) using multiple domain discriminators, e.g. MDAN (Zhao et al. 2018) and DCTN (Xu et al., 2018). or 2) mini- mizing moment based distribution distance between different domain pairs, e.g. M*SDA-8 (Peng et al. 2019), or 3) exploiting dynamiccmultiple feature extractor(s) to better extract domain-agnosto features, e.g. MDDA (Zhao et al. 2020) and DIDA-Net (Deng et al. 2022). Instead of focusing on distribution alignment, we attend utilizing generative models to alleviate the noise accumulation of the discriminative classifier when pseudo-labels are used. Thus, we propose a Distribution Based Class-wise Feature Augmentation (D-CFA) and Generative- Discriminative Consistency (GDC).
Normalizing Flow (NFlow) is a likelihood based generative model (Dinh et al. 2014 2016 Rezende & Mohamed 2015), similar generative adversarial network (GAN) (Goodfellow et al. (014)) and variational auto-encoder (VAE) (Kingma & Welling 2013). It transforms a simple distribution like standard Gaussian to match a complex one of real data by composing several invertible and differ- entiable mappings. With such mappings, we can evaluate the exact probability density for new data points (Kobyzev et al. 2020), which cannot be achieved by using GAN or VAE. NFlow has been applied to a variety of generation tasks, such as image generation (Kingma & Dhariwal 2018 Ho ctt al. 2019 Durkan et al. (019) and video generation (Kumar et al. 2019). In this paper, we exploit the NFlow models to model the class-wise feature distribution so that within-class feature augmenta- tion can be performed to bridge domain gap and alleviate noise accumulation. Furthermore, we take full use of NFlow models' characteristic of the probability density estimation, which is to regard all these wiss NFlow models as a generative classifier for flasswwie probability prediction. The prediction is then used enforce consistency regularization discriminative classifier.
3 METHODOLOGY
In this section, detail our GeMo-NoRT for unsupervised domain adaptation (UDA). GeMo-NoRT incorporates a daggetdisttibutioon based class-wise wise feature augmentation (D-CFA) and generative- discrininative consistency (GDC). The overview of our GeMo-NoRT is shown in Figure
3

---

Under review as a conference paper at ICLR 2023
Ground-truth labels/
Pseudo-labels
Classifier
Cross-entropy loss
ff
Source
CNN
Mixing
Consistency loss
F
Target
Target
NFlow
Class :
Data flow both source and target
Target prediction
NFlow
Data flow of target only
Class C
Sampled features
Generative classifier
Figure 2: Overview of our GeMo-NoRT. The GeMo-NoRT first extract features fi from source and target images using feature extractor CNN. The target features together with their pseudo-labels are then input to C' normalizing flows (NFlows) to model the class distributions, where C' is the class number. These generative NElows are used for D-CFA and GDC. The D-CFA samples feature J. from the y/-th NFlow based distribution and mixes with the feature Si. where y4 the (pseudo-) label of fs. The GDC uses all the NFlow models as generative classifier to provide consistency regularization for the discriminative classifier. Both the D-CFA and GDC are designed improve the noise robustness of the discriminative classifier and meanwhile reduce domain gap. Finally, the discriminative classifier also supervised by cross-entropy loss using the ground-truth labels of source data or the pseudo-labels of target data.
3.1 PRELIMINARIES
3.1.1 PROBLEM SETTING.
We focuses on unsupervised domain adaptation (UDA) for image classification. In UDA, we are given K labeled source domains = (S......Sp } and an unlabeled target domain T, where 1 for single-source domain adaptation (SSDA) and K 2 for multi-source domain adaptation (MSDA). each source domain St, we have Ns, pairs of image Ir and corresponding label y/s i.e.
St = f v. > Following the previous MSDA works, we assume that the the same label space is shared among the source and target domains. We then aim train model the training set of both source and target domains S U... U Sx UT so that the model can perform well on the test set of the target domain.
No5 For the target domain, only unlabeled images available, T (x: M-1-
3.1.2 INSTANCE BASED FEATURE AUGMENTATION (IFA).
Before introducing our distribution based class-wise wise feature augmentation (D-CFA), we first revisit the naive instance based feature augmentation (IFA) preliminaries.
IFA mixes the features of two different instances that are from the same class to bridge the domain gap. Specifically, we first extract the feature representations {,rS { using a feature extrac- tor (i.e. the backbone CNN in Figure D where B is the batch size for each domain. Then, the augmented feature ft (domain-specific superscript omitted for brevity) is
i. =afi (1- where i i.y. y
(1)
mar(au, - ag), orp is sampled from Beta distribution, an Beta(0.1,0.1) If f, or is from the target domain, we use its pseudo-label (only high-confidence predictions are accepted as pseudo-labels in this paper while low-confidence ones discarded).
4

---

Under review as a conference paper at ICLR 2023
3.2 DISTRIBUTION BASED CLASS-WIDS FEATURE AUGMENTATION (D-CFA)
Note that the naive IFA has two limitations: 1) The features used for mixing are from the same model, thus cannot help eliminate the noise accumulation problem; 2) The features of discrete in- stances are not as diverse as features sampled from a distribution, limiting the diversity of augmented features. To address these two issues, we propose to leverage generative models for the distribution- based feature augmentation and introduce D-CFA.
The D-CFA mixes a feature of an instance with the feature sampled from the target distribution of the same class (modeled by the generative models). It aims to alleviate the noise accumulation and bridge the source-targer domain gap in each class. This can help the classifier better adapt to the target domain.
Different from the IFA in Eq. D-CFA samples the features Jj from the y--th class distribution of the target domain for mixing. The class distribution is modeled by using a Multivariate Gaussian or a normalizing flow (NFlow) My. (Durkan et al. 2019). Taking the NFlow for example, we train C NFlow models [Ma)em using the target features and pseudo-labels Us o | Ji=1 with one NFlow for each class. After the NElow models are well trained, we sample some features ft from My. for augmentation, i.e. fa p(])Mg;)) Then, D-CFA is performed
1. + (1-a)..
The distribution-based continuous features f; is more diverse than the instance- discrete fea- tures fy in Eq. so they can better bridge the domain gap in each class when mixed with source features. More importantly, fo contains class-wise target knowledge from the generative models which can help train a noise-robust discriminative classifier (verified in Table 5). This is because compared with fú the augmented feature S, is closer or more similar the 'genuine' features of the class lis i.e. f.. In this case, f; is likelier to have the correct label of is than fi, i.e., we augment f; to f, so that D; is likelier to be a correct label of ft. Thus, (fc, D:) brings less negative impact com- pared with (fi, 9.). fi can be regarded as a 'genuine' feature of the class ÿ; because My, models the distribution of all the high-confidence samples (of which predicted probabilities are lager than threshold r) in the class yi- As the majority of high-confidence samples usually have clean labels, the class label of the whole population's 's distribution, modeled by My should be reliable.
If the label noise has been corrected, then the D-CFA plays a role as intra-class feature augmentation rather than "correcting" noisy label.
A probability view of D-CFA against label noise. The feature f; is usually observed with its correct label in real world. According to maximum likelihood estimation, their joint probability should be large. We thus assume that the join probability of feature ft and its pseudo-label ÿ, will be large if dJ is correct, otherwise Ú; is noise. We then maximize their joint probability to reduce label noise:
maxp(fi.
max ((f.))(f.)))))
(3)
The D-CFA fixes the pseudo-label is but treat fi as the random variable, so it reformulates Eq. 3 to
max p((()))).
ft
Thus, the D-CFA augments fa to f. so that the probability of the feature sampled from class I (mod- eled by normalizing flow) can be maximized. In this way, D-CFA provides a simple yet effective approximate solution to the maximization problem, i.c., ft arg max,, p(f.l))))
3.3
DIAAAIIIVVEDDSSSSRIIANAAAT CLASSIFIER CONSISTENCY
Recall that in D-CFA, we have the class distributions of target data modeled by [Mc]C Each Me can be used to predict the probability of an instance f. following the distribution of the c-th class, i.e. (e....MM.). Therefore, we can easily obtain the normalized probability of fa on the e-th classes W...W.W....MM
by S (f..M. Et So.. Here, Nu Σ.) is the class prior probability parame- terized by mean Ma and covariance Σ.. As a result, all these NFlow models {M,)c together can be regarded generative classifier off the shelf.
Pe(filMa)
5

---

Under review as a conference paper at ICLR 2023
Based on this observation, we further enforce consistency regularization the target domain data by matching the predictions of the discriminative classifier, i.c. a fully-connected layer followed by soft-max function, these of the generative classifier. The consistency regularization is termed as Unnerative-Discriinnae
Classifier Consistency (GDC). The GDC assumes that distilling the knowledge from the generative classifier the discriminative prevent the discriminative classifier from over-fitting the label noise (see Table 5). This assumption holds because knowledge in these two intrinsically different classifiers is usually complementary.
can reduce the domain gap and
Denote the predictions of the discriminative and generative classifiers on the target data (f7) ) as
The GDC loss, LGDC, is formulated as pD and d respectively, with p Se (MM) c=1
PC (MM)
LGDC
1
Σ
Ip
P
Pi
11
(5)
where the gradient is only backward to p. as only the discriminative classifier is used for inference.
3.3.1 THEORETICAL INSIGHTS.
We further present the theoretical insights of the GDC for reducing domain gap DeviDavid et al. 2010 Given a hypothesis class H. vh E 7 we have
(h) Rh)h) d (S,T) X,
(6)
where (h) is the risk of h on the target domain while Rs(h) on the source domain. And,
dHaH(( T) = 2 sup
|=~s[I(((()) + (((x)) - E E + (()))]
(N,)))H?
A= m= RT()].
1-) is a indicator function. (S T) is the HAH distance, which plays the most important role in bounding (h). The term Eg (A((r) * f((x)) in the HAH distance is assumed be large value. This assumption holds because 1) h is trained on both source and target domains, while h is trained on the target domains only; and 2) they are intrinsically different classifiers. As such, their predictions can be less consistent on source samples. Given large Ez~s (h(x) * (x))))), we then minimize EM-T (1(()) + [(xx)] to approximately obtain the supreme in dS T). In our case, h = pD o F and H = p (I)) where F is the features extractor. This results in
dHaH(S,T) R min
F.p pc EnNT[1(p" F(x) + G F(x))).
Considering that Eq. g is the approximation for the (HA*((, we can further minimize the approximation reduce HAH distance. This twice minimization is equivalent single min- imization operation in Eq. g In our method, the minimization problem is implemented with the GDC in Eq. Thus, minimizing the GDC can reduce the HAH distance, further bound (h)
3.4
TRAINING AND INFERENCE
3.4.1
TRAINING FEATURE EXTRACTOR AND DISCRIMINATIVE CLASSIFIER.
During the training phase, the feature extractor and Nomain-shared discriminative classifier are su- pervised by cross-entropy loss well the GDC loss in Eq. 5
For the labeled source data, we use the cross-entropy which is defined as
KB
L,
log (J:S)
KB
where po (f.5) is the - (ground-truth) prediction p(S.) p(f.)) represents the output proba- bility of the shared discriminative classifier for 2r..

---

Under review as a conference paper at ICLR 2023
Table I: SSDA results on Office-Home. The best results are in bold.
pr- AAr
Ar-PP
-e-
C C--Ro
W Re
ge
0
A5-
14-
Melhods
Avg.
ResNer 50 le ata 2016
38.3
53.9
57.4
36,9
41.2
312
50.0
41.9
59.9
56.0
46.2
00.4
46.1
DANN Gamnn
46.1
63.2
47.0
45.6
51.8
43.7
59.3
58.5
76.8
70.1
60.9
68.5
57.6
68.4
54.4
SymNers (hang
63.6
73.8
64.2
47.6
71.3
82.6
78.5
74.2
79.4
67.2
RSDA-MSTX Lerern 2020
67.9
75.8
66.4
53.2
57.8
53.0
77.7
74.0
85.4
81.3
76.5
82.0
70.9
SRDC (Tang of 2020
68.7
76.3
69.5
52.3
57.1
53.8
76.3
76.2
85.0
81.0
78.0
81.7
71.3
BSP+T5A4 2041b
66.7
75.7
64.3
57.6
55.7
75.8
76.3
83.8
80.7
75.1
81.2
71.2
(Uw7))
For the unlabeled target data, we adopt pseudo-labels for cross-entropy calculation, following a semi-supervised learning method, FixMatch (Sohn al. 2020). Concretely, a weakly-angmented version of a target image is imput to the model to obtain its predicted class o77 If the prediction is high-confidence, e.g. qy. (T threshold), we accept as pseudo-label. The cross-entropy loss is then imposed on the strongly- auggente version of the same image:
1 B
L = B i=1
Σ
1997
> T) log log PoT (f)),
(10)
where 96T is predicted probability on the class S. 1()) is indicator function.
Let us define X as hyper-parameter then the total loss given by
L = Lg + Lu + ALGDC.
(1I)
3.4.2 TRAINING NORMALIZING FLOw (NFLOW) MODELS.
The NFlow models [Ma]e are trained to model the class distributions of the target data. They are fed with the gradient-detached features of target data { ) and their corresponding pseudo- labels 1 ) only these 0.' with 937 > have pseudo-labels, otherwise they are discarded,
and then output probability for each target instance p(f (MgT). Such probability is then used to maximize the log- ligeliikl so that the NFlow models can match the class distributions of the target domain. Equivalently, the loss Flow for optimizing the NFlow models can be defined by minimizing the negative log-likelihood which is
B Σ
INFloww
logle(s? (
(12)
B
3.4.3 INFERENCE.
We only use the discriminative classifier for inference while discard the NFlow models and D-CFA.
4 EXPERIMENTS
We conduct extensive experiments on SSDA dataset, Office-Home Venkateswara al. 2017), and two popular MSDA datasets, including Digit-Five, PACS (Li et al. 2017). to evaluate our method. We introduce the datasets, protocols, and implementation details the Appendix.
4.1 COMPARISON WITH THE STATE OF THE ART
We compare our GeMo-NoRT with following ootie--f-th-attt methods. DANN Ganin al. 2016
MDAN (Zhao et al. 2018), DCTN (Xu et al. 2018). MCD (Saito et al. 2018). SymNets Zhang 2019). -SDA-MSSNN (Gu et al.] 2020). SRDC (Tang et al.] 2020). and M&DDA (Peng
et al. 2019) align the distributions of each domain using domain discriminators or metric distance.
CMSS (Yang et al. 2020) select source images via a curriculum manager to achieve better source- target alignment. LIC-MSDA (Wang et al. 2020) constructs a knowledge graph to capture shared class knowledge among domains for better inference. T-SVDNet (Li et al. 2021a) explores high- order correlations among multiple domains and classes using Tensor Singular Value Decompo- sition (T-SVD). Such correlations are then used to better bridge domain gap. DRT (Li et al., (021c)
and DIDA-Net (Deng al. 2022) uses dynamic network better achieve domain alignment.

---

Under review as a conference paper at ICLR 2023
Table 2: MSDA results on PACS. The best results are in bold. * denotes our implementation.
Methods
ArtPaint.
Cartoon
Sketch
Photo
Avg.
Source-only
81.22
78.54
72.54
95.45
81.94
MDAN Zhao ct al. 2018
83,54
82.34
72.42
92.91
82.80
DCTN Xu el al. 2018
84.67
86.72
71.84
95.60
84.71
MDSDA- Peng
2019
84.20
85.68
74.62
94.47
84.74
MDDA (Zhao et 020
86.73
86.24
77.56
93.89
86.11
LIC-MSDA Wang ei
2020
90.19
90.47
81.53
97.23
89.85
T-SVDNet (Li et al. 202 la
90.43
90.61
85.49
98.50
91.25
TSA" (Li et al. 202 lb
98.25
81.38
85.95
88.46
88.51
DIDA-Nct (Deng et al.
2022
93.39
90.81
84.77
98.36
91.83
GeMo-NoRT (Ours)
93.55
91.38
85.72
98.50
92.29
Table 3: MSDA results on Digit-Five. The best results are in bold.
denotes our implementation.
Methods
MNIST
USPS
MNIST-M
SVIN
Synthetic
Avg.
Source-only Yang et al.
2020
92.3+0.91
90.740.54
63.7=0.83
71.5
83.4:0.79
80.3
DANN Ganin al. 2016
97.9+1..3
93.410.79
70.8:0.94
68.511.85
87.310.68
83.6
DCTN Xu al. 2018
96.2+0.80
92.8+0300
70.5++1.0
77.6+00.0
8688+0.80
84.8
MCD Sato et al. 2016
96.211..1
95.310.74
72.5-1.67
78.810.78
87.410.55
86.1
S (Peng el al. 2019
98.410.68
96.110.81
1..1
81.310.86
89.610.56
87.6
CMSS Yang al. 2020
99.0+0.08
97.7+0.13
75.3+0.57
88.4+0.54
93.7+0.21
90.8
LIC-MSDA Wang
2020
99.011.40
98.310.40
85.611..0
83.2.10.60
93.0110.50
91.8
DRT (Li 2202
99.3+0.05
98.4+0.12
81.0=0034
86.7+0.38
93.9+0.34
91.9
T-SVDNei [i al. 2021a
99.3+0.11
98.610.22
91.2.10.44
84.911147
95.7110.0
93.9
TSA" Li el al. 2b
98.24:0.66
94.7110.2
68.910.37
6..4
88.410.18
82.3
DIDA- (Dnng et al.
2022
99.3:10.7
98.6+0.10
85.7
91.7
97.310001
94.5
GeMo-NoRT (Ours)
99.2410.55
98,810.04
89.0
92.011.54
97.410.13
95.3
SSDA Results on Office-Home. In Table 1 we compare our GeMo-NoRT with other state-of-the-art methods on a single-source domain adaptation dataset, Office- We can see that GeMo-NoR? beats the domain aligmment based methods, e.g, SRDC (Tang et al. (2020), RSDA-MSTN (Gu et al., 2020 and SymNets (Zhang et al., (019)) Our method also surpasses the latest BSP (Chen al. 4TA (Li et al. Artistic (Ar) or Clipart (CI), GeMo-NoRT favorably outperforms all the other competitors.
202 1b) by about 1 % in terms of average accuracy. When the target domain is
Our method is less effective on World (Rw) and Product (Pr) probably because the noisy pseudo-label issue on these two domains is not as severe as Ar or CL For instance, on Pr or Rw, the performance of these methods without noise-robust design, e.g., TSA, can easily get more than 74%, while on Ar or CI, the accuracy are only about 60%. This implies that the noise level on Pr or Rw is much less than that on Ar or Cl. So our noise-robust design can be less effective.
MSDA Results on PACS. Table 2 shows that our SeMo-NoRTT surpasses all the previous state-of the- art methods on PACS, with over 1.04% % performance gain. is worth noting that LIC-MSDA (Wang et al. 2020), T-SVDNet (Li et al. 102 TSA (Li et al. 202 and DIDA-Net (Deng et al. 2022) also leverage class information by using labudo-labels for the unlabeled target data, but both of them are inferior to our GeMo-NoRT. We owe the superiority of our GcMoo-NRT to the noise-robust training brought by the generative models' knowledge. On each specific domain, our method also achieves the best accuracy regardless of the drastic domain gap. This justifies that our GeMo-NoRT can bridge the domain gap and train a noise-robust model for MSDA.
MSDA Results Digit-Five. As shown in Table our GeMo-NoRT achieves the state-of afftth--rt performance on Digit-Five in term of the average accuracy. On the challenging USPS, SVHN, and Synthetic domains, our GeMo-NoRT manifests consistent improvements over the other methods. This shows that our GeMo-NoRT can handle the challenge of large domain gap.
4.2 FURTHER ANALYSIS
4.2.1 ABLATION STUDY ON PACS UNDER MSDA SETTING.
Effectiveness of Instance Based Feature Augmentation (IFA). IFA randomly mixes features of differ- ent instances in mini-batch. To see whether it helps improve the model's performance, we compare the IFA with the baseline in the first two rows of Table is clear that the IFA increases the average accuracy of the baseline method by 1.72%. This can be explained by that randomly mixing features mini-batec can also reduce the domain gap.
8

---

Under review as a conference paper at ICLR 2023
Significance of D-CFA. For the D-CFA, com- pare two variants, namely multivariate Gaussian based D-CFA and NFlow based D-CFA. In Ta- ble 4 we can see that Gaussian based D-CFA only achieves similar performance to the IFA. This is probably because the class-wise distribu- tion across multiple domains can follow a much more complex distribution than Gaussian. The in- accurate Gaussian modeling may generate feature noise which hinders the effectiveness of feature mixing based augmentation.
Table 4: Ablation study on PACS. CFA: Class-
wise Feature Augmentation. GDC: Generative and Discriminative Consistency. We evaluate two different distribution modelling methods:
Multivariate Gaussian and NFlow.
Methods
CFA
GDC
Avg.
Baseline
88.79
Instance based
90.50
90.51
Gaussian based
contrast, NFlow based D-CFA is better than the former two by about 1.03%, suggesting the significance of ac- curate distribution modeling for feature augmen- tation. In addition, we show in Table that the NFlow based D-CFA can reduce the noise level of pseudo-labels by integrating the knowledge in generative models into the discriminative one.
91.56
91.54
NFlow based
92.29
Importance of Generative and Discriminative Consistency (GDC). The GDC is a consistency loss that further exploits an ensemble of larget knowledge from each NFlow model for training a noise- robust and Nomain-adaptive discriminative classifier. Table 4 shows that the GDC increases the accuracy of Gaussian based D-CFA from 90.51% to 91.56%, and NFlow based D-CFA from 91.54% to 92.29%. We owe the effectiveness of GDC to its complementary knowledge for training a noise- robust discriminative classifier and reducing domain gap.
4.2.2 NOISE LEVEL ANALYSIS.
We argue that GeMo-NoRT can reduce label noise. To support this argument, we estimate the noise level of the pseudo-labed labuls generated by the discriminative classifier in Table [S] We can observe that the baseline method accepts 94. 12% pseudo-labels of the target training data but about 41.81 % pseudo-labels are inaccurate. These high-confidence but inaccurate predictions demonstrates that the discriminative classifier has over-fitted the label noise. As result, the baseline obtains a poor test accuracy of 75.02% on the Sketch domain of PACS. The D-CFA reduces the amount of high- confidence instances avoid over-confident on some noisy instances, and also increases the accu- racy of the predictions for all the target training data. This can decrease the noise level by 8.01 % (from 41.81% 1 to 33. 33.80%). which contributes to better test accuracy. The GDC further decreases the noise level by 6.70% (from 33.80% to 26.90%.) Correspondingly, the accuracy on the test set increased considerably. These observations illustrate that with the knowledge from the genera- tive classifiers integrated in, the discriminative classifier less over-fits the noisy labels, thus more noise-robust. This further underpins good performance on the test set of the target domain.
We further present more analysis and visualization of features in the Appendix.
5 CONCLUSION
This paper proposed a method named GeMo-NoRT to simultaneously alleviate the target pseudo- label noise and the domain gap for MSDA. To achieve these goals, GeMo-NoRT models the class- wise distribution of the target data using generative models to enforce D-CFA and GDC. Exten- sive experiments show that our GeMo-NoRT achieves state-of-the-art performance in all setups.
Table 5: Comparison of GeMo-NoRT (D-CFA+GDC) with the baseline on the Sketch domain of PACS. RHCP (%): the Ratio of High-Confidence Predictions (accepted as pseudo-labels) from dis- criminative classifier. Noise (%): the noise level in these pseudo-labed labels (i.e., high-confidence pre- dictions). Acc-P (%): the accuracy of all the predictions from the discriminative classifier.
Methods
RHCP
Noise
Acc-P
Test Acc.
Baseline
94.12
41.81
57.59
75.02
D-CFA (NFlow based)
92.94
33.80
65.39
81.96
GcMo-NoRT (D-CFA+GDC)
85.79
26.90
69.19
85.72
9

---

Under review as a conference paper at ICLR 2023
REFERENCES
Yogesh Balaji, Rama Chellappa, and Soheil Feizi. Normalized wasserstein for mixture distributions with applications in adversarial learning and domain adaptation. In ICCV, 2019.
Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jennifer Wort- man Vaughan. A theory of learning from different domains. ML, 2010.
Bharath Bhushan Damodaran, Benjamin Kellenberger, Rémi Flamary, Devis Tuia, and Nicolas Courty. Deepjdot: Deep joint distribution optimal transport for unsupervised domain adaptation. In ECCV, 2018.
Xinyang Chen, Sinan Wang, Mingsheng Long, and Jianmin Wang. Transferability vs. discriminabil- ity: Batch spectral penalization for adversarial domain adaptation. In ICML, 2019.
Zhongying Deng, Kaiyang Zhou, Da Li, Junjun He, Yi-Zhe Song, and Tao Xiang. Dynamic instance domain adaptation. JEEE 7-IP, 31, 2022.
Laurent Dinh, David Krueger, and Yoshua Bengio. Nice: Non-linear independent components esti- mation. arXiv preprint arXiv:1410.8516, 2014.
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density estimation using real nvp. arXiv preprint arXiv:1605.0888 088033, 2016.
Conor Durkan, Artur Bekasov, lain Murray, and George Papamakarios. Neural spline flows.
NeurIPS, 2019.
Yaroslav Ganin and Victor Lempitsky. Unsupervised domain adaptation by backpropagation. In ICML, 2015.
Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, François Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural net- works. JMLR, 2016.
lan Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In NeurIPS, 2014.
Arthur Gretton, Karsten M Borgwardt, Malte Rasch, Bernhard Schölkopf, and Alexander Smola. A kernel two-sample test. JMLR, 2012.
Xiang Gu, Jian Sun, and Zongben Xu. Spherical space domain adaptation with robust pseudo-label loss. In CVPR, 2020.
Junjun He, Zhongying Deng, and Yu Qiao. Dynamic multi-scale filters for semantic segmentation. In ICCV, 2019.
K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. In CVPR, 2016.
Jonathan Ho, Xi Chen, Aravind Srinivas, Yan Duan, and Pieter Abbeel. Flow++: Improving flow- based generative models with variational dequantization and architecture design. In ICML, 2019.
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv: 1412,6990, 2014.
Diederik Kingma and Max Welling. Auto-encoding variational bayes. arXiv:1312.61 14, 2013.
arXiv preprint
Durk P Kingma and Prafulla Dhariwal. Glow: Generative flow with invertible 1x1 convolutions. NeurIPS, 2018.
Ivan Kobyzev, Simon JD Prince, and Marcus Brubaker. Normalizing flows: An introduction and review of current methods. IEEE T-PAMI, 43(11), 2020.
Manoj Kumar, Mohammad Babaeizadeh, Dumitru Erhan. Chelsea Finn, Sergey Levine, Laurent Dinh, and Durk Kingma. Videoflow: A flow-based generative model for video. arXiv preprint arXiv:1903.000 2019.
10

---

Under review as a conference paper at ICLR 2023
Y Lecun and L Bottou. Gradient-based learning applied to document recognition. IEEE, 1998.
Da Li, Yongxin Yang, Yi-Zhe Song, and Timothy M Hospedales. Deeper, broader and artier domain generalization. In CVPR, 2017.
Ruihuang Li, Xu Jia, Jianzhong He, Shuaijun Chen, and Qinghua Hu. T-svdnet: Exploring high- order prototypical correlations for multi-source domain adaptation. ICCV, 2021a.
Shuang Li, Mixue Xie. Kaixiong Gong, Chi Harold Liu, Yulin Wang, and Wei Li. Transferable semantic augmentation for domain adaptation, In CVPR, 2021b.
Yunsheng Li, Lu Yuan, Yinpeng Chen, Pei Wang, and Nuno Vasconcelos. Dynamic transfer for multi-source domain adaptation. In CVPR, 2021c
Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015a.
Mingsheng Long, Yue Cao, Jianmin Wang, and Michael Jordan. Learning transferable features with deep adaptation networks. In ICML, 2015b.
Mingsheng Long, Han Zhu, Jianmin Wang, and Michael Jordan. Unsupervised domain adaptation with residual transfer networks. In NeurIPS, 2016.
Mingsheng Long, Zhangjie Cao, Jianmin Wang, and Michael I Jordan. Conditional adversarial domain adaptation. arXiv preprint arXiv: 10667, 2017.
Ilya Loshchilov and Frank Hutter. Sgdr: Stochastic gradient descent with warm restarts. arXiv preprint arXiv:1608.0390 2016.
Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. JMLR, 2008.
Jaemin Na, Heechul Jung, Hyung Jin Chang, and Wonjun Hwang. Fixbi: Bridging domain spaces for unsupervised domain adaptation. In CVPR, 2021.
Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Ng. Reading digits in natural images with unsupervised feature learning, In NeurlPS-W. W, 2011.
Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. In NeurlPS-W W, 2017.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high- performance deep learning library. NeurlPS, 2019.
Xingchao Peng, Qinxun Bai, Xide Xia, Zijun Huang, Kate Saenko, and Bo Wang. Moment matching for multi-source domain adaptation. In ICCV, 2019.
Danilo Rezende and Shakir Mohamed. Variational inference with normalizing flows. In ICML, 2015.
Kuniaki Saito, Kohei Watanabe, Yoshitaka Ushiku, and Tatsuya Harada. Maximum classifier dis- crepancy for unsupervised domain adaptation. In CVPR, 2018.
Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recogmition. arXiv preprint 1xXiv:1409.1553 2014.
Kihyuk Sohn, David Berthelot, Chun-Liang Li, Zizhao Zhang, Nicholas Carlini, Ekin D. Cubuk, Alex Kurakin, Han Zhang, and Colin Raffel. Fixmatch: Simplifying semi-supervised learning with consistency and confidence. In NeurlPS, 2020.
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Du- mitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In CVPR, 2015.
11

---

Under review as a conference paper at ICLR 2023
Hui Tang. Ke Chen, and Kui Jia. Unsupervised domain adaptation via structurally regularized deep clustering. In CVPR, 2020.
Eric Tzeng, Judy Hoffman, Ning Zhang, Kate Saenko, and Trevor Darrell. Deep domain confusion: maximizing for domain invariance. arXiv preprint arXiv:1412.3477 2014.
Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell. Adversarial discriminative domain adaptation. In CVPR, 2017.
Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep
hashing network for unsupervised domain adaptation. In CVPR, 2017.
Hang Wang, Minghao Xu, Bingbing Ni, and Wenjun Zhang. Learning to combine: Knowledge
aggregation for multi-source domain adaptation. In ECCV, 2020.
Yuan Wu, Diana Inkpen, and Ahmed El-Roby. Dual mixup regularized learning for adversarial domain adaptation. In ECCV, 2020.
Ruijia Xu, Ziliang Chen, Wangmeng Zuo, Junjie Yan, and Liang Lin. Deep cocktail network: Multi- source unsupervised domain adaptation with category shift. In CVPR, 2018.
Luyu Yang, Yogesh Balaji, Ser-Nam Lim, and Abhinav Shrivastava. Curriculum manager for source selection in multi-source domain adaptation. In ECCV, 2020.
Xingrui Yu, Bo Han, Jiangchao Yao, Gang Niu, Ivor Tsang, and Masashi Sugiyama. How does disagreement help generalization against label corruption? In /CML., 2019.
Yabin Zhang, Hui Tang, Kui Jia, and Mingkui Tan. Domain-symmette networks for adversarial domain adaptation. In CVPR, 2019.
Han Zhao, Shanghang Zhang, Guanhang Wu, José MF Moura, Joao P Costeira, and Geoffrey J Gordon, Adversarial multiple source domain adaptation. In NeurIPS, 2018.
Sicheng Zhao, Guangzhi Wang, Shanghang Zhang, Yang Gu, Yaxian Li, Zhichao Song, Pengfei Xu, Runbo Hu, Hua Chai, and Kurt Keutzer. Multi-source distilling domain adaptation. In AAAI, 2020.
Kaiyang Zhou, Yongxin Yang, Yu Qiao, and Tao Xiang. Domain adaptive ensemble learning. arXiv preprint arXiv:2003.07325, 2020.
A APPENDIX
The Appendix is organized follows. Section A. revisi the Transferable Semantic Augmentation (TSA) (Li et al. 2021b). Section A.2 provides experimental settings, including datasets. protocols, and implementation details. Section presents further analysis for GeMo-NoRT. Section A.4 shows the t-SNE visualization (Maaten & Hinton 2008) of the learned features.
A.1 REVISIT TSA
Transferable Semantic Augmentation (TSA) Li et al. 20216) adopts Gaussian distribution to model the domain difference in each class that cross-domann semantic augmentation can be performed to bridge the domain gap.
Denote PT_ u the mean of target and source domain features in the class c, respectively, Here, pseudo-label for the target domain is obtained as ý = arg max pT_ TSA then model the inter-domain difference, i.e., Ape. !u! n using Gaussian distribution A ((A)es Σ!). Σ7 is the intra-class covariance of the target domain. After that, TSA augment source feature f by
i ~ + +AAMo XΣ?),
(13)
where À is hyper-parameter.
12

---

Under review as a conference paper at ICLR 2023
TSA only focus reducing domain gap by applying augmentation to source domain features. In contrast, our GeMo-NoRT can not only reduce domain gap, but also deal with target label noise by applying augmentation to target features. In addition, TSA model the domain difference using Gaussian distribution. Instead, we use normalizing flow (NFlow) to better model the class-wise distribution itself rather than the domain difference, and further propose consistency regularization on the generative classifier (i.e., all the NFlow models as a whole) and the discriminative one to address noise accumulation.
A.2 EXPERIMENTAL SETTING
Datasets and Protocols. Office-Home /Venkateswara et al. 2017 includes four domains, namely Clip Art (CI), Artistic (Ar), Real-World (Rw), and Product (Pr). It has 15,500 images of 65 cat- egories. We follow the single-source setting in (Tang et al., 2020) to evaluate our method on all the 12 transfer tasks. Digit-Five is a MSDA datset which comprises five domains, namely USPS, MNIST (Lecun & Bottou, 1998), MNIST-M (Ganin & Lempitsky] 20155) Synthetic Digits (Ganin & Lempitsky 2015). and SVHN (Netzer et al. (011). The protocol is the same as (Peng et al. 2019): All the 9,298 images of USPS are used for training when it is used
source domain; For the rest four domains, 25,000 images are randomly sampled for training while 9,000 images for testing. PACS consists of four domains, including Cartoon, Photo, Sketch and Art Painting, totally 9,991 images of 7 categories. The official train-val splits in (Li et al. 2017) are adopted for MSDA task. For MSDA, take turns choosing one domain as target and the rest source domains.
We train the model on the training set of source and target domains, and report the average results of three runs on the test of the target domain.
Implementation Details, On Office-Home, we adopt ImageNet pre-trained ResNet-50 as backbone, following (Tang al. 2020). We then optimize the model for 100 epochs with SGD. We set the initial learning rate to 0.001, batch size to 32 for each domain, and the threshold in Eq. (11) is 0.95. On Digit-Five, we use the same backbone as (Peng al.) 2019: a CNN with three convolution layers followed by two fully connected layers. We train the model with SGD for 30 epochs. We set the initial learning rate to 0.05 and decay it using the cosine annealing strategy (Loshchilov Hutter) 2016). The batch size B is 64 for each domain, and the threshold is 0.75. For the backbone model used on Digit-Five and Hofice-Home, we further incorporate fully-connected layer as bottleneck to reduce the feature dimension from 2048 to 512. This can reduce the computational cost for training the NFlow models. On PACS, we follow (Wang et al. 2020) and adopt an ImageNet pre- trained ResNet- 18 (He et al.) (016) as backbone. We optimize the model with Adam (Kingma & Ba 2014) for 100 epochs. We set the initial learning rate 5e-4, batch size B = 16, and T 0.95.
For all the experiments, we adopt neural spline flow (Durkan al. 2019) our NFlow model. The NFlow model stacks three blocks, with each block comprising an actnorm, invertible 1x1 con- volution (Kingma & Dhariwal, 2018) and four-layer multi-layer perceptron (MLP) as coupling transform. We use Adam optimizer with an initial learning rate of 5e-4 to train the NFlow. We exploit a memory module cache the latest features to facilitate end-to-end training since there can be no instance of some classes in mini-batch. We apply the D-CFA and GDC after 10 epochs so that the NFlow models are properly trained. The weight for GDC loss, i.e. À in Eq. (12), is 0.5.
All our experiments are based on PyTorch (Paszke et al. 2017 2019) and Dassl codebase (Paszke htw.:/aasssspp....oooooooo pytorch
jet al. 2017, Zhou et al. 2020) (htpps: pectps:/go http::://githbb. com Ka
Our code will be released.
A.3 FURTHER ANALYSIS FOR GEMO-NORT
In this section, we will provide more experimental results and further analysis for GeMo-NoRT on PACS under MSDA setting.
A.3.1 FURTHER ANALYSIS ON GDC.
Superiority of Using Generative Classifier in GDC. The GDC in Eq. 5 exploits the generative classifier to apply consistency regularization on the discriminative one. We also compare this de- sign choice with using the discriminative classifier itself for the consistency, which is termed self- consistency. Concretely, we adopt label smoothing strategy the predictions of the discriminative
13

---

Under review as a conference paper at ICLR 2023
The GDC vs. self-consistency (using the discriminative classifier itself for consistency regularization).
Table 6:
Table 7: Apply the GDC on all the target data only the disagreed target data between generative and discriminative classifiers.
Methods
Avg. 92.29
Methods
Avg.
GDC (generative classifier)
GDC on all the target data
92.29
Self-consistency
90.65
GDC on disagreed target data
91.86
Table 8: Evaluation on different metric functions in GDC. Results reported on PACS under MSDA setting.
Table 9: Modelling only target distribution modelling all domains'. Results reported on PACS under MSDA setting.
Methods
Avg.
Methods
Avg.
L2 distance
92.29
GeMo-NoRT (target domain) GeMo-NoRU (all domains)
92.29
LI distance
90.35
90.55
KL divergence
89.50
classifier and use the smoothed predictions to enforce consistency on non-smoothed predictions. T shows that the GDC outperforms the self- self-consistency. due to its complementary knowledge used for alleviating noise accumulation and reducing domain gap.
apply the GDC to all the target data. Here we further evaluate applying the GDC only on these target data of which the predictions disagreed by generative and discriminative classifiers. As shown in Table 7 we can see that only using disagreed data (i.e., without using agreed data) decreases the accuracy on PACS by 0.43% but is still better than without GDC, i.e., 91.54% in Table These two comparisons demonstrate that both the agreed data and disagreed data contribute to the better performance of GDC. The GDC the agreed data can possibly prevent the discriminative classifier from over- fitting label noise, while the disagreed data can help reduce the domain gap per Eq.
Whether All the Target Data Needed for Applying GDC? In practice,
Alternativ metric function for La- The GDC adopts L2 distance by default. We also investigate L1 distance and KL divergence in Table It is clear that GDC based on L2 distance works better than 1.1 distance with 1. 1.94% gap, and beats the version based on KI. divergence by 2.79%.
A.3.2 MODELING ONLY TARGET DISTRIBUTION VS. MODELING ALL DOMAINS' DISTRIBUTIONS.
By default, we only model the target distribution of each class using NFlow. We further compare this design choice with modeling all the domains' distribution of each class. The comparative results on PACS are shown Table D We find that only modeling than modeling all, possibly because the generative models trained less source-bel biased (i.c., not dominated by source data). This can make these generative models more complementary to the source-biased discriminative classifier, further contributing better performance.
target distribution clearly better only the target domain
A.3.3 SENSITIVITY OF PEOPER--RRAMTER.
In Eq. (12), there is hyper-parameter À in our GeMo-NoRT which is the loss weight for the GDC. We evaluate the sensitivity of the performance with respect to À in Figure 3 We can see that the performance is generally insensitive to X, with À 0.5 leading to the best performance of 92.29%. The performance of E [0.3, 0.7] consistently better than without GDC (i.e., X = 0), which manifests the effectiveness of the GDC.
A.4 VISUALIZATION.
We further provide the visualization final features in Figure to better understand the D-CFA and GDC in our GeMo-NoRT. We can observe that incorporating the D-CFA to the baseline model leads to less features lying around the decision boundary (see the top left area Figure 4a and Figure 4b). The GeMo-NoRT further includes the GDC to prevent the discriminative classifier from
14

---

Under review as a conference paper at ICLR 2023
95
93
91
89
87
85
0.1
0.2
0.3
0.4
0.5 0.6 0.7 0.8 0.9
Figure 3: Sensitivity of X for GDC PACS dataset.
(c) GeMo-NoRT (D-CFA GDC)
(a) Baseline
(b) Baseline D-CFA
Figure 4: Visualization of features from baseline (FixMatch), baseline+D-CFA and GeMo-NoRT on PACS using t-SNE (Maaten & Hinton 2008). Red color denotes the target domain of Sketch while other colors denote source domains. Different digits (0-6) represents different classes. Best viewed with zoom-in.
over-fitting the label noise. As depicted in Figure 4c incorporating GDC to our method can increase the separability of different classes and better align different domains. As result, GeMo-NoRT achieves the best classification performance.
15


Reviews:
[{"review_id": "yoguahGoUcM", "reviewer": "Reviewer_8FeU", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "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": "This work proposed an NFlow-based noise-robust UDA method. Specifically, they trained an NFlow (Durkan et al. 2019)  generative model of the feature distribution for each class by using the noisy pseudo labels generated from the source. With the classwise NFlow models, they introduced a modified feature mix-up scheme (i.e. D-CFA), and a consistency regularization loss on these NFlow-based classifiers and the task classifier (i.e. GDC). The experiments show that the proposed method can improve the DA performance by 1% compared to the SOTA methods on office-home for single-source UDA, as well as MSDA and PAC for multi-source UDA.        ", "summary_of_the_review": "In summary, the work proposed a novel generative model based noise-robust UDA method. They theoretically and experimentally justified that the proposed techniques can decrease the noise level of pseudo labels. However, there are still some concerns about the method and experiment results. ", "strength_and_weaknesses": "Strength:\n\n- The work proposed a generative model based $\\\\textit{noise-robust}$ UDA method. They introduced an NFlow-based feature Mix-Up scheme (D-CFA): Instead of using instance features, they use the classwise NFlow models to sample features to do feature mix-up. It can provide enough diversity while eliminating the noise from instance features. Also, they proposed a consistency constraint (GDC) on these NFlow-based classifiers and the task classifier. \n- The theoretical justification for GDC and theoretical discussions from the perspective of probability about D-CFA are given in the paper.  \n- Their experiment results showed that GDC decreased the noise level by 8.01% and D-CFA further decreased the noise level by 6.70%.\n\nWeakness:\n\n-  I have some concerns about the theoretical discussions of  GDC in the paper. The definition of  $=>$ in EQ3 is unclear. If it is $\\geq$, the deduction has to be given. \n- The experiment results are not very strong. Though the proposed method can largely decrease the noise level, the final classification performance was only marginally improved by 1% compared to SOTA.    \n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "ya0aD20KKK", "reviewer": "Reviewer_ahQT", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "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": "The authors propose a novel method to handle the noisy pseudo-label issue in UDA settings. They first train normalizing flow models to estimate the distribution of the target domain bases on generated pseudo-labels. Then they use the generative models to construct the D-CFA on features in the source domain. Besides, they use the GDC loss to require that predictions of the discriminative model and generative model (i.e., the normalizing flows) are consistent. Finally, they conduct experiments on several datasets to prove the effectiveness of the methods.", "summary_of_the_review": "As mentioned in the Strength and Weakness section, I think the experiments are comprehensive while the theoretical analysis needs further explanation. As a result, I am negative about the paper in this round.", "strength_and_weaknesses": "The authors study an important problem and propose novel techniques to deal with the noisy pseudo-label issue in UDA settings. The experiments are comprehensive and ablation studies are provided. The paper is generally well-written. However, I still have several concerns.\n\nFor the method part, I have several questions about the theoretical analysis. As a result, I doubt the effectiveness of the methods from a theoretical perspective.\n1. For the probability view of D-CFA against label noise, the approximation steps are unclear and need further theoretical analysis. Firstly, the authors suppose that $y_i$ and $\\hat{y}_i$ are independent, which may not be correct. The reason is that the pseudo-labels are generated to be close to the true label, making the two labels dependent. Secondly, even if the labels are independent, it is still unclear how to get Equation (4) from Equation (3). For example, why $p(f_i|\\hat{y}_i,y_i)$ can be approximated as $p(f_i|\\hat{y}_i)$?\n2. For the theoretical insights in Section 3.1.1. I do not agree with the authors' claim on the $H\\Delta H$ divergence. Since $h$ and $h'$ are optimized according to the sup function in the divergence, they are not trained on the same labeled source function. As a result, it may not be correct to claim that the distance can be approximated by the supreme in the target distribution.\n\nFor the experiment part.\n1. I do not understand the results in the Office-Home dataset. The proposed method achieves superior results when the target domain is Ar or Cl while they are not the highest results when the target domain is Pr or Rw. Could the authors explain this phenomenon?\n\nMinor issues:\n1. The third line in Section 3.1.1: $k1$ $\\rightarrow$ $K > 1$", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "nH-ZhhHytK", "reviewer": "Reviewer_YwCr", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "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": "This work proposes a new domain adaptation method for both single-source and multi-source conditions. The main idea is to alleviate the error accumulation of target pseudo labels and reduce the domain gap at the prediction level. Technically, they use a generative model (normalizing flows) to model the class-wise distribution of the target data and solve a probability maximization problem. Experiments on three benchmarks demonstrate the effectiveness.", "summary_of_the_review": "In summary, the paper proposes an interesting approach to a relevant problem. Clarity and reproducibility could be improved with a minor revision. At this point, my main concern is the difference with TSA. This point requires clarification and some solid empirical support before warranting acceptance of this paper.", "strength_and_weaknesses": "Strength:\n1. The paper is nicely written and the proposed method is well described.\n2. Useful illustrations are provided that illustrate essential parts of the problem or method.\n3. The empirical evaluation is thorough and conducted in diverse settings, including single- and multi-source settings.\n\nWeaknesses:\n1. The main concern for me is the difference with TSA (Li et al. 2021b). First, the idea of using the class-wise target distribution to perform augment is similar to TSA. There should include more comparisons and discussions. Second, this work exploits NFlow instead of Gaussian distribution to model the class-wise distribution of target data but the motivation is not clear and is not well-proven. For example, in Relate Work section, the authors claim that NFlow models can be performed to bridge the domain gap and alleviate noise accumulation. How about Gaussian-based models?  Third, it would be nice to revisit TSA before introducing the proposed D-CFA.\n\n2. Concern about noise correction. From Fig. 1(a), we can see that target samples around the decision boundary of the discriminative classifier (red star) are prone to be mixed. My concern is that would these samples be corrected over and over again.\n\n3. More explorations are needed. It is a bit unclear that two assumptions \"the pseudo-labels are intact but the features are corrupted\" and \"the features are intact but the labels are corrupted\" are in the Introduction.\n\n4. A doubt about the feasibility of class-wise distribution. D-CFA samples the features from the class distribution of the same class (depending on pseudo labels predicted by the generative models), however, due to domain shift, untrustworthy pseudo-labels may affect the construction of the distribution. Thus, the sampled features might be incorrect.\n\n5. About experimental results. First, the improvement on Office-Home is limited (72.1 vs TSA: 71.2 & SRDC: 71.3) and more recent results should be included. Second, it might be better to provide the results of TSA on MSDA in Table 3 and Table4. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "h1JuK04Mms8", "reviewer": "Reviewer_j3cT", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "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": "This paper presents a novel UDA method that utilizes generative models trained in the feature space to alleviate a domain gap. The generative model is trained in a feature space for each subset of the target data categorized into a common pseudo-class, and generated samples from this model are used for mixup-like augmentation of extracted features. Learning with this augmentation effectively reduces a domain gap, which makes a classifier trained on top of the feature perform well on the target data. Experimental results with several popular benchmark datasets show that the proposed method performs on par or better than state-of-the-art UDA methods.\n", "summary_of_the_review": "The design of the proposed algorithm is interesting, but I have several concerns on its validity. I vote for \"weak reject.\"", "strength_and_weaknesses": "<Strength>\n\n- The proposed method seems to be applicable to a wide range of model architectures.\n- This manuscript is well-organized and easy to follow.\n\n\n<Weakness>\n\n- The proposed method requires training of several NFlow models, which may lead to prohibitive computation cost especially when the number of classes is large. In spite of this, the performance gain seems not so significant in the experiments.\n- To train the NFlow models, we also need a sufficiently large number of target samples for every class, which may limit the applicability of the proposed method in practice. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject