Divide to Adapt: Mitigating Confirmation Bias for Domain Adaptation of Black-Box Predictors
Authors: Jianfei Yang
Xiangyu Peng
Kai Wang
Zheng Zhu
Jiashi Feng
Lihua Xie
Yang You
Venue: ICLR 2023 notable top 25% (2023)
Keywords: model adaptation
black-box predictors
transfer learning

Abstract: Domain Adaptation of Black-box Predictors (DABP) aims to learn a model on an unlabeled target domain supervised by a black-box predictor trained on a source domain. It does not require access to both the source-domain data and the predictor parameters, thus addressing the data privacy and portability issues of standard domain adaptation methods. Existing DABP approaches mostly rely on knowledge distillation (KD) from the black-box predictor, i.e., training the model with its noisy target-domain predictions, which however inevitably introduces the confirmation bias accumulated from the prediction noises and leads to degrading performance. To mitigate such bias, we propose a new strategy, \textit{divide-to-adapt}, that purifies cross-domain knowledge distillation by proper domain division. This is inspired by an observation we make for the first time in domain adaptation: the target domain usually contains easy-to-adapt and hard-to-adapt samples that have different levels of domain discrepancy w.r.t. the source domain, and deep models tend to fit easy-to-adapt samples first. Leveraging easy-to-adapt samples with less noise can help KD alleviate the negative effect of prediction noises from black-box predictors. In this sense, the target domain can be divided into an easy-to-adapt subdomain with less noise and a hard-to-adapt subdomain at the early stage of training. Then the adaptation is achieved by semi-supervised learning. We further reduce distribution discrepancy between subdomains and develop weak-strong augmentation strategy to filter the predictor errors progressively. As such, our method is a simple yet effective solution to reduce error accumulation in cross-domain knowledge distillation for DABP. Moreover, we prove that the target error of DABP is bounded by the noise ratio of two subdomains, i.e., the confirmation bias, which provides the theoretical justifications for our method. Extensive experiments demonstrate our method achieves state of the art on all DABP benchmarks, outperforming the existing best approach by 7.0\% on VisDA-17, and is even comparable with the standard domain adaptation methods that use the source-domain data.

Published as a conference paper at ICLR 2023
DIVIDE TO ADAPT: MITIGATING CONFIRMATION BIAS FOR DOMAIN ADAPTATION OF BLACK-BOR PREDIC-
TORS
Jianfei Yang"; Xiangyu Peng"; Kai Wang Zheng Zhu", Jiashi Feng', Lihua Xie',
Yang You².
Nanyyng Technological University
National University of Singapore "Tiinghua University 'ByteDance
ABSTRACT
Domain Adaptation of Black-box Predictors (DABP) aims to learn a model on an unlabeled target domain supervised by a black-box predictor trained domain. It does not require access to both the source-domain data and the predictor parameters, thus addressing the data privacy and portability issues of standard domain adaptation methods. Existing DABP approaches mostly rely on knowledge distillation (KD) from the black-box predictor, iee., training the model with its noisy target-domann predictions, which however inevitably introduces the confirmation bias accumulated from the prediction noises and leads degrading performance. To mitigate such bias, we propose a new strategy, divide-to-adape that purifies cross doos--d knowledge distillation by proper domain division. This is inspired by observation make for the first time in domain adaptation: the target domain usually contains easy-to-adapt and hard-to-adapt samples that have different levels of domain discrepancy w.r.t. the source domain, and deep models lend to fit easy- to-adapt samples first. Leveraging casy-to-adapt samples with less noise can help KD alleviate the negative effect of prediction noises from black-box predictors. In this sense, the target domain can be divided into an aasy-to-adapt subdomain with less noise and hard-to-adap subdomain at the early stage of training. Then the adaptation is achieved by semi-supervised learning. We further reduce distribution discrepancy between subdomains and develop weak-strong augmentation strategy to filter the predictor errors progressively. As such, our method is simple yet effective solution reduce еггог accumulation lation for DABP. Moreover, we prove that the target error of DABP is bounded by the noise ratio of two subdomains, i.e., the confirmation bias, which provides the theoretical justifications for our method. Extensive experiments demonstrate our method achieves state of the art on all DABP benchmarks, outperforming the existing best approach by 9.5% on VisDA-17, and is even comparable with the standard domain adaptation methods that use the source-domain data!.
source
cross-domain knowledge distil-
INTRODUCTION
Unsupervised domain adaptation (UDA) (Pan & Yang, 2009) aims to transfer knowledge from labeled source domain to an unlabeled target domain and has wide applications (Tzeng et al., 2015; Hoffman et al., 2018; Zou et al., 2021). However, UDA methods require to access the source- domain data, thus raising concerns about data privacy and portability issues. To solve them, Domain Adaptation of Black-bo box Predictors (DABP) (Liang et al., 2022) was introduced recently, which aims to learn a model with only the unlabeled target-domain data and black-box predictor trained on the source domain, e-g., API in the cloud, avoid the privacy and safety issues from the leakage of data and model parameters.
"Equal contribution (yang(478
Codes available at https: / //i thub. com/ wxwppnggppgg//////e HKTA

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A few efforts have been made to solve the DABP problem. One of them is to leverage knowledge distillation (Hinton et al., 2015) and train the target model to imitate predictions from the source predictor (Liang et al., 2022). Another one is to adopt learning with noisy labels (LNL) methods to select the clean samples from the noisy target-domain predictions for model training (Zhang et al., 2021). Though inspiring, they have the following limitations. (i) Learning the noisy pseudo labels for knowledge distillation inevitably leads to confirmation bias (Tarvainen & Valpola, 2017), i.e., accumulated model prediction errors. (ii) The LNL-based methods aims select clean subset of the target domain to train the model, which would limit the model's performance due to decreased amount of usable data for model training. (iii) Existing DABP methods lack theoretical justifications.
To address the aforementioned issues, this work proposes simple yet effective strategy, divide-to- adapt, which suppresses the confirmation bias by purifying cross-domain knowledge distillation. strategy divides the target domain into an easy-to-adaps subdomain
Intuitively, the with less prediction noise and a hard-to-adapt subdomain. This is inspired by a popular observation: deep models tend to learn clean samples faster than noisy samples (Arpit et al., 2017). For domain adaptation, we make a similar discovery: deep models tend to learn easy-to-adapt samples faster than hard-to- to--tdpp samples, and thus we can leverage the loss distribution of cross cross-domain knowledge distillation at the early stage for subdomain division. By taking the -o-aapt subdomain as a labeled set and the hard-to-adapt subdomain an unlabeled set, can solve DABP problem via leveraging prevailing semi-supervised learning methods (Berthelot et al., 2019; Sohn et al., 2020). The divide-to-adapl strategy purifies the target domain progressively for knowledge distillation while fully utilizing all the target dataset without wasting any samples.
To implement the above strategy, this paper proposes Black-Box ModEl Adap'Tation by DomAin Division (BETA) that introduces two key modules to suppress the confirmation bias progressively. Firstly, we divides the target domain into an easy-to-adapt and sard-to-adapt subdomains by fitting the loss distribution into Gaussian Mixture Model (GMM) and setting a threshold. The easy-to-adapt samples with less noise help purify the cross-domain knowledge distillation for DABP. Secondly, we propose mutually-distille progressively mitigate error accumulation. The distribution discrepancy between two subdomains is further aligned by an adversarial regularizer to enable the prediction consistency on the target domain. A domain adaptation theory is further derived to provide justifications for BETA.
twin networks with weak-strong augmentation on two subdomains to
We make the following contributions. (i) We propose novel BETA framework for the DABP problem that iteratively suppresses the error accumulation of model adaptation from the black- source- domain predictor. To the best of our knowledge, this is the first work that addresses the confirmation bias for DABP. (ii) We theoretically show that the error of the target domain is bounded by the noise ratio of the hard-to-adapt subdomain, and empirically show that this error can be suppressed progressively by BETA. (iii) Extensive experiments demonstrate that our proposed BETA achieves state-of-the-an performance consistently on all benchmarks. It outperforms the existing best method by 9.5% on the challenging VisDA-17 and 2.0% on DomainNet.
2 RELATED WORK
Unsupervised Domain Adaptation. Unsupervised domain adaptation aims to adapt a model from labeled source domain to unlabeled target domain. Early UDA methods rely on feature projection (Pan et al., 2010a) and sample selection (Sugiyama et al., 2007) for classic machine learning models. With the development of deep representation learning, deep domain adaptation methods yield surprising performances in challenging UDA scenarios. Inspired by two-sample test, discrepancy minimization of feature distributions (Koniusz et al., 2017: Yang et al., 202 Xu features (Cui et al., 2020a) based on statistic
et al.. 2022a) is proposed to learn moment matching (Tzeng et al., 2014; Sun & Saenko, 2016). Domain adversarial learning further employs domain discriminator to achieve the same goal (Ganin et al., 2016; Zou et al., 2019; Yang et al., 2020b) and achieves remarkable results. Other effective techniques for UDA include entropy minimization (Grandvalet & Bengio, 2005; Xu et al., 2021), contrastive learning (Kang et al., 2019), domain normalization (Wang et al., 2019; Chang et al., 2019). semantic alignment (Xie et al., 2018; Yang et al., 2021a), meta- meta-learning (Liu et al., 2020), self-suuprvision (Saito et al., 2020), semi-supervsed learning (Berthelot et al., 2021) curriculum learning (Zhang et al., 2017: Shu et al., 2019), intra-domain alignment (Pan et al., 2020), knowledge distillation (Yang al., 2020a) and
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self-training (Chen et al., 2020; Zou et al., 2018). Despite their effectiveness, they require access to the source domain data and therefore invoke privacy and portability concerns.
Unsupervised Model Adaptation and DABP. Without accessing the source domain, unsupervised model adaptation, i.e., source-free UDA, has attracted increasing attention since it loosens the assumption and benefits more practical scenarios (Guan & Liu, 2021). Early research provides theoretical analysis of hypothesis transfer learning (Kuzborskij & Orabona, 2013), which motivates the existence of deep domain adaptation without source data (Liang et al., 2020a; Huang et al., 2021; Li et al., 2020; Xu et al., 2022b). Liang et al. propose to train the feature extractor by self-supervised learning and mutual information maximization with the classifier frozen (Liang et al., 2020a). This paper deals with a more challenging problem: only leveraging the labels from the model trained in the source domain for model adaptation. Few works have been conducted in this field. (Zhang et al., 2021) proposes a noisy label learning method by sample selection, while (Liang et al., 2022) uses knowledge distillation with information maximization. Whereas, we propose to perform domain division and suppress confirmation bias for cross-domain knowledge distillation.
Confirmation Bias in Semi-Supervvsed Learning. Confirmation bias refers to the noise accumu- lation when the model is trained using incorrect predictions for semi-supervised or unsupervised learning (Tarvainen & Valpola, 2017). Such bias can cause the model to overfit the noisy feature space and then resist new changes (Arazo et al., 2020). In UDA, et al,, 2020; Morerio et al., 2020) and knowledge distillation (Liang et al., 2020a; Kundu et al., 2019; Zhou et al., 2020) are effective techniques but be degraded due to confirmation bias. Especially for the transfer task with a distant domain, the pscudo labels for the target domain are very noisy and deteriorate the subsequent epochs of training. To alleviate the confirmation bias, several solutions are proposed including co-training (Qiao et al., 2018; 8;; Li et al., 2019), Mixup (Zhang et al., 2018; Chen et al., 2019), and data- augmented unlabeled examples (Cubuk et al., 2019). Our paper proposes BETA which is the first work that formulates and addresses the confirmation bias for DABP.
(Saito et al., 2017: Gu
METHODOLOGY
The idea of our proposed BETA is to mitigate the confirmation bias for DABP by dividing the target domain into two subdomains with different adaptation difficulties. As shown in Figure 1, BETA relies on two designs to suppress error accumulation, including a domain division module that purifies the target domain into cleaner subdomain and transfers DABP to a semi-supervised learning task, and a two-networks mechanism (i.e., mnutuall-ddsttlll twin networks) that further diminishes the self- self-training errors by information exchange. We firstly introduce the problem formulation and the key modules, and then make the algorithmic instantiation with more details.
3.1 PROBLEM FORMULATION
For domain adaptation of black-box predictors, the model has access to a black-box predictor h trained by source domain {(x] yt N with N, labeled samples where x² E Xx, E Y.. and an unlabeled target domain {x[}< 1 with N₂ unlabeled samples where x² E Nr. Assume that the label spaces are the same across two domains, i.e,, Vd = Yr. while the inputs data have different distributions, i.e. x ~ Ds and x ~ Dr. In other words, there exists a domain shift (Ben-David et al., 2007) between Ds and Dr. The objective is to learn mapping model X, + Vd. Different from standard UDA (Pan et al., 2010b; Tzeng et al., 2014; Long et al., 2017), DABP prohibits the model from accessing the source-domain data X.. and the parameters of the source model hy Only a black-box predictor trained on the source domain, iee., an API, is available. Confront these constraints, we can only resort to the hard predictions of the target domain from the source predictor, i..., Dr (&,),, in the DABP setting.
3.2 DOMAIN DIVISION
Different from the strategy of directly utilizing X², 5i for knowledge distillation (Liang et al., 2022), propose divide the target domain X; into easy-to-adapt subdomain X ~ De and a hard- to-adapr subdomain X ~ Dn, with X, = X, U Xr. Previous studies show that deep models are prone to fitting clean examples faster than noisy examples (Arpit et al., 2017). In domain adaptation,
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DIvOll Adiipp
Source miputs
Romate Servar
CUDVIONNS
Mielp
Source
Loss
Mutualy-Disnied Twin
CNN
CNN
GMM
CNN
MSE
CNN
DA Loss
Torget Iiplts
Warm-up
DisAllationn
Domain Division
Semi- SuperSiped
Optimization
Learning
Figure 1: The mutually-distilles twin networks in BETA initialized by the predictions from the source API. Then the divide-to-adapt strategy is applied for domain division, and the two subdomains with augmentation are leveraged for semi-supervised learning (MSE and CE loss) and domain adaptation (DA Loss, i.e., Lade and L.i)).
the target domain consists of samples that have different similarities to the source-domant samples, and we find that deep models are prone fitting easy-to-adapt samples first that are more similar to the source domain. Based on the observation, we can obtain the two subdomains with different domain discrepancy by training loss. For example in Figure is seen that two peaks appear the loss distribution on the target domain data, and each peak corresponds to one subdomain. We further calculate the A-distance (Ben-David domain, and the result shows that De has less domain discrepancy than Dr. This can be observed more intuitive by the subdomain samples in the appendix.
al., 2010) (da) between the two subdomains and the source
Inspired by this observation, we first warm up the network, e.g., CNN, for several epochs, and then obtain the loss distribution by calcu- lating the per-sample cross-entropy loss for a K K-way classification problem as
140
Sourte
Source
120-
demsi:
Target
100
Cen (xx) =
K
3 (x+)), (I)
@Sunples
80-
Subiomenn 4,00, (.),,,))= 1 1.74
Easy to adopt
60
Subdimein
where hy is the softmax probability for class k from the target model. As shown in Figure 1, the loss distribution appears to be bimodal and two peaks indicate the clean and noisy clusters,
d (gg. 1.88
20-
0.0
which be fitted by GMM using Expec- tation Maximization (EM) (Li et al., 2019). Figure 2: The loss distribution on A- (Office-31). In noisy label learning, the clean and noisy subset division is achieved by a Beta Mixture Model (BMM) (Arazo al., 2019). However, in DABP, the noisy pseudo labels obtained by h, are dominated by asymmetric noise (Kim et al., 2021), i.e., the noisy samples that do not follow uniform distribution. In this case, the BMM leads to undesirable flat distributions and cannot work effectively for our task (Song al., 2022). Asymmetric noise in 3%2 also causes the model to perform confidently and generate near-zero losses, which hinders the domain division of GMM. To better fit the losses of the target domain with asymmetric noise, the negative entropy is used as a regularizer in the warm-up phase, defined as:
Losss
K
Lue
Σ
h log() (x))).
After fitting the loss distribution two-component GMM via the Expectation-Maxinii Maximization algorithm, the clean probability ef is equivalent to the posterior probability pxc))(xx)) where c is the Gaussian component with smaller loss and (xx))) is the cross-entropy loss of x(. Then the clean and
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noisy subdomains are divided by setting threshold based on the clean probabilities:
A = {(x,, (xx),)))( Ds) E (X2, Jih), of 27)
(3)
A₂ ((x, x; E X,, of < <):
where p; = hb (x{) is the softmax probabilities. Intuitively, the clean subdomain consists of easy-to- adapt samples, while the noisy subdomain consists of hard-to-adapp samples. The semi-supervised learning methods (Berthelot et al., 2019) can be directly applied with X₂ used as the labeled set and Nr as the unlabeled set. Compared to sample selection (Zhang et al., 2021) and single distillation (Liang et al., 2022), domain division enables the utilization of all accessible samples by semi-supervised learning and dilutes the risk of the confirmation bias by leveraging cleaner signals of supervision for model adaptation.
3.3 MUTUALLY-DISTIEE
TWIN NETWORKS WITH SUBDOMAIN AUGMENTATION
The easy-to-adapt subdomain is purified by domain division but still has inevitable wrong labels. Overfitting to these wrong labels enforces the model to generate fallacious low losses for domain division, and hence accumulates the wrong predictions iteratively, which is the confirmation bias. Apart from domain division, we propose Mutually-distinn distilled Twin Networks (MTN) to further mitigate such bias, inspired by the two-networks design in (Qiao et al., 2018; Li et al., 2019) where the confirmation bias of self-training can be diminished by training two networks to decontaminate the noise for each other. Specifically, we employ two identical networks initialized independently, where one network performs semi-supervised learning according to the domain division and pseudo labels of the other network. In this fashion, two networks are trained mutually and receive extra supervision to filter the error.
In BETA, further revamp this design by subdomain augmentation to increase the divergence of domain division, enabling two networks to obtain sufficiently different supervisions from each other. Suppose that two networks h; ., where 01, 02 are parameters generate two sets of domain respectively. We take 1, and (A?) , X² for example. Two augmentation strategies tailored: the weak augmentation (e.g., random cropping and flipping), and the strong augmentation (i.e., RandAugment (Cubuk et al., 2020) and AutoAugment (Cubuk al., 2019). The samples from the easy-to-adapt subdomain are mostly correct, so we augment them using two strategies and obtain their soft pseudo labels by the convex combination of averaging all augmentations and the pseudo label according to the clean probability oi Whereas, the hard-to-adapp subdomain is noisy, we only apply the weak augmentation to update their pseudo labels but use strong augmentations in the subsequent learning phase. Furthermore, we employ the co-guessing strategy (Li et al., 2019) refine the pseudo labels for Xr. The refined subdomains are derived as:
division (X) x and
M
P = [xx,, 1711%% = e. + (1 09)
Σ 178
[h (A (x,, 31) E x
(5)
M
2M
82 = ((x, Pole
1
Σ
1h
(ATH (x:)) + (44) xx)
(6)
2M
m=1
where (-) denotes the m-th weak and strong augmentation function, and M denotes the total number augmentation views.
3.4 ALGORITHMIC INSTANTIATION
After the warm-up, domain division, and subdomain augmentation, detail the algorithmic choices of other modules and the learning objectives of our framework.
Hard knowledge distillation. For each epoch, first perform knowledge distillation from the predictions of the source model h2 by the relative entropy, iee. the
divergence
Ltd Ex,Ex, D (x:)).
where (=z(- denotes the Ki-diverg, and the pseudo label ÿ, is obtained by the EMA prediction of h2 (x,). Different from DINE (Liang et al., 2022) that uses source model probabilities, only leverage the hard pseudo labels that are more ubiquitous for API services.
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Mutual information maximization. To circumvent the model to show partiality for categories with more samples during knowledge distillation, we maximize the mutual information as
Lmi H(Zzex, h4 (x)) Ex (1)))))),
(8)
where (.) denotes the information entropy. This loss works jointly with Lid- Besides, after the semi- cemi-supervised learning, we use this loss to fine-tune the model to enforce the model to comply with the cluster assumption (Shu et al., 2018; Liang al., 2022; Grandvalet Bengio, 2005).
Domain division enabled semi-supervised learning, We choose Mix.atth (Berthelot et al., 2019) as the semi- suniiiuueeeieedd learning method since includes a mix-up procedure (Zhang et al., 2018) that can further diverge the two networks while refraining from overfitring. The mixed sets Xe Ar are obtained by Xe = Mixup(&e (ee, &e U Rn) and Li. = Mixup( (R,, & U Kr). Then the loss functions is written
Lad = Lrce (X.) + Lumse (Ai,) + freg: where Lee denotes the cross-entropy loss, Lmae denotes the mean squared error, and the regularizer Creg uses uniform distribution to eliminate the effect of class imbalance, written
Eveg Σ Te log
TTk
Σ
lr(x))
(10)
XE
Subdomain alignment. We assume that there exists distribution discrepancy between the easy- to-adapt and the hard-to-adapt subdomains, which leading the performance gap between them. Regarding this gap, we add an adversarial regularizer by introducing a domain discriminator I?(-):
Ladv ExEx, log (2))) + x log (1 (x))
(11)
Overall objectives. Summarizing all the losses, the overall objectives are formulated as
(Ckd Lms) + (Ldd - -adv))
(12)
step1
step2
where y syper-parameter that empirically set 0.1. step 1, we perform distillation for two networks independently to form tight clusters by maximizing mutual information, while in step 2, the proposed BETA revises their predictions by mitigating the confirmation bias in a synergistic manner. The domain division is performed between two steps.
3.5 THEORETICAL JUSTIFICATIONS
Existing theories on UDA eтror bound (Ben-David et al., 2007) are based on the source-domain data, so they are not applicable DABP models (Liang et al., 2022), which hinders understanding of these models. To better explain why BETA contributes to DABP, we derive an error bound based on the existing UDA theories (Ben-David et al., 2010). Let h denote a hypothesis, Ye. Yh and ge. Un denote the ground truth labels and the pseudo labels of Xe. Xr, respectively. As BETA is trained on mixture the two subdomains with pseudo labels, the error of BETA can be formulated as a convex combination of the errors of the aasy-to-adapt subdomain and the hard-to-adan adapt subdomain:
Ea (h) = ae (h, Ue) (1 ox) (h, 0n),
(13)
where a is the trade-off hyper-parameter and e. (h, ÿe), (h, 9n. represents the expected error of the two subdomains. We derive upper bound of how the error e., (h) is close an oracle error of the target domain (h, yr) where is the ground truth labels of the target domain.
Theorem
Let h be a hypothesis in class H. Then
(ea(h) - (h, v1)1 S alduan(Pe DA) + + Ph.
(14)
where the ideal risk is the combined error of the ideal joint hypothesis X = (tt)) ) + en (h*),, the WRDDD [h(x)) + M)(x)] ENNDD (h(x) # hd (x(2)),, and ph denotes the pseudo label rate of Uh- The ideal joint hypothesis is given by h² arg minnee((E. + en(h)), deriving the ideal risk X (h²) + en (Ie)) and the pseudo risk (h" (e) en (h", (6))
distribution discrepancy dHAHH(De. Dn) = 2uup

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Table I: Accuracies (%) Office-31 for black-box model adaptation. H. Avg. accuracy of the hard tasks whose source-only accuracies are below 65%.
denotes the average
Method
Publication
A-D
D-*A
W
W-+A
Avg.
Avg.
ResNet-50
79.9
76.6
56.4
92.8
60.9
98.5
77.5
58.7
LNL-OT
ICLR-19
66.7
83.2
LNL-KL
83.6
HD-SHOT
TPAMI-21
83.1
66.1
95.1
68.9
98.1
83.0
67.5
SD-SHOT
IPAMI-21
89.2
83.7
67.9
95.3
71.1
97.1
84.1
69.5
DINE
CVPR-22
91.6
86.8
72.2
96.2
73.3
98.6
86.4
72.8
BETA (Ours)
93.6
88.3
76.1
95.5
76.5
99.0
88.2
76.3
RSP+DANN
ICMI.119
98.2
72.6
88.5
MDD
JCML-19
93.5
94.5
74.6
98.4
72.2
100.0
88.9
73.4
ATDOC
CVPR-21
94.4
94.3
75.6
98.9
75.2
99.6
89.7
75.4
Table 2: Accuracies (%) on Office-Home for black-box model adaptation. (t' denotes 'transfer to')
Mothod
DABP
Ar:C
ArDr
Ar:Ro
Cl:Ar
CLiPr
Cl:R
Pr:Ar
Pr:l
PriRe
Re:Ar
Re:CI
Re:Pt
Avg.
Il Avg.
INL-OT
49.1
71.7
77.3
60.2
68.7
73.1
57.0
46.5
76.8
67.1
52.3
79.5
64.9
55.6
LNL-KI.
49.0
71.5
77.1
59.0
68.7
72.9
564
46.9
76.6
66.2
52.3
79.1
64.6
55.4
HD-SHOT
77.0
SD-SHOT
50.1
75.0
78.8
63.2
72.9
76.4
60.0
48.0
79.4
69.2
54.2
81.6
67.4
58.1
DivideMix
51.7
74.7
78.5
61.8
72.4
73.3
59.8
48.0
82.9
68.0
56.4
81.6
67.4
58.4
BETA (Ours)
V
57.2
78.5
82,1
68.0
78.6
79.7
67.5
$6.0
83.0
71.9
58.9
84.2
72.1
64.4
BSPICDAN
X
$2.0
68.6
76.1
58.0
70.3
70.2
58.6
50.2
77.6
72.2
59.3
81.9
66.3
58.1
MDD
54.9
73.7
77.8
60.0
71.4
71.8
61.2
53.6
78.1
72.5
60.2
82.3
68.1
60.2
In the above theorem, the error is bounded by the distribution discrepancy between two subdomains, the noise ratio of Xn, and the risks. The ideal risk À neglectly small (Ganin et al., 2016), and the pseudo risk À is bounded by Ph shown in the appendix. Hence, the subdomain discrepancy and Ph dominate the error bound. Empirical results show that dHaH (De, Dx) is usually small for the two subdomains, and Ph keeps dropping during training as shown in Figure 3(a), which tightens the upper bound consequently. The proof with detailed analytics is in the appendix.
4 EXPERIMENTS
4.1 SETUP
Datasets. Office-31 (Saenko et al., 2010) is the most common benchmark for UDA, which consists of three domains (Amazon, Webcam, DSLR) in 31 categories. Office-Home (Venkateswara et al., 2017) consists of four domains (Art, Clipart, Product, Real World) in 65 categories, and the distant domain shifts render it more challenging. VisDA-17 (Peng et al., 2017) (017)im is a large-scale benchmark for synthetic-to-real object recognition, with source domain with 152k synthetic images and target domain with 55k real images from Microsoft COCO. DomainNet (Peng et al., 2019) is the largest DA dataset containing 345 classes in 6 domains: Clipart (clp), Infograph (inf), Painting (pnt), Quickdraw (qdr), Real (rel), Sketch (skt).
Implementation details. We implement our method via PyTorce (Paszke et al., 2019), and report the average accuracies among three runs. To show the capacity of handling the confirmation bias, we further report the average accuracies across hard tasks whose source-only accuracies are below 65% (H. Avg.). We employ ResNet-50 for Office-31, Office- for VisDA-17 as the backbones (He et al., 2016), and add a new MLP-based classifier, which is commonly used in existing UDA works (Long et al., 2017: Chen et al., 2019; Liang et al., 2022; Saito et al., 2018). The domain discriminator consists of fully-connected layers (2048-22) 256-2) that perform binary subdomain classification (Long et al., 2018). The ImageNet pre-trained model is utilized as initialization. The model is optimized by for CNN layers and 1e-2 for the ML.P classifier. Following DINE (Liang et al., 2022), the
and DomainNet, and ResNet-101
SGD with the learning rate le-3
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Table 3: Accuracies (%) on VisDA-17 for black-box model adaptation.
Method
DABP
plane
beyel
hus
knife
meycle
plant
sichrid
Imin
track
Per-class
Avg.
ResNet1001
61.3
24.6
17.9
75.3
69.5
8.5
79.0
31.6
61.1
31,0
81.4
9.2
48.9
35.2
LNL-OT
76.7
$2.6
81.2
82.7
72.0
LNL-KL
82.7
83.4
76.7
44.9
90.9
38.5
78.4
71.6
82.4
80.3
82.9
50.4
71,9
70.8
HD-SHOT
75.8
85.8
78.0
43.1
92.0
41.0
79.9
78.1
84.2
86.4
81.0
65.5
74.2
74.4
SD-SHOT
79.1
85.8
77.2
43.4
91.4
41.0
80.0
78.3
N4.7
86.8
81.1
65.1
74.5
74,8
DINE
81.4
86.7
77.9
55.1
92.2
80.8
79.9
87.3
87.9
84.3
58.7
75.6
85.1
SAPN
X
93.6
61.3
84.1
70.6
94.1
91.8
79.6
89.9
55.6
89.0
24.4
76.1
70.9
CDAN4E
94.3
60.8
79.9
72.7
89.5
86.8
92.4
81.4
88.9
72.9
87.6
32.8
78.3
74.7
DTA
93.7
82.2
85.6
83.8
93.0
81.0
90.7
82.1
95.1
78.1
86.4
32.1
81.5
78.7
Table 4: Accuracies (%) DomainNet for black-box model adaptation. The indicates the source domain while the column indicates the target domain.
dp
prt
9fr
Avg.
cpp
per
q
Ang.
q+
Avg
15.5
36.0
10.1
52.8
418
31.4
12.1
29.6
11.1
90.4
$7.3
20.4
13,4
41.2
13.0
61.8
41.1
34,1
32.1
32.0
2.7
47.4
36.4
28.1
inf
29.5
37.6
3.4
53.5
26.5
30.1
34.9
41.6
3.7
56.5
30.7
33.6
79.6
23.2
4.8
16.7
27.8
76.4
pm
92.5
124
4.3
00.3
54.7
29.9
pm
47.3
18.4
322
62.5
41.9
54.7
<dr
11.2
1.1
1.9
4.3
7.7
53
9dr
9.4
0.7
3
5.3
5.6
1.6
ods
11.7
0.9
2.1
9.1
8.1
6.4
196
11.1
46.2
51.1
11.5
31.3
35.3
Avg.
suggested training strategies including the momentum (0.9), batch size (64), and weight decay (1e-3). The number of epochs for warm-up is empirically set to 3, and the training epoch 50 except 10 for VisDA-17. The hyper-parameted of MixMatch are kept as same as the original paper (Berthelot al., 2019), attached in the appendix. As networks of MTN perform similarly, we report the accuracy of the first network.
Baselines. For fair comparison, we follow the protocol and training strategy for the source domain in DINE (Liang et al., 2022), and compare our BETA with state-of-the-an DABP methods. Specifically, LNL-KL (Zhang et al., 2021). LNL-OT (Asano al., 2019), and DivideMix (Li et al., 2019) are noisy label learning methods. HD-SHOT and SD-SHOT obtain the model using pseudo labels and apply SHOT (Liang et al., 2020a) by self-training and the weighted cross-entropy loss, respectively. We also show state-of-the-art standard UDA methods for comparison, including CDAN (Long et al., 2018), MDD (Zhang et al., 2019), BSP (Chen et al., 2019), CST (Liu et al., 2021), SAFN (Xu et al., 2019), DTA (Lee al., 2019), ATDOC (Liang al., 2021), MCC (Jin et al., 2020). BAA (Liang ct al., 2020b) and JUMBOT (Fatras et al., 2021).
4.2 RESULTS
Performance comparison. We show the results Office-31, Office-Home, VisDA-17, and Domain- Net in Table 1, 3, and 4 respectively. The proposed BETA achieves the best performances on all benchmarks. On average, and 2.0% on Office-31, Office-Home, VisDA-17, and DomainNet, respectively. The improvement is marginal for Office-31 as it is quite simple. Whereas, for the challenging VisDA-17, the BETA gains a huge improvement of 9.5%, even outperforming standard UDA methods, e.g., CDAN, BSP, SAFN, MDD. This demonstrates that the suppression of confirmation bias by BETA can be effective as the domain alignment techniques.
method outperforms the state-of-the-art methods by 1.8%, 2.4%, 9.5%,
Hard transfer tasks with distant domain shift. Since our method effectively mitigates the confir- mation bias, it works more effectively for the hard tasks with extremely noisy pseudo labels from the source-only model. For the hard tasks with lower than 65% source-only accuracy (i.e. Avg.), observed that the BETA outperforms the second-best method by 3.5%, 4.0%, and 1 11.6% on Office-31, Office-Home, and VisDA- 17, respectively, which beats the normal UDA methods. For DomainNet, the source-only model produces less than 50% accuracy for all of the transfer tasks, which leads to negative transfer for DINE, e.g., qdr qdr-sskt. Whereas, BETA achieves robust improvement for most tasks, outperforming DINE by 2.0% in average. This demonstrates that method can deal with transfer tasks with distant shifts and BETA can alleviate the negative effect of error accumulation caused by source-only models with poor performance.
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Table 5: Ablation studies of learning objectives and MTN on Office-Home.
Diaa
Cka
Dis
Lade
MTN
Ar-+II
Cl-+Ar
CI-Pr
Pr-tAr
Pr-+CI
Re-+CI
H. Avg.
44.1
41.2
50.4
55.5
65.4
76.5
64.4
50.7
38.1
61.8
54.6
63.8
75.3
62.3
48.0
55.7
60.0
56.6
65.0
76.7
64.1
51.6
60.4
62.4
55.4
67.6
78.4
54.5
58.5
63.3
56.8
68.1
78.7
67.3
55.3
59.2
64.2
57.2
68.0
78.6
67,5
56.0
58.9
64.4
80.0
Classiication Error Rate (56)
100
Hard-to-adapt subdomain Pr: (K.D.)
Hard- coard-to-adee to-app subdemain (Ouss
79.5
Easy-to-adapt subdomain (K.
90.0
Accuracy (%6
19.0
Easy adapt subdomain (Ours)
(16)
78.5
89.5
60
78.0
MTN Network-1
MIN Network-2
77.5
between A
88.5
0
10
20
30
40
50
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Epoch
Domain Division Threshold
(a) Confirmation bias
(b) Studies on and MTNs.
Figure 3: Quantitative results the estimated confirmation bias, and hyper-parameter sensitivity.
4.3 ANALYSIS
Ablation study. We study the effectiveness of key components in BETA, with results shown in Table It is seen that the semi superviee loss enabled by domain division significantly improves the source-only model by 11.4%. The mutual twin networks, knowledge distillation, and mutual information contribute to 0.6%, 1.1% %, and 0.9% improvements, respectively. As the two subdomains drawn from the target domain quite similar, the distribution discrepancy
always effective.
Confirmation bias. We study the confirmation bias using the noise ratio of the two subdomains in terms of knowledge distillation (K.D.) and BETA on Office-Home (Ar+CI) show the effectiveness of the domain division and MTN. As shown in Figure 3(a), the error rate of K.D. only drops for the first a few epochs and then stops decreasing. Whereas, the error rate of BETA keeps decreasing for about 20 epochs since the confirmation bias is iteratively suppressed. The error gap between K.D. and ours on the hard-to-adapt and easy-to-adapt subdomain reaches around 10% and 3%, respectively, validating that our method reduces the етгоr rate Ph. and minimizes the target error in Theorem 1.
hyyee-paraaeter sensitivity and MTN. We study the syper-parameter on Office-Home (CI++r)) across three runs. We choose 7 ranging from 0.3 to 0.9, as too small 7 leads to noisy domain division while very large т leads to a very small number of samples at the easy-to-adapt subdomain. As shown in Figure 3(b), the accuracies of BETA range from 78.2% to 78.8%, and the best result achieved at 0.8. For the MTN module, is observed that the two networks of BETA achieve similar trends over different and one network slightly outperforms another consistently. We further plot the Intersection over Union (IoU) between two easy-to-adapt clean subdomains X X? gets greater, which means that larger т leads
generated by domain division, and it decreases to more difference of the domain division. The diverged domain division can better mitigate the error accumulation for MTN. Thus, the best result divergence of two domain divisions and the sample number of the easy-to-adapt clean subdomain.
0.8 is reasonable trade-off between the
5 CONCLUSION
In this work, we propose to suppress confirmation bias for DABP. This is achieved by domain division that purifies the noisy labels in cross-domain knowledge distillation. We further develop mutually-distille twin networks with subdomain augmentation and aligument to mitigate the error accumulation. Besides, we derive theorem show why mitigating confirmation bias helps DABP. Extensive experiments over different backbones and learning setups show that BETA effectively suppresses the noise accumulation and achieves state-of-the-art performance all benchmarks.

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Acknowledgements. This work is supported by NTU Presidential Postdoctoral Fellowship, "Adap- tive Multimodal Learning for Robust Sensing and Recognition in Smart Cities" project fund, at Nanyang Technological University, Singapore. This research is jointly supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD- 2021-08 1-08-008). We thank Google TFRC for supporting us get access the Cloud TPUs. This work is jointly supported NUS startup grant, the Singapore MOE Tier-l grant, and the ByteDance grant.
REFERENCES
Eric Arazo, Diego Ortego, Paul Albert, Noel Connor, and Kevin McGuinness. Unsupervised label noise modeling and loss correction. In International conference on machine learning, pp. 312-321.
PMLR, 2019.
Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. Pseudo-labeling and confirmation bias in deep semi-supervised learning. In 2020 International Joint Conference on Neural Networks (IJCNN), pp. 1-8. IEEE, 2020.
Devansh Arpit. Stanislaw Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder Kanwal, Tegan Maharaj. Asja Fischer, Aaron Courville, Yoshua Bengio, et al. A closer look at memorization in deep networks. In International conference on machine learning, pp. 233 232. PMLR, 2017.
Yuki Markus Asano, Christian Rupprecht, and Andrea Vedaldi. Self-labelling via simultaneous clustering and representation learning. 2019.
Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of representations for domain adaptation. In Advances in Neural Information Processing Systems, pp. 137-144, 2007.
Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jennifer Wortman Vaughan. A theory of learning from different domains. Machine learning, 79(1-2): 2010.
David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raf- fel. Mixmatch: A holistic approach to semi-supervised learning. Advances in Neural Information Processing Systems, 32, 2019.
David Berthelot, Rehecca Roelofs, Kihyuk Sohn, Nicholas Carlini, and Alexey Kurakin. Adamatch: A unified approach to semi-supervised learning and domain adaptation. In International Conference on Learning Representations, 2021.
Woong-Gi Gi Chang, Tackgeun You, Seonguk Seo, Suha Kwak, and Bohyung Han. Domain-speciie batch normalization for unsupervised domain adaptation. In Proceedings of the IEEF/CVF conference on Computer Vision and Pattern Recognition, pp. 7354-7362, 2019.
Xinyang Chen, Sinan Wang, Mingsheng Long, and Jianmin Wang. Transferability vs. discriminability: Batch spectral penalization for adversarial domain adaptation. In International Conference on Machine Learning, pp. 1081-1090 2019.
Yining Chen, Colin Wei, Ananya Kumar, and Tengyu Ma. Self-training avoids using spurious features under domain shift. Advances in Neural Information Processing Systems, 33:210611-200 2020.
Koby Crammer, Michael Kearns, and Jennifer Wortman. Learning from multiple sources. Journal of Machine Learning Research, 98),, 2008
Ekin D Cubuk, Barret Zoph, Dandelion Mane, Vijay Vasudevan, and Quoe V Le. Autoaugment: Learning augmentation strategies from data. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 113-123, 2019.
Ekin Cubuk, Barret Zoph, Jonathon Shlens, and Quoe Le. Randaugment: Practical automated data augmentation with reduced search space. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition Workshops, pp. 702-703, 2020.
Shuhao Cui, Xuan Jin, Shuhui Wang, Yuan He, and Qingming Huang. Heuristic domain adaptation. Advances in Neural Information Processing Systems, 33:7571-7583, 2020a.
10

---

Published as a conference paper at ICLR 2023
Shuhao Cui, Shuhui Wang, Junbao Zhuo, Chi Su, Qingming Huang, and Qi Tian. Gradually vanishing bridge for adversarial domain adaptation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 12455-12464, 12464, 2020b.
Kilian Fatras, Thibault Séjourné, Rémi Flamary, and Nicolas Courty, Unbalanced minibatch optimal transport; applications to domain adaptation. In International Conference on Machine Learning, pp. 3197-3197. PMLR, 2021.
Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, François Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adversarial training of neural networks. The Journal of Machine Learning Research, 17(1):2096- 2030, 2016.
Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In Advances in neural information processing systems, pp. 529-536, 2005.
Xiang Gu, Jian Sun, and Zongben Xu. Spherical space domain adaptation with robust pseudo-label loss. In Proceedings of the IEEE/CVE Conference on Computer Vision and Pattern Recognition, pp. 9101-9110, 2020.
Hao Guan and Mingxia Liu. Domain adaptation for medical image analysis: a survey. IEEE Transactions Biomedical Engineering, 2021.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770-778, 2016.
Geoffrey Hinton, Oriol Vinyals, Jeff Dean, al. Distilling the knowledge in neural network. arXiv preprint 1503:0550330533/ 2(7), 2015.
Judy Hoffmman, Eric Tzeng, Taesung Park, Jun- Zhu, Phillip Isola, Kate Saenko, Alexci Efros, and Trevor Darrell. Cycada: Cycle-consistent adversarial domain adaptation. In International conference on machine learning, pp. 1989-1998. PMLR, 2018.
Jiaxing Huang, Dayan Guan, Aoran Xiao, and Shijian Lu. Model adaptation: Historical contrastive learning for unsupervised domain adaptation without source data, Advances in Neural Information Processing Systems, 34, 2021.
Ying Jin, Ximei Wang, Mingsheng Long, and Jianmin Wang. Minimum class confusion for versatile domain adaptation. In European Conference on Computer Vision, pp. 464-480. Springer, 2020.
Guoliang Kang, Lu Jiang, Yi Yang, and Alexander G Hauptmann. Contrastive adaptation network for unsupervised domain adaptation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4893-4902, 2019.
Tachyeon Kim, Jongwoo Ko, JinHwan Choi, Se- Young Yun, et al. Fine samples for learning with noisy labels. Advances in Neural Information Processing Systems, 34, 2021.
Piotr Koniusz, Yusuf Tas, and Fatih Porikli. Domain adaptation by mixture of alignments of second-or higher-order scatter tensors. In Proceedings of the IEEE conference computer vision and pattern recognition, pp. 1478-4487 2017.
Jogendra Nath Kundu, Nishank Lakkakula, and R Venkatesh Babu. Um-adapt: Unsupervised multi-task adaptation using adversarial cross-task distillation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 1436-1445, 2019.
Ilja Kuzborskij and Francesco Orabona. Stability and hypothesis transfer learning. In International Conference on Machine Learning, pp. 942-9500 PMLR, 2013.
Seungmin Lee, Dongwan Kim, Namil Kim, and Goyng Jeong. Drop to adapt: Learning discriminative features for unsupervised domain adaptation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 91-100, 2019.
Junnan Li, Richard Socher, and Steven CH Hoi. Dividemix: Learning with noisy labels as semi- supervised learning. In International Conference on Learning Representations, 2019.

---

Published as a conference paper at ICLR 2023
Rui Li, Qianfen Jiao, Wenming Cao, Hau-San Wong, and Si Wu. Model adaptation: Unsupervised domain adaptation without source data. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9641-9650, 2020.
Jian Liang, Dapeng Hu, and Jiashi Feng. Do really need access the source data? source hypothesis transfer for unsupervised domain adaptation. In International Conference on Machine PMLR, 2020a.
Learning, pp.
Jian Liang, Yunbo Wang. Dapeng Hu, Ran He, and Jiashi Feng. A balanced and uncertainty-awan approach for partial domain adaptation. In European Conference on Computer Vision, pp. 123-140 Springer, 2020b.
Jian Liang, Dapeng Hu, and Jiashi Feng. Domain adaptation with auxiliary target domain-oriented classifier. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recogni- tion, pp. (6632-16642) 2021.
Jian Liang. Dapeng Hu, Jiashi Feng, and Ran He. Dine: Domain adaptation from single and multiple black-box predictors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022.
Hong Liu, Mingsheng Long, Jianmin Wang, and Yu Wang. Learning to adapt to evolving domains. Advances in Neural Information Processing Systems, 33:22338 33:22338-22348, 2020.
Hong Liu, Jianmin Wang, and Mingsheng Long. Cycle self-training for domain adaptation. Advances in Neural Information Processing Systems, 34, 2021.
Mingsheng Long, Han Zhu, Jianmin Wang, and Michael Jordan. Deep transfer learning with joint adaptation networks. In International Conference on Machine Learning (ICML), 2017.
Mingsheng Long, Zhangjie Cao, Jianmin Wang, and Michael I Jordan. Conditional adversarial domain adaptation. In Advances in Neural Information Processing Systems, 2018.
Pietro Morerio, Riccardo Volpi, Ruggero Ragonesi, and Vittorio Murino. Generative pseudo-label re-
finement for unsupervised domain adaptation. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp. 3130-3139, 2020.
Fei Pan, Inkyu Shin, Francois Rameau, Scokju Lee, and In So Kweon. Unsupervised intra-domant adaptation for semantic segmentation through self-supervision. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3764-3773, 2020.
Sinno Jialin Pan and Qiang Yang. A survey on transfer learning. IEEE Transactions on knowledge and data engineering. 13400):335 2009.
Sinno Jialin Pan, Ivor W Tsang, James T Kwok, and Qiang Yang. Domain adaptation via transfer component analysis. JEEE transactions on neural networks, 22(2): 2010a.
Sinno Jialin Pan, Qiang Yang, et al. A survey transfer learning, IEEE Transactions knowledge and data engineering, 22(10): 13455-333,,,,, 2010b.
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, nigh-performance deep learning library. Advances in neural information processing systems, 32, 2019.
Xingchao Peng, Ben Usman, Neela Kaushik, Judy Hoffmann Dequan Wang, and Kate Saenko. Visda: The visual domain adaptation challenge. arXiv preprint arXiv:1710.0600 2017.
Xingchao Peng, Qinxun Bai, Xide Xia, Zijun Huang, Kate Saenko, and Bo Wang. Moment matching for multi-source domain adaptation. Proceedings of the IEEE International Conference on Computer Vision, pp. 1406-1415, 2019.
Siyuan Qiao, Wei Shen, Zhishuai Zhang, Bo Wang, and Alan Yuille. Deep co-training for semi- supervised image recognition. In Proceedings of the european conference on computer vision (eccr), pp. 135-152, 2018
12

---

Published as a conference paper at ICLR 2023
Kate Saenko, Brian Kulis, Mario Fritz, and Trevor Darrell. Adapting visual category models to new domains. In European conference on computer vision, pp. 2112211-222 Springer, 2010.
Kuniaki Saito, Yoshitaka Ushiku, and Tatsuya Harada. Asymmetric tri-training for unsupervised domain adaptation. In International Conference on Machine Learning, pp. 2017.
PMLR,
Kuniaki Saito, Kohei Watanabe, Yoshitaka Ushiku, and Tatsuya Harada. Maximum classifier discrepancy for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3723-3732, 2018.
Kuniaki Saito, Donghyun Kim, Stan Sclaroff, and Kate Saenko. Universal domain adaptation through self supervision. Advances in neural information processing systems, 33: 13:16282-16292, 2020.
Inkyu Shin, Sanghyun Woo, Fei Pan, and In So Kweon. Two-phase pseudo label densification for self-training based domain adaptation. In European conference on computer vision, pp. 532-548. Springer, 2020.
Rui Shu, Hung H Bui, Hirokazu Narui, and Stefano Ermon. A dirt-t approach to unsupervised domain adaptation. In Proc. 6th International Conference on Learning Representations, 2018.
Yang Shu, Zhangjie Cao, Mingsheng Long, and Jianmin Wang. Transferable currieulum for weakly- supervised domain adaptation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pp. 4951-4958, 2019.
Kihyuk Sohn, David Berthelot, Nicholas Carlini, Zizhao Zhang, Han Zhang, Colin A Raffel, Ekin Do- gus Cubuk, Alexey Kurakin, and Chun-Liang Li. Fixmatch: Simplifying cemi-supervised learning with consistency and confidence. Advances in Neural Information Processing Systems, 33:596-608, 2020.
Hwanjun Song, Minscok Kim, Dongmin Park, Yooju Shin, and Jae-Gil Lee. Learning from noisy labels with deep neural networks: A survey. IEEE Transactions Neural Networks and Learning Systems, 2022.
Masashi Sugiyama, Shinichi Nakajima, Hisashi Kashima, Paul Buenau, and Motoaki Kawanabe. Direct importance estimation with model selection and its application to covariate shift adaptation. Advances in neural information processing systems, 20, 2007.
Baochen Sun and Kate Saenko. Deep coral: Correlation alignment for deep domain adaptation. In European Conference on Computer Vision, pp. 443-450. Springer, 2016.
Antti Tarvainen and Harri Valpola. Mean teachers are better role models: Weight- consistency targets improve semi- supervupe deep learning results. Advances in neural information processing systems, 30, 2017.
Eric Tzeng, Judy Hoffman, Ning Zhang, Kate Saenko, and Trevor Darrell. Deep domain confusion: Maximizing for domain invariance. CoRR, abs/1412.3474, 2014. URL @bs/1411 3474.
org/
Eric Tzeng, Judy Hoffman, Trevor Darrell, and Kate Saenko. Simultaneous deep transfer across domains and tasks. In Proceedings of the IEEE International Conference Computer Vision, pp- 4068-4076, 2015.
Hemanth Venkateswara, Jose Fusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In Proc. CVPR, pp. 5018-5027, 2017.
Ximei Wang, Ying Jin, Mingsheng Long, Jianmin Wang, and Michael I Jordan. Transferable normalization: Towards improving transferability of deep neural networks. Advances in neural information processing systems, 32, 2019.
Shaoan Xie, Zibin Zheng, Liang Chen, and Chuan Chen. Learning semantic representations for unsupervised domain adaptation. In International conference on machine learning, pp. 5423-5432. PMLR, 2018.
13

---

Published as a conference paper at ICLR 2023
Ruijia Xu, Guanbin Li, Jihan Yang, and Liang Lin. Larger norm transferable: An adaptive feature norm approach for unsupervised domain adaptation. In Proceedings of the IEEE/CVF International Conference Computer Vision, pp. 1426-1435, 2019.
Yuecong Xu, Jianfei Yang, Haozhi Cao, Zhenghua Chen, Qi Li, and Kezhi Mao. Partial video domain adaptation with partial adversarial temporal attentive network. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 9332-933222 -2219341, 2021.
Yuecong Xu, Haozhi Cao, Kezhi Mao, Zhenghua Chen, Lihua Xie, and Jianfei Yang. Aligning correlation information for domain adaptation in action recognition. IEEE Transactions on Neural Networks and Learming Systems, 2022a.
Yuecong Xu, Jianfei Yang, Haozhi Cao, Keyu Wu, Min Wu, and Zhenghua Chen. Source-free video domain adaptation by learning temporal consistency for action recognition. In Computer Vision- ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXXIV, pp. 147-164. Springer, 2022b.
Jianfei Yang, Han Zou, Shuxin Cao. Zhenghua Chen, and Lihua Xie. Mobileda: Toward edge-domain adaptation. IEEE Internet of Things Journal, 7(8):6909-699) 2020a. doi: 10.1 10.1109//101:2020. 2976762.
Jianfei Yang, Han Zou, Yuxun Zhou, Zhaoyang Zeng, and Lihua Xic. Mind the discriminability: Asymmetric adversarial domain adaptation. In European Conference on Computer Vision, pp- 589-606. Springer, 2020b.
Jianfei Yang, Jiangang Yang. Shizheng Wang, Shuxin Cao, Han Zou, and Lihua Xie. Advancing imbalanced domain adaptation: Cluster-level discrepancy minimization with a comprehensive benchmark. IEEE Transactions on Cybermetics, 2021a.
Jianfei Yang, Han Zou, Yuxun Zhou, and Lihua Xie. Robust adversarial discriminative domain adaptation for real-world cross cross-domain visual recognition. Neurocomputing, 433:28-36, 202
Haojian Zhang, Yabin Zhang, Kui Jia, and Lei Zhang. Unsupervised domain adaptation of black-box source models. arXiv preprint (tt:::2011022255 2021.
Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In International Conference on Learning Representations, 2018.
Yang Zhang, Philip David, and Boqing Gong. Curriculum domain adaptation for semantic segmenta- tion of urban scenes. Proceedings of the IEEE international conference on computer vision, pp. 2020-2030, 2017.
Yuchen Zhang, Tianle Liu, Mingsheng Long, and Michael Jordan. Bridging theory and algorithm for domain adaptation. In International Conference on Machine Learning, pp. 7404-7413, 2019.
Brady Zhou, Nimit Kalra, and Philipp Krähenbühl. Domain adaptation through task distillation. In European Conference on Computer Vision, pp. 664-680. Springer, 2020.
Han Zou, Yuxun Zhou, Jianfei Yang, Huihan Liu, Hari Prasanna Das, and Costas Spanos. Consensus adversarial domain adaptation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pp. 5997-6004, 2019.
Han Zou, Jianfei Yang, and Xiaojian Wu. Unsupervised mnergy-based adversarial domain adaptation for cross-domain text classification. In Findings of the Association for Computational Linguistics: ACI-IICNIP 2021, J pp. 1208-1218, 2021.
Yang Zou, Zhiding Yu, BVK Kumar, and Jinsong Wang. Unsupervised domain adaptation for semantic segmentation via bass-ealanced self- oeff-training. In Proceedings of the European conference on computer vision (ECCV), pp. 289-305, 2018
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A APPENDIX
A.1 PROOF OF THEOREM
We prove the Theorem which extends the learning theories of domain adaptation BBen-David et al., 2010) for the black-box domain adaptation and provides theoretical justifications for our method.
Denote X3 Dr as the target domain with its sample distribution. X. DD and X2 Dr denote the easy-to-adapt clean subdomain and the hard-to-adapt noisy subdomain with their corresponding sample distributions, respectively. Denote yes U/ and Ve: Uh the ground truth labels and the pseudo labels of Ne Nr respectively. Let h denote a hypothesis. As our method performs training on mixture of the clean set and the noisy set with pseudo labels, the error of our method can be formulated as convex combination of the errors of the clean set and the noisy set:
ca (h) = ace (h, fe) + (1 - aecc (h, (n.),
(15)
where a is the trade-off easy-to-adayy clean set Xe and the -tddptt noisy set Nn, respectively, defined by
and e. (h, De), en (h, in) represents the expected error of the
ca (h, Ue) = Ez-D, [1(()) Dell
(16)
En (h, 9n) E,,,D [1/(x) 0m1).
(17)
We use the shorthand 6. (h) = E. (h, fe) in the proof.
Then, we derive an upper bound of how the error e (h) is close to oracle error the target domain (h,,, ye) where ys is the ground truth labels of the target domain, which is illustrated in Theorem 1:
Theorem 2 Let h be a hypothesis in class H. Then
(ea(h) (e, S a(dHAAH(De: DA) + X + Ph:
(18)
where the ideal risk is the combined error of the ideal joint hypothesis = ca(hi) + en (h()), the distribution discrepancy duan(Dee Dn) = 2 Sup,,,ee [EDD, [h(z) # [x(x))] BeNDA (h(x) # h' d'(x)), and ph denote the pseudo label rate of Un. The ideal joint hypothesis is given by he arg min + en())), deriving the ideal risk X = <e(h") + E% (h())) and the pseudo risk ea("", (1hh,,0 (c) + en (h",h))
Proof:
(ha chh ve)l
= laccehh, De) + (1 - ()en Dn) ace (e) - (1 - a)en(h,
(19)
<a(lco(h, ye) - en (h, un)1 + (c, 8e) - ca(h, ūn))) + (ca(h, Un) - en (h, yn)l
(20)
= aa(a + (b) + tc
(21)
Then seek the upper bound of cus Eb. e. by applying the triangle inequality for classification errors (Crammer et al., 2008) as stated in Lemma 1.
Lemma For any hypotheses fi, f2, Sa in class H.
d2),,2) s fff..fa + ((f2.f))
(22)
For Ca>
6a = (c(h,, ye) ) Cr (h, vh)l
2 (e, Vel (ch h²) - en (e(( (h, vn)l
(23)
< (h()) + (( (h)
(24)
< 5 dHnne Dn) +
(25)
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Published as a conference paper at ICLR 2023
For <b.
6 (e De) en (h, Un)l
3 (h (c) + (e h:) en (1, + (a(hh,9n
(26)
ANAH(De (Do, Dr) (Ee(h"
cl ((0))))) Mee ;
(27)
1
_ 2 (D, +
(28)
(29)
For Ec>
cc (c, (k) (h, un)) S (0n vh)l = Ph
By summarizing ca, Cb Co. we yield the inequality in Theorem 1:
(1) - (h(
(30)
1 (ds Di) + 2)] + Ph
s (allddnanDD (De, Dn) + A) +
(31)
= ((dHHA((De, Dr.) + + +) Pm
(32)
Furthermore, the pseudo risk is bounded by the ideal risk, the pseudo rate the clean set Pe and the noisy set Ph. derived as follows:
X = ea("", , (n) + en(h", (1))
(33)
I (ce(h" ye) + ce 0e)) )) + (cn(h,, yn) cyhn 0n))
(34)
= X + ca(Ues Uc) + En(un, Un.)
(35)
= Pe + Ph:
(36)
Given constant A, when the easy-to-adapt subdomain is mostly correct, i.e., Pe so O, the pseudo risk bounded by the pseudo rate of the noisy set Ph.
A.2 HYPER- PARARRRR SETTINGS
We show the hyper- parameeresssrs utilized in our experiments in Table 6, including for domain division, for MixUp, Amse that controls the weight of Lmse and the sharpening factor T. In semi-supervised learning, to prevent the noisy samples to cause етror accumulation, we set Amse to be 0. The Mixup follows a Beta distribution with a 1.0. The sharpening factor T 0.5. We use Office-31 and Office-Home. In VisDA-17, since the model may not perform confidently for the large challenging dataset, we s = 0.5 to ensure sufficient samples easy-to-adapt subdomain.
0.8 for
Hyper-parameter/ Dataset
Office-Home
Office-31
VisDA-17
0.8
0.8
0.5
1.0
1.0
Amac
0.
0.
T
0.5
0.5
0.5
Table 6: Hyper-parameter parameters for different datasets.
A.3 CONVERGENCE OF LOSSES
Figure 4 shows the convergence of the losses of BETA during the training procedure. The adversarial loss keeps small since the two subdomains are all drawn from the same domain and thus the distribution divergence between the two subdomains should be small. The mutual information is maximized as shown in the curve of Lmi- The semi-supervised loss Las fluctuates while decreasing since two networks utilize the subdomains obtained by each other for semi-super learning, which decreases error accumulation.
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Lmi
ddd
addv
Loss
Lxd
10
30
40
50
Epoch
Figure 4: The training procedure of the method.
Table 7: Accuracies (%) on Office-Home for partial-ses model adaptation. (:' denotes 'transfer
Method
Re:Pr
Avg-
Avg.
ResNer-30
44.9
70.5
80.7
57.5
61.3
67.2
60.9
40.8
76.0
71.9
47.6
76.9
62.9
52.2
LNL-KL
38.9
53.8
60.5
49.2
50.5
55.9
50.0
38.9
57.0
59.6
51.2
41.9
HD-SHOT
51.2
76.2
85.7
68.8
70.6
77.5
69.2
49.6
81
75.9
54.1
80.7
70.1
60.6
SD-SHOT
54.2
81.8
88.9
74.8
76.5
81.0
73.5
50.6
79.8
58.4
83.7
74,0
64.7
DINE
58.1
83.4
89.2
80.0
80.6
74.2
56.5
80.6
84.8
76.2
BETA (Ours)
61.7
88.5
91.6
77.7
80.1
86,3
75.2
58.4
87.0
81.1
61.5
86,7
78.0
69.1
BA'US
60.6
83.2
88.4
71.8
72.8
83.4
75.5
61.6
$6.5
79.3
62.8
86.1
76.0
67.5
MCC
63.1
80.8
86.0
70.8
72.1
80.1
75.0
60.8
85.9
78.6
65.2
82.8
75.1
67.8
JUMBOT
84.4
A.4 APPLICATIONS TO MORE UDA SCENARIOS.
Apart from closed-set UDA, we also demonstrate the effectiveness of our method for partial-set UDA tasks. To this end, we select the first 25 classes in alphabetical order as the target domain from Office-Home, As shown in Table 7, it seen that LNL-OT and LNL-KL lead to negative transfer due to the label shift. Compared to existing state-of-ther ofethh-art methods, the proposed BETA achieves the best accuracy of 78.0%, and even outperforms some standard UDA methods (Fatras et al., 2021; al., 2020). The improvements for partial-set tasks not large, BETA is not tailored to address the label shift.
Moreover, the proposed BETA be easily extended to the semi-supervised domain adaptation and multi-source domain adaptation. For the semi-supervised domain adaptation, we just add the labeled samples in the target domain to the easy-to-adapt subdomain, which enables BETA in semi-supervised manner (Berthelot et al., 2021). The labeled samples help BETA build a cleaner division for DABP problem. For the multi-source domain adaptation, we can just change the source API to an average prediction or voting of multiple source APIs.
A.5 EXPERIMENTS UNDER CHALLENGING SCENARIOS.
As the proposed method is partially based on the semi-supervised learning and self-training, there are two factors that might hinder the adaptation capacity of BETA: the number training samples and the noise ratio. To study if BETA can lead to improvement in the extreme situations, choose four hard tasks Ar- (44.1%), 1),, Cr-AA (54.5%), Pr-AAr (52.8%), Re-CC (46.7%), and only choose super small subset (30 samples per class) of the original domain the unlabeled target domain data. The results have been shown in Table 8, which demonstrates that our method still brings a large improvement using only limited number of unlabeled samples with super low noise ratio. However, the improvement margin is less than that of the original setting (with more samples).
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Method
Ar-*CI
CI-+Ar
Pr->Ar
Re->CI
Average
Source-only
46.97
51.65
52.00
47.28 54.26
49.48
BETA
53.79
60.32
61.10
57.37
Table 8: Accuracy (%) on Office-Home for challenging situations.
A.6 ABLATION STUDY ON VISDA-17.
To demonstrate the effectiveness of the proposed design Lad, we further supplement the ablation study on VisDA-17. Note that MTN is applied to all runs in the ablation study. The results are shown in Table 9. is shown that each loss brings some improvement, but the largest improvement is brought by Las- The combination of Lkd and Lad lead to a small decreasing accuracy, due to the very noisy label of the source model that hinders the knowledge distillation. Surprisingly, we find that only our proposed Lad and information maximization can achieve a new state-of-the-art (SOTA) performance of 85. % on VisDA-17, outperforming existing SOTA method (DINE) by 9.5%. Previously in the manuscript, all the four losses were leveraged for all datasets and experiments. Through this ablation, we can see that the proposed Cad brings the largest improvement of 36.2% against the source-only model. The performances of BETA can be further improved if we fine-tune the
Table Ablation study of four learning objectives on VisDA-17.
Task
plane
beyel
bus
borse
knife
person
sktbrd
train
truck
Per-class
Source-enly
64.3
24.6
47.9
75.3
69.6
8.5
79.0
31.6
64.4
31.0
81.4
9.2
48.9
Cad
87.7
Eed + Eros
81.4
86.7
77.9
55.1
92.2
34.6
80.8
79.9
87.3
87.9
84.3
58.7
75.6
Lad
90.2
85.4
95.5
93.1
83.8
91.1
55
85.1
Ced + Lrmi Lad
94.8
84.1
79.9
70.1
94.3
83.7
83.3
82.8
92.4
88.6
88.2
45.4
82,3
Ded Lad Lado
83.9
82.3
71.0
95.3
88.3
45.1
82.6
A.7 HYPER-PARAMETER SENSITIVITY ON VISDA-17.
To further validate the Hyper-parameter sensitivity, we conduct an additional experiment on VisDA-I1 17. Similarly, we vary from [0.4, 0.7], and the results have been in Table 10. From the results, it observed that with varying ryper-parameters т, the proposed method can still achieve signifi- cant improvements against the source-only model and the existing state-of-the-an method (DINE). Even the worst case (r=0.4) brings an improvement of 32.9% against the source-only model, and outperforms the existing of-te-rft model (DINE) by 6.2%. In real-world applications, recommend directly using the empirical value (0.6+0.2) that can perform well on all the datasets in this paper. Note that cannot be a very large value, as this could lead limited number of the easy-to-adapt subdomain. It cannot be set to a very small value, as this could lead to very noisy split of two subdomains.
Table 10: Sensitivity study of hyper-parameter on VisDA-17.
Method
plane
beyel
bas
car
horse
knife
meycle
plant
sktbrd
train
truck
Por-class
Source-only
64.3
24.6
47.9
75.3
69.6
8.5
79.0
31.6
64.4
31.0
81.4
9.2
48.9
DINE
81.4
86.7
77.9
55.1
92.2
34.6
80.8
79.9
87.3
87.9
84.3
58.7
75.6
BETA (r=0.4)
95.1
83.0
81.8
70.4
94.5
72.6
87.7
79.4
95.0
90.5
87.6
44.5
81.8
BETA (==0.5)
96.2
83.9
82.3
71.0
95.3
73.1
88.4
80.6
95.5
90.9
88.3
45.1
82.6
BETA (r=0.6)
95.3
83.4
81.5
70.8
94.6
72.2
90.7
88.2
45.3
82.1
BETA (+=0.7)
94.3
82.3
80.7
70.1
93.8
72.1
87.1
79.9
94.2
89.8
87.2
44.3
81.3
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A.8 COMPARISON TO ADAMATCH, INTRADA, DIVIDEMIX, AND CURRICULUM LEARNING
We compare our method with existing works that may share partial similar ideas. Semi-supervised learning for domain adaptation proposed in AdaMatch (Berthelot et al., 2021) and IntraDA (Berth- elot et al., 2021) proposes to reduce intra-domain discrepancy for semantic segmentation. The differences with these methods lie the problem formulation, motivation, and the framework design. In this paper, we aim to deal with DABP problem where the model cannot access the source-domain data and model parameters, while these works highly rely on the source data. Without any labeled data, our method is motivated by new observation, and performs domain division to generate two subdomains. Then we design the twin network structures to further mitigate the confirmation bias during self-training.
We also see some works that proposes easy-to-hard strategy (Cui et al., 2020b; Shin et al., 2020; Shu al., 2019). However, all of these works require the source domain data for training, and thus these papers cannot used in our scenario. Besides, these works rely on intermediate domain generation or curriculum learning, none of which leverages our observation and idea, "deep models tend to fit easy-to-adaph samples". We further compare our method with the DivideMix (Li et al., 2019) that draws the similar observation in noisy-label learning.
Table 11: The differences between our method and DivideMix.
BETA
DivideMix
Task
Domain Adaptation of Black Predictior (DABP). the noise of the target domain in DABP is caused by domain shift between two different domains.
Learning with Noisy Labels (LNL). The noise of LNL is ran- domly added.
Method
(a) BETA uses GMM to divide the target domain and Mix- Match with different augmentation for remi-supervised learning. (similar) (b) BETA applies knowledge distilla- tion between models in parallel the semi-supervised learning, which is purified by the subdomain division to suppress error accumulation during distillation.
DivideMix uses GMM to divide the data and then use MixMatch for semi- supervised learning.
(c) Subdo- main alignment is proposed to align the internal domain shift. (d) Subdomain augmentation is proposed to en- hance structural regularization (i.e., mutual information and mix-up). Strong- weak augmentation fully utilizes the high-confidence samples in X, and single weak augmen- tation does not introduce more noise to X₁. This process enhances the Lini in (8) that encourages the model to better comply with the cluster assumption and prevent the partiality for categories.
Theory
BETA analyzes the algorithm design theoretically and its connection with the learning shift of DABP. A new bound of DABP derived explain the rationale behind the optimization.
N.A.
Experiments
Experiments Office-Homm demonstrate that BETA out- performs DivideMix by 4.7% on average. For the hard tasks with distant domain shift, BETA outperforms Di- videMix by 6.0% on average.
Experiments conducted on LNL
benchmarks.
A.9 STANDARD DEVIATION
For the experimental results in this paper, the codes for 3 time using random seeds. Due to the page limit, we only report the mean accuracy in the paper. Here we further provide the standard deviation (std) in Table 12, which shows that our method can achieve robust improvement in these
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Figure 5: The t-SNE visualization of the target domain on the VisDA-17 dataset the 1st, 3rd, and 10th training epoch (left to right). Each color indicates one category of VisDA-17.
datasets. We show the std values for all tasks in Office-Home, Office-31 and VisDA-17, and the average std for DomainNet.
Table 12: Standard deviation of the results all benchmarks.
Office311
A-D
A-W
D-A
D-W
W-A 0.1
W-D
Avg.
0.1
0.3
0.2
0.2
Office-Home
Ar-CII
Ar-Fi
Ar-Re
CI-
CI-Pr
CI
Re
Pr AAr
PF-CII
Pi-Re 0.5
Re AAr
Re-CCI
Re-tP
Avg.
0.2
0.3
VisDA-17: 0.5, DomainNet 0,3
A.10 T-SNE VISUALIZATION OF BETA.
Figure shows the feature distribution of the target domain at the 1st, 3rd, and 10th training epoch, and the color indicates the category of VisDA. It is observed that the clusters get tighter with clearer boundaries during training, though there still exists some intrinsic confusion among some classes that remains to be tackled in the future.
A.11 CODES AND DATASETS
We have attached the codes in the supplementary materials. The README. introduces the two steps: (i) train a source-only model, and (ii) train the BETA using the hard predictions of the source- only model. The datasets should be prepared in the data folder using the official websites and their licenses should be followed (Saenko al., 2010; Venkateswara et al., 2017; Peng et al., 2017).
A.12 EFFECTIVENESS OF DOMAIN DIVISION
In Figure 6, we show the domain division results at the first epoch (after the warm-up) Office- Home (Art->Clipart. The three rows contain three categories: alarm clocks, candles, and TV (monitors). The domain shift very large between Art and Clipart, and the source-only accuracy is only 44.1% %. Even so, the domain division module still accurately divides the clean casy-to-adapt subdomain and the hard-to-adapt subdomain. In the easy-to-adapt subdomain, the contours objects similar to those of the source domain, such as the alarm clock. The domain shift between the mosy-to-adapt subdomain and the source domain smaller, as shown in the candle samples with black background. For the TV, the casy-to-adapt samples have very clear contours and easy to recognize. In comparison, the hard-to-adapt subdomain is more challenging in terms shape, color, and style. Our domain division strategy outputs AUC of 0.814 for the binary classification of clean samples and noisy samples whose pseudo labels are generated by the source-only model, which enables the semi-supervised learning in BETA to be reasonable. During the training. the AUC keeps increasing to 0.828 and further mitigates the confirmation bias progressively.
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LOSi
(a) Source domain (Art)
12
12
6
(b) Easy-to-adapt subdomain (Clipart)
2:11
ON
(c) Hard-to-adapt subdomain (Clipart)
Figure 6: The domain division results on Office-Home (Art-
21


Reviews:
[{"review_id": "bsyS5wLMTZD", "reviewer": "Reviewer_JUAJ", "summary": "", "questions": "", "limitations": "", "rating": 8, "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": "The paper studies the domain adaptation when the target domain is unlabeled. A black-box predictor trained on the source domain is employed to assign noisy/pseudo labels to the unlabeled target domain data. In this way, the problem is transformed to learning with noisy labels. The noisy label problem is further solved by adapting semi-supervised learning techniques.", "summary_of_the_review": "The paper considers an interesting problem and proposes an effective solution. Although it seems to be similar to DivideMix, it successfully implement this idea on a different problem. They also have theoretical results to support their method. The paper would be improved if the authors further discuss the relationship between Theorem 1 and the mitigation of conformation bias.", "strength_and_weaknesses": "**Strength**\n1. The paper is well motivated and the the considered problem is meaningful. \n2. The combination of ideas from LNL and semi-supervised learning are organic, which handle the confirmation bias well.\n3. The derived bound helps explain the effectiveness of the proposed method.\n\n\n**Weakness**\n1. The most concerned point is that the proposed framework is very similar to DivideMix [36]. It looks like implementing DivideMix on another topic. The authors need to highlight the novelty compared with DivideMix.\n2. Theorem 1 needs to be further explained. It would improve the paper if the conformation bias is proved to be lower than the naive method with the result from Theorem 1.\n3. Intuitively, the conformation bias may not always be mitigated by semi-supervised learning (SSL). The benefit of the proposed method may jointly depend on the number of samples in the target domain and the noise rate of hard-domain samples. In algorithms such as MixMatch, it has beed proved that SSL algorithm may hurt some sub-populations if the corresponding pseudo noise rate is high and the unlabeled sample size is small [R1]. It is interesting to see whether there is similar observations in this paper. If so, the conformation bias is not mitigated in this case.\n4. Minor: Does $\\rho_h$ indicate the noise/error rate of the hard-domain samples? \n\n[R1] Zhu, Z., Luo, T. and Liu, Y., 2021. The rich get richer: Disparate impact of semi-supervised learning. ICLR 2022.", "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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "Y1aNBtmPAZZ", "reviewer": "Reviewer_yM8j", "summary": "", "questions": "", "limitations": "", "rating": 5, "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 studies domain adaptation of black-box predictors (DABP) where the adaptation procedure on target domain has no access to source model and data. To solve this task, this paper proposes a BETA method which divides target samples into easy-to-adapt instances and hard-to-adapt ones and utilizes augmentation manner to obtain more clean samples for model training. This work achieves better performance than the mentioned baselines.", "summary_of_the_review": "This work studies domain adaptation of black-box predictors (DABP) where the adaptation procedure on target domain has no access to source model and data. To solve this task, this paper proposes a BETA method which divides target samples into easy-to-adapt instances and hard-to-adapt ones and utilizes augmentation manner to obtain more clean samples for model training. This work achieves better performance than the mentioned baselines.\n\nFor the current version, I have several concerns.\n\n1. The abstract claims that “an observation we make for the first time … target domain usually contains easy-to-adapt and hard-to-adapt samples…”. However, this observation has been well-observed and studied by many domain adaptation works [1, 2, 3, 4]. These works typically use the probability output of model to determine the easy or hard samples. Thus, this concept is not novel, and the sample division strategy used in Eq. (3) and Eq. (4) is basically same with the existing works.\n\n2. The proposed method is not novel for domain adaptation field. Using the linear combination of samples to augment the high-confident instances has been explored by [5]. The mutual information maximization is also used by many domain adaptation works such as SHOT [6]. Thus, the current method seems to be the combination of many existing methods. In addition, [5] and other recent UDA works have achieved higher performance than the mentioned baselines. However, these works are missing in Table 1-3.\n\n3. When dividing target samples into two sub-domains, the error is naturally divided into two parts to form the inequality as Eq. (14). Thus, Theorem 1 does not illustrate that the proposed method can achieve better sub-domain alignment.\n\n[1] Cui, Shuhao, et al. \"Gradually vanishing bridge for adversarial domain adaptation.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2020.\n\n[2] Shu, Yang, et al. \"Transferable curriculum for weakly-supervised domain adaptation.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 33. No. 01. 2019.\n\n[3] Shin, Inkyu, et al. \"Two-phase pseudo label densification for self-training based domain adaptation.\" European conference on computer vision. Springer, Cham, 2020.\n\n[4] Chen, Chaoqi, et al. \"Progressive feature alignment for unsupervised domain adaptation.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2019.\n\n[5] Na, Jaemin, et al. \"Fixbi: Bridging domain spaces for unsupervised domain adaptation.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2021.\n\n[6] Liang, Jian, Dapeng Hu, and Jiashi Feng. \"Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation.\" International Conference on Machine Learning. PMLR, 2020.\n", "strength_and_weaknesses": "Strengths:\n\n1. The experimental results on some DABP tasks are better than the mentioned works.\n\nWeaknesses:\n\n1. The current paper lacks some necessary references.\n2. The proposed method is not novel in domain adaptation field.\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": {}}, {"review_id": "LghdpguJTXj", "reviewer": "Reviewer_uuuU", "summary": "", "questions": "", "limitations": "", "rating": 8, "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": "Based on a simple observation that intra-domain target samples have different levels of domain discrepancy, this paper proposed a new approach, divide-to-adapt, to address the problem of black-box domain adaptation. The main contributions are two parts: dynamically mitigating the confirmation bias for black-box domain adaptation and providing some theoretical justifications. Experiments on image classification benchmarks demonstrate the effectiveness of the proposed approach.", "summary_of_the_review": "To sum up, I find this paper tackles a practical problem for domain adaptation without source data and model parameters. Yet, it still requires clarification and some solid empirical support before warranting acceptance of this paper.", "strength_and_weaknesses": "Strength:\n\n1. The paper is nicely written and the methodology is well described.\n\n2. Theoretical validation and thorough experiments indicate that the proposed strategy, divide-to-adapt, is a good solution for black-box domain adaptation.\n\n3. It is also impressive that the proposed method outperforms the sota approach by 7.0% on VisDA-17 and even surpasses standard domain adaptation using source data.\n\nWeaknesses:\n\n1. The idea of considering domain adaptation as the semi-supervised setting has been studied in AdaMatch [a] and dividing the target domain into easy and hard subdomains for adaptation has been explored in IntraDA [b].  However, the above relevant works have not been included in this manuscript. The authors should provide more discussion.\n\n2. The technical contribution feels a bit scattered. As the framework can be decomposed into a set of smaller contributions, each improving the performance by a smaller amount. Though authors have provided an ablation study to analyze the individual contribution of each component. However, I find it is quite hard to line the contributions to the motivations.\n\n3. It seems that the proposed method performs better with fewer categories (7.0% gain on VisDA-17 with 12 categories while 1.8% gain on Office-31 with 31 categories and 2.0% gain on DomainNet with 365 categories). Also, I'd rather like to see the ablation studies of each component on VisDA-17 in Table 5.\n\n4. Currently the target application seems to be a bit narrow, as it is only image classification on three benchmarks. I think it would be very interesting to see the applications to other settings e.g., semi-supervised learning, and semi-supervised domain adaptation like AdaMatch [a].\n\n5. As the proposed domain division relies on threshold \\tau, it would be better to provide the mean and std of the numerical results under different random seed for each experiment.\n\nRefs:\n\n[a] David Berthelot, Rebecca Roelofs, Kihyuk Sohn, Nicholas Carlini, Alexey Kurakin: AdaMatch: A Unified Approach to Semi-Supervised Learning and Domain Adaptation. ICLR 2022.\n\n[b] Fei Pan, Inkyu Shin, François Rameau, Seokju Lee, In So Kweon: Unsupervised Intra-Domain Adaptation for Semantic Segmentation Through Self-Supervision. CVPR 2020: 3763-3772.\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": {}}, {"review_id": "CXNJteTfjr", "reviewer": "Reviewer_jpbu", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "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 address the Domain Adaptation of Black-box Predictors (DABP) by using a \"dive to adapt\" strategy.\n\nThe contribution are:\n- a new divide to adapt strategy\n- Theoritical analysis that demonstrates the boundary on the error on the target domain\n- experiments to compare with state of the art benchmarks.", "summary_of_the_review": "This work proposed a simple yet effective framework for DABP.\n\nFew analysis (quantitative and qualitative) are done on the influence of the \\tau parameter of the splitting step.\nIt appears not to be influent on one dataset but that is the easiest dataset...", "strength_and_weaknesses": "Strength:\n- the method is well introduced\n- experiments are sounding\n\nWeaknesses:\n- in the ablation studies more experiment could have been done on the splitting hyper parameter \\tau especially on more than one dataset.\nthis experiment could also look  qualitatively where the splitting occurs in the dataset.", "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": "-HgoFyrijgM", "reviewer": "Reviewer_zK5K", "summary": "", "questions": "", "limitations": "", "rating": 6, "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": "In this work, the authors propose a method to increase the accuracy of classification in the task Domain Adaptation of Black-box Predictors. It aims to suppress the confirmation bias efficiently, and extends this work with a learning framework called BETA. Specifically, inspired by the phenomena that deep models tend to learn easy-to-adapt samples faster than hard-to-adapt samples, the authors divide the target domain into an easy-to-adapt subdomain and a hard-to-adapt subdomain. With treating the former as a labeled set and the latter as an unlabeled set, the authors solve DABP via semi-supervised learning methods. Additionally, the authors propose mutually-distilled twin networks with weak-strong augmentation method to mitigate error accumulation.", "summary_of_the_review": "I hope the authors can address my concerns in Section II.", "strength_and_weaknesses": "Strength:\nThis paper is overall easy to read. The authors describe the task clearly and the work is well organized. The motivation behind this work is clearly presented, i.e., to alleviate the confirmation bias. It is novel to solve DABP problem with semi-supervised learning method. The authors present a comprehensive comparison with previous works. According to the provided result of experiment, the proposed framework outperforms the competing algorithms.\n\nWeakness:\n- I am confused that whenever we get a batch of new test data, is it necessary to do extra studies on threshold value to find a suitable value according to different data distributions? \n- More discussion to DivideMix should be added. This work shares similar spirits to dividemix and the authors should clarify it.", "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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "Not applicable"}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: notable-top-25%