Wildly Unsupervised Domain Adaptation and Its Powerful and Efficient Solution
Authors: Feng Liu
Jie Lu
Bo Han
Gang Niu
Guangquan Zhang
Masashi Sugiyama
Venue:  (2020)

Abstract: In unsupervised domain adaptation (UDA), classifiers for the target domain (TD) are trained with clean labeled data from the source domain (SD) and unlabeled data from TD. However, in the wild, it is hard to acquire a large amount of perfectly clean labeled data in SD given limited budget. Hence, we consider a new, more realistic and more challenging problem setting, where classifiers have to be trained with noisy labeled data from SD and unlabeled data from TD---we name it wildly UDA (WUDA). We show that WUDA ruins all UDA methods if taking no care of label noise in SD, and to this end, we propose a Butterfly framework, a powerful and efficient solution to WUDA. Butterfly maintains four models (e.g., deep networks) simultaneously, where two take care of all adaptations (i.e., noisy-to-clean, labeled-to-unlabeled, and SD-to-TD-distributional) and then the other two can focus on classification in TD. As a consequence, Butterfly possesses all the conceptually necessary components for solving WUDA. Experiments demonstrate that under WUDA, Butterfly significantly outperforms existing baseline methods.

Under review conference paper at ICLR 2020
WILDLY UNSUPERVISED DOMAIN ADAPTATION AND ITS POWERFUL AND EFFICIENT SOLUTION
Anonymous authors Paper under double-blind review
ABSTRACT
In unsupervised domain adaptation (UDA), classifiers for the target domain (TD) are trained with clean labeled data from the source domain (SD) and unlabeled data from TD. However, in the wild, it is hard to acquire a large amount of perfectly clean labeled data in SD given limited budget. Hence, we consider new, more realistic and more challenging problem setting, where classifiers have to be trained with noisy labeled data from SD and unlabeled data from TD-we we name it wildly UDA (WUDA). We show that WUDA ruins all UDA methods if taking no care of label noise in SD, and to this end, we propose a Butterfly framework, a powerful and efficient solution to WUDA. Butterfly maintains four models (e.g., deep networks) simultancously. where two take care of all adaptations (i.e., noisy-to-clean,
and SD-to-TD-aistributionna and then the other two can focus on classification in TD. As a consequence, Butterfly possesses all the conceptually necessary components for solving WUDA. Experiments demonstrate that under WUDA, Butterfly significantly outperforms existing baseline methods.
1 INTRODUCTION
Domain adaptation (DA) aims to learn discriminative classifier in the presence of a shift between training data in source domain and test data in target domain Been- et al., 2010; Ganin and Lempitsky, 2015; Xiao and Guo, 2015; Zhang et al., 2015; 2013). Currently, DA can be divided into three categories: supervised DA (Tzeng et al., 2015), semi-supervised DA (Guo and Xiao, 2012) and unsupervised DA (UDA) (Saito et al., 2017). When the number of labeled data is few in target domain, supervised DA also known as few-shot DA (Motian et al., 2017). Since unlabeled data in target domain can be easily obtained, UDA exhibits the greatest potential in the real world (Ganin and Lempitsky, 2015; Ganin et al., 2016; Gong et al., 2012: 2016; Long et al., 2015; Saito et al., 2017; 2018).
UDA methods train with clean labeled data in source domain (i.e., clean source data) and unlabeled data in target domain (i.c.. unlabeled target data) to obtain classifiers for the target domain (TD), which mainly consist of three orthogonal techniques: integral probability metrics (IPM) (Ghifary et al., 2017; Gong et al., 2016; Gretton et al., 2012; Lee and Raginsky, 2018; Long et al., 2015), adversarial training (Ganin et al., 2016; Gong et al., 2018; Hoffman et al., 2018; Li et al., 2018; Saito et al., 2018; Tzeng et al., 2017) and -aarraaiil--raining----
psendo labeling (Saito et al., 2017). Compared to IPM- and labeling- based method (i.e., asymmetric tri-training domain adaptation (ATDA) (Saito et al., 2017)) can construct high-quality tprget-speccfic representation, providing better classification performance.
methods, the pseudo-
However, in the wild, the data volume of source domain tends to be large. To avoid the expensive labeling cost, labeled data in source domain normally come from amateur annotators the Internet (Lee et al., 2018; Schroff et al., 2011: Tommasi and Tuytelaars, 2014). This brings us a new, more realistic and more challenging problem, wildy unsupervised domain adaptation (abbreviated as WUDA, Figure 1). This adaptation aims

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The blue line denotes that UDA transfers knowledge from clean source data (P.) to unlabeled target data (Pz,). How- ever, perfectly clean data is hard to acquire. This brings wildty unsupervised domain adaptation (WUDA), namely transfer- ring knowledge from noisy source data (Ps (Ps) unlabeled target data (Px,). ). Note that label corruption process (black dash line) is unknown in practice. To handle WUDA, compromise lution is two-step approach (green line), which sequentially combines label-noise algorithms (P, - P.. label correction) and existing UDA (P', - P..). This paper proposes a ro- hust one-step approach called Butterfly (red line, P. - Psu directly). which eliminates noise effects from P..
One slep approach: Butterfly
Label comruntionn
Existing UDA
Ps
Ps
Px
Two alep approach Label correction
Two approach Evistng UDA
P5
Figure 1: Wildly unsupervised domain adaptation (WUDA).
transfer knowledge from noisy labeled data in source domain (P.. i.e., noisy source data) to unlabeled target data (Px,). ). Unfortunately, existing UDA methods share an implicit assumption that there are noisy source data. Namely, these methods focus on transferring knowledge from clean source data (P.) to unlabeled target data (Pz,). Therefore, these methods cannot well handle the WUDA.
To validate this fact, we empirically reveal the deficiency of existing UDA methods (Figure 2). To improve these methods, straightforward solution is a two-step approach. In Figure 1, we can first use label-noise algorithms to train a model on noisy source data, then leverage this trained model to assign pseudo labels for noisy source data. Via UDA methods, we can transfer knowledge from pseudo-labeles source data (P,) unlabeled target data (Pa.). Nonetheless, pseudo-labeled source data are still noisy, and such two-step approach may not eliminate noise effects.
To circumvent the issue of two-step approach, we present a robust one-step approach called Butterfly. In high level, Butterfly directly transfers knowledge from P, to Pa.. and uses the transferred knowledge to construct sarget-specific representations. In low level, Butterfly maintains four networks dividing two branches (Figure 3): Two networks in Branch-I are jointly trained on noisy source data and pseudo-labeled target data (data in mixture domain (MD)); while two networks in Branch-ll are trained on aseudo-labeled target data.
The reason why Butterfly can be robust takes root in the dual-checking principle (DCP): Butterfly checks high-correctness data out, from not only the data in MD but also the pseudo-labeled target data. After cross- propagating these high-correctness data, Butterfly can obtain high-quality (DIR) and target-specific representations (TSR) simultaneously an itcrative manner. If we only check data in MD (i.e., single checking), the error existed in ppeudo-labeled target data will accumulate, leading to low-quality DIR and TSR.
-ivaiiiniiivainntt representations
We conduct experiments on simulated WUDA tasks. including 4 MNIST- SYND tasks, 4 tasks and 24 human-sentimen tasks. Besides, we conduct experiments on real-world WUDA tasks. Empirical results demonstrate that Butterfly can robustly transfer knowledge from noisy source data to unlabeled target data. Mcanwhile, Butterfly performs much better than existing UDA methods when source domain (SD) suffers the extreme (c.g., 45%) noise.
2 WILDLY UNSUPERVISED DOMAIN ADAPTATION
this section, we first define a new, more realistic and more challenging setting called wildly unsupervised domain adaptation (WUDA), and explain the nature of WUDA. Then, empirically show that representative UDA methods cannot handle WUDA well, which motivates us to propose Butterfly (see Section 3).
Definition (Wildly Unsupervised Domain Adaptation). Let X, be a multivariate random variable defined the space X with respective a probability density Pa. (X,, Y.) be multivariate random variable defined
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S-Neet
2Ah
ATD4
hotos Rate
Proted Nata
Natio
Nateo
(a) Symmetry-flip noise: S +M (left), M-+5 (right)
(b) Pair-flip noise: S-*M (left), M->5 (right)
Figure 2: WUDA ruins representative UDA methods. Representative UDA methods includes deep adaptation networks (DAN, a IPM based method (Long et al., 2015)), comain-adversarial neural network (DANN, a adversarial training based method (Ganin al., 2016)), asymmetric tri-training domain adaptation (ATDA, pseudo-labe based method (Saito et al., 2017)) and transferable curriculum learning (TCL, robust UDA method (Shu et al., 2019)). B-Net is our proposed WUDA method. We report target-domain accuracy of all methods when the noise rate of source domain changes (a) from 5% to 70% (symmetry-flip noise) and (b) from 5% to 45% (pair-flip noise). Clearly, when the noise rate of source domain increases, target-domain accuracy of representative UDA methods drops quickly while that of B-Net keeps stable consistently.
on the space X' x C with respective probability density Ps. where C = ..,,...,KK Let Ps, be the marginal probability density of Pa. Given i.i.d. data D = {(Foi Fi and Dr = {au) drawn from P. and Pzo in wildly unsupervised domain adaptation, aim to Irain with D2 and D, to accurately annolate data drawn from Pz,, where Ps, + PP..
Remark 1. In Definition 1, D. is noisy source data, D, is unlabeled target data, and P. and Pa. are two probability measures corresponding to densities (r(,,, Us) and Pz, (aie).
Nature of WUDA. Specifically, there are five distributions involved in WUDA setting: I) marginal distribution on source data, i.e., Px. in Definition 1; 2) a marginal distribution on target data, i.e. Px, in Definition 1; 3) incorrect conditional distribution of label given T., ( xx)); 4) a correct conditional distribution of label given x., p(y. (x,) and 5) a correct conditional distribution of label given tt, P(ys (ce)-
Based on Definition 1 and Appendix A.2, noisy source data D, are drawn from (s Ma) - Pa, (I=) p)p(u=|Z.) + pg))) where P is the noise rate in source data. Namely, source data D. are mixture of correct source data from Ps, (xx)p(ys (Ix) and incorrect data from pz, (2, ((y. (xx).. Target data D, are drawn from Pr.. In WUDA setting, we aim to train a classifier with D. and De. This classifier is expected to accurately annotate data from Px, i.e., to accurately simulate distribution 5).
WUDA ruins representative UDA methods. We take simple example to illustrate why WUDA ruins representative UDA methods. We corrupt source data using symmetry flipping (Patrini et al., 2017) and pair flipping (Han et al., 2018) (Appendix B). Namely, the corrupted source data (D₂ in Definition 1) are drawn from P. whose density is P. (Z., ys) = Pr. (Ix)((1 [1 p)p(y, + pq(y, We draw the target data D, from Pr, whose density Pa;- To instantiate source and target data, we leverage MNIST and SYND (Figure 6 in Appendix C), respectively.
Thus, we first construct two WUDA tasks with symmetry-fin noise: corrupted
(S++) and corrupted MNIST- (M-+)). In Figure 2 (a), we report target-domain accuracy of representative UDA methods, when the noise rate p of SD changes from 5% to 70%. It clear that target-domain accuracy of these representative UDA methods drops quickly when p increases. This means that WUDA ruins representative UDA methods. Then, we construct another two WUDA tasks with pair-flip noise. In Figure (b), we report target-domain accuracy, when the noise rate p of SD changes from 5% 45%. Again, WUDA still ruins representative UDA methods. Note that pair-flip noise is much harder than symmetry-flip noise, and its noise rate cannot be over 50% in practice (Han et al., 2018).
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Noisy data
Pscudo-labeled larget data
DIR
High comeciios Micner Dets
Input
Branch-J
Chocking
DIR
Mixture Domatn
Sharing Weights
Checking
Input
Branch-Il
CNN
Chocking
High comecicnne
Fiz
Target domsin
Taiget Dey.
TSR
Figure 3: Butterfly Framework. Two networks (Fi and F2) in Branch-I are jointly trained noisy source data and pseudo-labell target data (mixture domain). Two networks in Branch-II (F1z and F12) are trained pseudo-labeled target data. By using dual-checking principle, Butterfly checks high-correctness data out from both mixture and pseudo-labeled target data. After cross-propagating checked data, Butterfly can obtain high-quality dlmaiin-nvariant representations (DIR) and largel-specific representations (TSR) simultaneously in an iterative manner. Note that the interaction between DIR and TSR happens via the shared CNN. Besides, the first training epoch, since do not have any pseudo-labeled target data, need use noisy source data as the pseudo-labelae target data, which follows Saito et al. (2017).
However, the proposed Butterfly network (abbreviated as B-Net, Figure 3) performs robustly when increases (blue lines in Figure 2). In following sections, we will introduce Butterfly framework, and explain why Butterfly achieves better target-domain accuracy consistently.
3 BUTTERFLY: TOWARDS ROBUST ONE-STEP APPROACH
To realize a robust WUDA approach, we propose a Butterfly framework (a one-step approach, Algorithm 1), which trains four networks dividing into two branches (Figure 3). By using DCP, Branch-I checks which data is correct in MD; while Branch-II checks which pseudo-labeled target data is correct. To ensure these checked data highly-correct, we apply the small-loss trick based on memorization effects of deep learning (Arpit et al., 2017). After cross- propapappggg these checked data (Bengio, 2014), Butterfly can obtain high-quality DIR and TSR simultaneously in an iterative manner.
Loss function in Butterfly. Four networks trained by Butterfly share the same loss function but with different inputs.
C(O, u. F,D,
Σ u, ((F(())))).)) E ==1
where n is the batch size, and F represents a network (e.g., F1, F2, Fa and F22). D (1x; }i)) is mini-batch for training a network, where {x,, De h could be data in MD or TD (Figure 3), and 0 represents parameters of F and u = [u1,..., wn]"" is an n-by-1 vector whose elements equal 0 or 1. ((s-)) .) is the cross-entropy loss. For two networks in Branch-I, following Saito et al. (2017), also add regularizer 10f110021 0y11 in their loss functions, where ff1 and 022 are weights of the first fully-connect layer of Fi and Fz. With this regularizer, F1 and F2 will learn from different features.
Nature of the loss L. In loss function L, have instances: (r;, G.). where 1,2, ... For the tt instance, we will compute its cross-entropy loss (i.e., ((F(a;), )), and we will denote this instance "selected" if u; 1. Thus, the nature of L is actually the average value of cross cross-entropy loss of these
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"selected" instances. Note that, we need to set a constrain to prevent Ei_ U, in L, which means that we need to select at least one instance to compute L.
Training procedure of Butterfly. For two networks in each branch, they will first check high-correctness data out and then cross update their parameters using these data.
Based on loss function defined in Eq. (I), entire training procedures of Butterfly are shown in Algorithm 1. First, we initialize training data for two branches (D for Branch-I and DJ for Branch-II), four networks (F1, F2, F11 and Fiz) and the number of pseudo labels (line 2). In the first epoch (T = 1), following Saito al. (2017), D is the same with D, (i.e., we use noisy source data as pseudo-labeles labeled target data) since we cannot annotate pseudo labels for target data when T = 1. After mini-batch Î fetched from Î (line 4), Fi and F22 check high-correctness data out and update their parameters (lines 5) using Algorithm 2. Using similar procedures, Fa and Fiz also update their parameters using Algorithm (lines 6-7).
In each epoch, after Nax mini-batch updating, we randomly select ni unlabeled target data and assign them pseudo labels using Fi and F2 (lines 8). Following Saito et al. (2017), the Labeling function in Algorithm I (line 8) assigns pseudo labels for unlabeled target data, when predictions of F1 and F3 agree and at least one of them is confident about their predictions (probability above 0.9 or 0.95). Using this function, we can obtain the pseudo-labeled target data DJ for training Branch-Il in the next epoch. Then, we merge DJ and D. to be D for training Branch-I in the next epoch (line 9). Finally, we update ni, R(T)) and (T)) in lines 10-11 according Saito al. (2017) and Han al. (2018). Note that R(T) is a piecewise-defined linear function. Namely, when T 2 Tg. R(T) = 1 - T; when T < Tu. R(T) = 1- - T/Tx x T.
In Algorithm 1, we use T to represent the noise rate (i.e., the ratio of data with incorrect labels) in MD and use to represent the noise rate in TD. However, in WUDA, we cannot obtain the ground- truth r and T.. Thus, we regard and Tt as hyper- parameters. Note that r and Ti are robustly set 0.4 and 0.05 in experiments.
Checking process in Butterfly. In Algorithm 2. we first obtain four inputs: 1) networks F1 and Fz, and 2) a mini-batch D, and 3) learning rate and 4) remember rate (line 1). Then, we will obtain the best un by solving a minimization problem (line 2). L represents the loss function defined in Eq. (1), 0n represents the parameters of the network Fj. Similarly we will obtain the best U2 (line 3). Og represents the parameters of the network F2. Next, 8 and Og are updated using gradient descent, where the gradients are computed using a given optimizer (lines 4-5). Finally, we substitute the updated 0₁ into Fi and the updated 0g into F2 and output F1 and F2 (line 6).
Solution to minimization problems in Algorithm 2. In line 2 or 3 in Algorithm 2, we need to solve a minimization problem: min "illu'uu'aaa] [D] C(0, u'; F, D) and return the best u' as (u) in line 2 and u2 in line 3). In this paragraph, we will show how to quickly solve this problem using a sorting algorithm. Recall the nature of the loss L. we know is the average value of cross-entropy losses of "selected" instances, and 1u' is the number of these "selected" instances. Thus this minimization problem is equivalent to "given a fixed F (F, or F2) and n instances in D, how to select at least instances such that L is minimized", where k = [a] DI]. To solve this problem, we first use a sorting algorithm (top_k k function in TensorFlow) to sort these n instances according to their cross-entropy losses E(Fi (1:;); Gt). Then, we select & instance with the smallest cross-entropy losses. Finally, let u, of these k instances be 1 and of the other instances be 0, and we can get the best u = [.,,..., un]] The average value of cross-entropy losses of these k instances is the minimized value of C(0, ui; F, D) under the constrain lu' > o(D
4 BUTTERFLY vs. TWO-STEP APPROACH
This section analyzes why Butterfly is better than two-step approach using theoretical results in Appendix D. Practitioner may safely skip it. Following Ben-David et al. (2010), we derive an upper bound of torget- risk for WUDA. Compared to existing UDA bounds, the WUDA bound has two extra terms (see Eq. (6)): A, (noise effect from source data), and A, (noise effects from pseudo labels of target data). We will use A, and A, to show why Butterfly (a one-step approach) can eliminate noise effects while two-step methods cannot.
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Algorithm 1 Butterfly Framework: quadruple training for WUDA problem
1: Input De, De, learning rate 13. fixed T, fixed Tt, epoch T. and max, iteration Naax # of escudo-labelee target data Bosit max of Bynit nh maxi
2: Initial Fí, F2, Fii, Fiz. D = D.. D D.. n² Renei
for 1, ..., max
3: Shuffle training set D:
I/ Noisy dataset
for N 1,...., N maz do
4: Fetch mini-batch from D:
5: Update Branch-I: Fi, F22 Checking(Fi, Fa, D, R(T)):
Check data in MD using Algorithm
6: Fetch mini-batch D. from Di:
7: Update Branch-II: Fai, Fia Checking(Fai, Fra, Do, Rc(T));
I/ Check data in TD using Algorithm 2
end
8: Obtain DJ Labelling F1, F2, De,
#f Label Dt, following Saito al. (2017) // Update MD
9: Obtain D D, U D1;
10: Update ni m n., mumu
11: Update R(T) 1 min T. T,T), (T) min m n,,m)
end
12: Output Far and F12
Algorithm 2 (F F2, D. 1), ())
1: Input networks Fi. F2, mini batch D, learning rate remember rate a;
2: Obtain arg minu; :11] >a|D] L(11, w/; Fi, D):
I/ Check high-correctness data
3: Obtain
[(0,, ulg P2, D);
// Check high-correctness data
4: Update 0: = 01 -(,, u2; F1, D);
// Update Oj // Update 0g
5: Update 82 = 82 L(2,, u1; F2, D);
6: Output F and 13
Two-step approach (a compromise solution). To reduce noise effects, straightforward solution is two- step approach. In the first step, we can train classifier with noisy source data using Co-teaching (Han et al., 2018) and use this classifier to annotate pseudo labels for source data. the second step, we use ATDA (Saito et al., 2017) to train target-domain classifier with pseudo-label-soune
data and target data.
However, two-step approach may not reduce noise effects A, (i.c., not alleviating noise effects from source data). In two-step approach, after using Co-teaching, A, will become Eq. (7)). The first part of A, may be less than that A due to Co-teaching, but the second term of A may be higher than that of A, since Co-teaching does not consider minimize it. Thus, it is hard say whether A, < A, This means that, the two-step approach may not really reduce noise effects A.. Besides, two-step approach does not take care of eliminating A, explicitly, Based above analysis, we find that two-step approach cannot eliminate A, and A..
effects A (see
One-step approach (Butterfly). To eliminate noise effects A = A. + Ac, Butterfly aims to select correct
data simultancously from noisy source data and secudo-labeled target data (see Section 3). Let Pi be the probability that incorrect data is selected from noisy source data, and Pài be the probability that incorrect data is selected from pseudo-labeled target data. Theorem shows that A + if pô1 + 0 and ph - 0. Since Butterfly can select correct data with high probability (i.e., Púi + 0 and Pún + 0), noise effects will be eliminated (A + 0).
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Torgs Teget/omain
Teret-cmmnn
B Nee Co+ATDA
ATDA
Eppch
Epech
Epoch
Epoch
(a) $20
(b) S-15
(c) P20
(d) P45
Figure 4: Target-domain accuracy vs. number of epochs on four SYND WUDA tasks.
5 EXPERIMENTS
Simulated WUDA tasks. We verify the effectiveness of our approach on three benchmark datasets (vision and text), including MNIST, SYN-DIGITS (SYND) and human-sentiment analysis (i.e., Amazon products reviews on book, dvd, electronics and kitchen). They are used to construct 14 basic tasks: MNIST (M-5), SYND->MNIST (S-M)) book->dvd (B-D),
(B-E), and kitchen elec- tronics (K EE)) These tasks are often used for evaluation of UDA methods (Ganin et al., 2016; Saito et al., 2017; 2018). Since all source datasets are clean, we corrupt source data using symmetry flipping (Patrini et al., 2017) and pair flipping (Han et al., 2018) (Appendix B) with noise rate P chosen from (0.2, 0.45]. So, for each basic task, we have four kinds of noisy source data: Pair-45% (P45), Pair-20% (P20), Symmeiry-45% (S45), Symmetry-20%% (S20). Namely, we evaluate the performance of each method using 32 simulated WUDA tasks: 8 digit tasks and 24 classification problem, so pair flipping is equal to symmetry flipping. Thus, we only have 24 human-sentiment tasks. Results on human numan-sentiment -entimeet tasks are reported in Appendix
tasks. Note that the human- -entansentiment task is a binary
Real-world WUDA tasks. We also verify the efficacy of our approach "ccross-dtaaeet benchmark" including Bing, Caltech256, Imagenet and SUN (Tommasi and Tuytelaars, 2014). In this benchmark, Bing, Caltech256, Imagenet and SUN contain common 40 classes. Since Bing dataset was formed by collecting images retrieved by Bing image search, it contains rich noisy data, with presence of multiple objects in the same image and caricaturization (Tommasi and Tuytelaars. 2014). We use Bing as noisy source data, and Caltech256. Imagenet and SUN as unlabeled target data, which can form three real-world WUDA tasks. Besides, we also test our method on two common UDA tasks MMNIS=+SVEH and SVHN-MNID to help compare with other UDA-based papers in literature.
Baselines. We realize Butterfly using four networks (abbreviated as B-Net) and compare B-Net with following baselines: 1) ATDA: representative pseudo label based UDA method (Saito et al., 2017); 2) deep adaptation networks (DAN): representative IPM based UDA method (Long et al., 2015); 3) DANN: representative adversiral training based UDA method (Ganin et al., 2016); 4) TCL: existing robust UDA method; 5) Co teaching+
(CD+A:DA): a two-step method (see Section 4); 6) Co teaching+TCL (Co+TCL): two-step method. Implementation details are demonstrated in Appendix F.
Results on simulated WUDA (including 8 tasks). Table I reports the accuracy on the unlabled target data (i.e., target-domain accuracy) in 8 tasks. As can be seen, average target-domain accuracy of B-Net higher than those of all baselines. On S20 case (the easiest case), most methods work well. ATDA has satisfactory performance although does not consider the noise effects explicitly. Then, when facing harder cases (i.e., P20 and P45), ATDA fails to transfer useful knowledge from noisy source data to unlabeled target data. When facing the hardest cases (i.e., M-5 with P45 and S45), DANN has higher accuracy than DAN and ATDA have. However, when facing the easiest cases (i.e., S-*M with P20 and S20), the performance of DANN is worse than that of DAN and ATDA. Although two-step method Co+ATDA (or Co+TCL) outperforms ATDA (or TCL) in all 8 tasks, it cannot beat one-step method: B-Net in terms of average target-domain accuracy. This result is an evidence for the claim in Section 4. In the task S-*M with P20, Co+ATDA outperforms all methods (slightly higher than B-Net), since pseudo-labeled source data almost correct.
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Terpe AcCERRIC
Teret-cmme
CO0ch
Epach
Epoch
Epsch
$20
(b) S45
(c) P20
P45
Figure 5: Target-domain accuracy vs. number of epochs on four MNIST WUDA tasks.
Table 1: Tomge accuracy on 8 digit WUDA tasks (SYND+MNIST), Bold value represents the highest
accuracy in each row.
Tasks
Type
DAN
DANN
ATDA
TCL
Co+TCL
Co+ATDA
B-Net
P20
90.17%
79.06%
55.95%
80.81%
88.56%
95.37% %
95.29%
P45
67.00%
55.34%
53.66%
55.97%
73.27%
75.43%
90.21
S-+M
$20
90.74%
75.19%
89.87%
80.23%
85.8%%
95.22%
95.88% %
S45
89.31%
65.87%
87.53%
68.54%
75.69%
92.03%
94.97% %
P20
40.82%
58.78%
33.74%
58.88%
59.08%
58.02%
60,36
P45
28.41%
43.70%
19.50%
45.31%
47. 47.15%
46.80%
56,62 %
M-
$20
30.62%
53.52%
49.80%
56.74%
56.91%
56.64%
57.05
S45
28.21%
43.76%
17.20%
49.91%
51.22%
54.29%
56.18%
Average
58.16%
58.01%
50.91%
62.05%
67.22%
71.73%
75,82
Figures 4 and show the target-domain accuracy number of epochs among ATDA, AT+ATDA and B-Net. Besides, we show the accuracy of ATDA trained with clean source data (ATDA-TCS) as a reference point. When accuracy one method close to that of ATDA-TCS (red dash line), this method successfully eliminates noise effects. From our observations, it is clear that B-Net is very close to ATDA-TCS in out of 8 tasks (except for S-*M task with P45, Figure 4-(d)), which is an evidence that Butterfly can eliminate noise effects. Since P45 case is the hardest one, it is reasonable that B-Net cannot perfectly eliminate noise effects. An interesting phenomenon that, B-Net outperforms ATDA-TCS means that B-Net transfers more useful knowledge (from noisy source data to unlabeled target data) even than ATDA-TCS (from clean source data to unlabeled target data).
M- tasks (Figure 5-(a), (C)). This
Results on real-world WUDA (including 3 tasks). Table 2 reports the target-domain accuracy for tasks. B-Net enjoys the best performance all tasks. It should be noted that, in both Bing *Caltech256 and Bing-+lmageNNrr tasks, ATDA slightly worse than B-Net. However, Bing->UU task, ATDA much worse than B-Net. The reason is that the DIR between Bing and SUN are more affected by noisy source data. This phenomenon is also observed when comparing DANN and TCL. Compared to CO+ATDA, ATDA is slightly better than Co+ATDA This abnormal phenomenon after using Co-teaching to assign pseudo labels for noisy source data, the second term in A may increase, which results in that A increases, i.e., noise effects actually increase. This phenomenon is evidence that two-step method may not really reduce noise effects.
be explained using A (see Section 4),
Results on two UDA tasks. Table 3 reports the target-domain accuracy for 2 common UDA tasks. The target-domain accuracy of DAN, DANN and ATDA results reported by Saito et al. (2017). Although the target-domain accuracy of B-Net is not always higher than that of ATDA, B-Net still has satisfactory performance on UDA problem. Note that, since B-Net WUDA method, is reasonable that B-Net the state-of-the-art UDA method.
Ablation study. Finally, we conduct thorough experiments to show the contribution of individual compo- nents in BeNet. We report average target-domain accuracy 32 simulated WUDA tasks (8 digit and 24
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Table 2: Target-domain accuracy on real-world WUDA tasks. The source domain is the Bing dataset that contains noisy information from the Internet. Bold value represents the highest accuracy in each row.
Target
DAN
DANN
ATDA
TCL
Co+TCL
Co+ATDA
B-Net
Caltech256
77.83%
78.00%
80.84%
79.35%
79.27%
79.89%
81.71 %
Imagenet
70.29%
72.16%
74.89%
72.53%
72.33%
74.73%
75.00 %
SUN
24.56%
26.80%
26.26%
28.80%
29.15%
26.31%
30.54%
Average
57.56%
58.99%
60.66%
60.23%
60.25%
60.31%
62.42%
Table 3: Target-domain accuracy on 2 UDA tasks. Bold value represents the highest accuracy in each row.
Tasks
DAN
DANN
ATDA
B-Net
MNIST SSVNN
35.70%
52.80%
52.64%
-MNIST
71.10%
71.10%
85.00%
85.82 %
Table 4: Results of ablation study. Average target-domain accuracy on simulated digit WUDA tasks (Digit), 24 simulated human-sentiment WUDA tasks (Sentiment) and 3 real-world WUDA tasks (Real-world). Bold value represents the highest accuracy in each row.
Datasets
B w/o C
DCP-D
DCP-M
B-Net-S
B-Net-T
B-Net-ST
B-Net-M
B-Net
Digit
74.52%
59.19%
70.85%
71.93%
52.00%
72.27%
73.89%
75.82 %
Sentiment
63.57%
61.37%
63.39%
61.49%
61.12%
61.73%
62.21%
63.77 %
Real-world
62.27%
59.82%
62.34%
61.91%
60.87%
62.24%
62.17%
62.42%
WUDA tasks) and 3 real-world WUDA tasks. We consider following baselines: 1) B w/o C: train B-Net by Algorithm 1, without adding 1 f into the loss function of B-Net. 2) DCP-D: realize DCP via Decoupling (Malach and Shalev-Shwartz, 2017) to check data in MD and TD. 3) DCP-M: realize DCP via MentorNet (Jiang et al., 2018) to check data in MD and TD. 4) B-Net-S: train B-Net where the check is turned for Source data in MD. 5) B-Net-T: train B-Net where the check turned on for Target data in TD. 6) B-Net-ST: train B-Net where the checks are turned on for Source data in MD and Target data in TD. 7) B-Net-M: train B-Net where the check turned on for all data MD. Note that in the full B-Net, the checks are turned on for all data in MD and Target data in TD.
Comparing B-Net with w/o C reveals whether the constraint 1 takes effects. Comparing B-Net with DCP-D and DCP-M shows whether realizing DCP via Co-teaching is the optimal way. Comparing B-Net with B-Net-S, B-Net-T, B-Net-ST and B-Net-M reveals whether DCP is necessary. Table 4 reports average target-domain accuracy of above baselines and B-Net. As can be seen, 1) B-Net benefits from adding the constraint to the loss function L; 2) realizing DCP by Co-teaching is better than using Decoupling or MentorNet; and 3) DCP is necessary since accuracy of B-Net is higher than those of B-Net-S, B-Net-T, B-Net-ST and B-Net-M.
6 CONCLUSIONS
This paper opens new problem called wildly unsupervised domain adaptation (WUDA). However, existing UDA methods cannot handle WUDA well. To address this problem, we propose a robust one-step approach called Butterfly. Butterfly maintains four deep networks simultancously: Two take care of all adaptations; while the other two can focus on classification in target domain. We compare Butterfly with existing UDA methods on 32 simulated and 3 real-world WUDA tasks. Empirical results demonstrate that Butterfly robustly transfer knowledge from noisy source data to unlabeled target data. future, we will extend our Butterfly framework address open-set UDA when source domain contains noisy data.

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A REVIEW OF GENERATION OF NOISY LABELS
This section presents review two label-noise generation processes.
A.1 TRANSITION MATRIX
We assume that there is clean multivariate random variable (X,, Y,) defined X' y with a probability density (x Vs), where y = {1,..., K} is a label set with K labels. However, samples of (X,, Y,) cannot be directly obtained and we only can observe noisy source data from the multivariate random variable (X,, Y.) defined X' x y with a probability density Ps (r B.). Ps (3 Ds) generated by transition probability Pr(Y, = j|Y,= i). i... the flip rate from a clean label to a noisy label j. When we generate (. Ve) using Q. we often assume that Σy.= (Z,. Uv) = ΣE. =1 Pa (2., Ue), i.e., the class conditional noise (Liu and Tao, 2016). All these transition probabilities are summarized into transition matrix Q, where Qú = Pr(Y, = j|y,- = i).
The transition matrix Q is easily estimated in certain situations (Liu and Tao, 2016). However, in more complex situations, such as clothing IM dataset (Xiao et al., 2015), noisy source data is directly generated by selecting data from pool, which mixes correct data (data with correct labels) and incorrect data (data with incorrect labels). Namely, how the correct label is corrupted to j (i + j) is unclear.
A.2 SAMPLE SELECTION
Formally, there is multivariate random variable (X,, Y., Va) defined on X x V with probability density p (I,, Vs, Ve). where V = {0, 1} and V, 1 means "correct" and V means "incorrect". Nonetheless, samples from (X,, Y., V₂) cannot be obtained and we only observe (X,, Y,) from distribution with the following density.
Ps U.)
Σ v.=0
p P.,,, (F (v.),
(2)
where pi, (v.) = fx Ex p. (ze, yo: Uv da,, The density in Eq. (2) means that we lost the information
from Vg. If we uniformly select samples drawn from (1( Vs). the noise rate of these samples is PV (0). It is clear that the multivariate random variable (Xs, V, 1) is the clean multivariate random variable (X,, Y.) defined in Appendix 1. Then, (xx: Ys) used describe the density of incorrect multivariate random variable (X,, Y. 0). Using Ps (Zor Us) and qo(x,, Uo), (x.. No) can be expressed by the following equation.
(2 Ue) = (1- (1 Uo) + (Ie.
(3)
where p (0). Here, we do not assume Σ =1 Ps (x., Us) = ΣK= from incorrect data, scholars aim to recover the information of V., i.e., to select correct data from data drawn from (x., U.) (Han al., 2018; Jiang et al., 2018: 8; Malach and
= (I( ys). To reduce noise effects
2017).
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(a) MNIST
(b) SYND
Figure Visualization of MNIST and SYND.
B TRANSITION MATRIX Q
Precise definitions of Symmetry flipping and Pair flipping are presented below, where is the noise rate and K is the number of labels.
p
K-1
P
Symmetry flipping:
K-1
p
K-1
K-1
K
--p
0
0
p
0
0
Pair flipping:
0
1
P
p
1-P_
Following Han et al. (2018); Jiang et al. (2018), we can corrupt clean-label datasets manually using the noise transition matrix Q
C DATASETS VISUALIZATION
Figure 6 shows datasets: MNIST and SYND. Figure 7 shows datasets: Bing, Caltech256, Imagenet and SUN (taking "horse" as the common class).
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(a) Bing provided by Bergamo and Torresani (2010)
(b) Caltech256 provided by Griffin et al. (2007)
(c) ImageNet provided by Deng et al. (2009)
(d) SUN provided by Xiao et al. (2010)
Figure 7: Visualization of Bing, Caltech256, ImageNet and SUN (taking "horse" as the common class).
D THEORETICAL ANALYSIS
This section presents some interesting theoretical findings related to WUDA problem. We use following notations in this section: 1) space X' Rdd and y {1, ..... K) as label set; 2) (x. ūe). (2(2,, Ve) and qe (x (Ze, ya) represent densities of noisy, correct and incorrect multivariate random variables (m...v) defined on A' V, respectively'! and Px,, (I.x). Ps, (I.)) and qz. (ar..) are their marginal densities; and 3) Pr. (3te) repre- sents density of m.r.v. 3y defined on X: and 4) we use ((h(x), h((x)) to represent loss function between two labelling functions: and 5) we use (h) = (p. {p ((((()))) Mo)] and (h) = Ep, (x.. (((((t)))))) Ma)] to represent eepeetenteeppeceed risks the noisy and correct m.r.v;; and 6) we use R, h') BE,, (e.) ((,())((())))))))))))))))))))))) N((xx))), (n..)
(h h²) = (x,, [[(((z)), h/ (xx)) and (h, h') Ep,, (m. h(
represent expected
'There two common ways express the density of noisy m.r.v. (see Appendix A). One way is to use mixture of densities of correct and incorrect m.r.V..
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discrepancy between two labelling functions h, h' under different marginal densities; 7) the ground-truth and pseudo labeling function of the target domain are denoted by f((2)) and f((2)).
D.1 WUDA RUINS UDA METHODS
Theoretically, we analyze why existing UDA methods cannot well transfer useful knowledge from noisy source data D, to unlabelled target data D, directly. We first present theorem to show relations between (h) and (h).
Theorem 1. For any labelling function h X if (T' Us) is generated by transition matrix Q as demonstrated in Appendix I, we have
(b) Ro(h) + Pe (u.))
(n' (x.)(Q T)E(Mxx)))
where E(h(x,)) (((h(z,). 1),... ((h(xx). K)}" and nzz,) lDv,ix, Pr,Ixx,, (K|=))
If
Po (T.. Ms) is generated by sample selection as described in in Appendix A.2, we have
(b) (1 Rc)) + pB (w.) In (2,)) (x,))(((xz)))).
(5)
where (xx) = -1
9Y.11. (X
Remark 2. In Eq. (5), (x.) Inn (xr.)e(h(3:) represents the expected risk on the incorrect m.r.v. To en- sure to obtain useful knowledge from Ps. we need to avoid (h) As Egg, (2.) [ng (xx)) ((h(r)))) Specifically, we assume: there is a constant 0 < M2 < co such that E,,,, (x.) Ing (x. (()()((()))))) & R2(h) + M..
Theorem shows that the expected risk (h) only equals (h) when two cases happen: Q)Q / and P = O and 2) some special combinations (e.g., special Ps,- 9x., Q, and E) to make the second term in Eq. (4) equal zero
make the second term in Eq. (5) equal (h). Case 1) means that data in source domain is clean, which is not real in the wild. Case 2) almost never happens, since it is hard to find such special combinations when Pa,, q2,, Q and are unknown. Thus, Rt (h) has an essential difference with R.(h), Then, following proof skills in Ben-David al. (2010), derive the upper bound of (h) as follows. Theorem 2. For any labelling function h X + V, we have
(h( S
(h)
+
[Ro R. (h, (h, fo)
(Rh -2, (h)l
(5) risk on moisy data
(it) discrepuncy between distributions
(128) domain dissimilarity
+ (h) R.Oh) + (h, J.) Ro(
Re St) Re (h, Jt)
(6)
(iv) noise effects from source A.
(0) noise effects from target &
Remark To ensure that we can gain useful knowledge from f(( we assume: there constant Mj < 3o such that E,,, (e)))((()))))))))))))))))))))) fr (=)) S R. (,, fo) + M, and E,,, ((M))))))) s Re fi) Mr. where ga, (x) Ps. (z) (A) and A {z (x) + f((x))
It is clear that the upper bound of R, (h, ft), shown in Eq. (6), has 5 components. However, existing UDA methods only focus on minimizing (i) (ti) (Ganin et al., 2016; Ghifary et al., 2017; Long et al., 2015) or (i) + (ti) + (ii1) (Saito et al., 2017), which ignores terms (iv) and (v) (i.e., = A, + A₂). Thus, in theory, existing UDA methods cannot handle wildly unsupervised domain adaptation well.
D.2 TWO-STEP APPROACH IS A COMPROMISE SOLUTION
To reduce noise effects, straightforward solution is two-step approach. In the first step, we can train a classifier with noisy source data using Co-teaching (Han et al., 2018) and use this classifier to annotate pseudo
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labels for source data. In the second step. we use ATDA (Saito et al., 2017) to train a target-domain classifier with pseudo-label-source and target data.
Nonetheless, the pseudo-labeke labeled source data is still noisy. Let labels of noisy source data Ts be replaced with pseudo labels V/, after pre- pre-prceessing Noise effects A will become pseudo-label effects Ap as follows.
P
R (h) R. (h)) + (b, fo) - (h, fi) + +
pscudo-label-souree effects A
where (h) and (h, conrespond to (h) and (h, fo) in A. It is clear that the difference between Ap and A is A A,. The first term A' may be less than that in A. due to Co-teaching, but the second term in A'2 may be higher than that in A, since Co-teaching does not consider to minimize it. Thus, it is hard to say whether A < As (i.c., Ap < A). This means that two-step approach may not really reduce noise effects.
D.3 WHY DOES BUTTERFLY CAN ELIMINATE NOISE EFFECT?
To eliminate noise effects A, we aim to select correct data simultaneously from noisy source data and pseudo-labeled target data. In theory, we prove that noise effects will be eliminated if we can select correct data with high probability. Let Pūz represent the probability that incorrect data is selected from noisy source data, and Pbi represent the probability that incorrect data is selected from aseudo-labeles target data. Theorem 3 shows that - if pûi - 0 and phi - and presents new upper bound of R, (h,
Theorem 3. Given two m.Ev. (X., Ya, U.) defined on X x y x V and (Xt, U.) defined on X x V, under the assumptions in Remarks 2 and We E (0, 1), there are 8, and 8G, if Ey,, (mx) (n))(((((re)) f((z)) S (h, + Pú1 Pûi < 8g and Pbn < 8G. for any labeling function h, we will have | (h, Je, w.) R2, fo)l (1, (h, Ro(h)) 2e.
(8)
Moreover, if Púi S 8 and phs S Ec, we will have
(h, s
(h, us)
+
[ (h, Se, ue) PC St. us))
R
(6) risk on noisy data
(iS) discrepancy between distributions
(166) domain dissimilarity
2e
2x
(ix) noise effects from source
A.
(w) noise effects from target D.
where p'z, (x) = Pe, (2)1B())//PP( Re us) = (1 Por)) 'I Eg (e. [1g(()( ye6) Rg (h, Uo) (a, (u,((u() f((x))), 1/ (I., Uo u.) is the density of (X,, Y., U2). F. (x uz) is the density of
(1 Pa.) " (uel) F((x))) Rgg fc, u.)
(1 po,)
(Xe, Uc). Pu, = fx Ey, =1 F.5 (I', Vo. 0)dx, < 1, Pu. = -x 12t00 (x,, 0)dx; < 1, B = X/A and V {0, 1).
Remark 4. In Appendix H.3.1, we give precise definitions of Po1 and por and demonstrate the meaning of Ey,, (o.) ((((()))))) (xx)) s R2 (h, fi) + pô1 Mt (Remark 5).
Data drawn from the distribution of (X,, Y., U.) can be regarded as a pool that mixes the selected (u, = 1) and unselected (u, 0) noisy source data. Data drawn from the distribution of (X,, U2) can be regarded as a pool that mixes the selected (ug- = 1) and unselected (u, = 0) pseudo-labeled target data. Theorem 3 shows that if selected data have high probability to be correct ones (pi1 0 and pbl - 0), then A, and A, approach 0, meaning that noise effects are eliminated. This motivates us to find a reliable way to select correct data from noisy source data and pseudo-labed target data and build up one-step approach for WUDA.
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Why Butterfly? Guided by Theorem 3, a robust approach should check high-correettess data out (meaning Púi - O and Poi - O). This checking process will make (iv) and (u), 2c + 2c, become O. Then, we can obtain gradients of fe.5 (h, u.). R. (h, fr, Us) and 12,5 (h, Sa, ue) w.r.t. parameters of h and use these gradients minimize them, which minimizes (i) and (ti) as (i) + (ti) I R (h, uz) (h, fe, u.) R (h, fe, ue). Note that (iit) cannot be directly minimized since we cannot pinpoint clean source data. However, following Saito et al. (2017), we can indirectly minimize (izt) via minimizing N²50 (h, u²) - fe. (h, Sc. ug), as (zii) & (h, fa) + R. (h) < R (h, u.) + R (h, ft, ug) + 2c, where the last inequality follows Eq. (8). This means that robust approach guided by Theorem 3 can minimize all terms in the right side of inequality in Eq. (9).
To realize this robust approach, we propose a Butterfly framework (Algorithm 1), which trains four networks dividing into two branches (Figure 3). By using dual-checking principle, Branch-I checks which data correct in the mixture domain; while Branch-ll checks which pseudo-labeled target data is correct. To ensure these checked data highly-correct, we apply the small-loss trick based on memorization effects of deep learning Arpit et al. (2017). After prossarrpggg these checked data Bengio (2014), Butterfly can obtain high-quality DIR and TSR simultaneously in an iterative manner. Theoretically, Branch-I minimizes (id) + (v). This means that Butterfly can minimize all terms in the right side of inequality in Eq. (9). Note that empirical estimators of R ug), R,, (h, fo uz)
(i) (#i) + (iéd) + (iv); while Branch-II II minimizes
and R (h. ft, u,) (in Theorem 3) can be expressed using the loss function of Butterfly (see Eq. (1)).
Relations to Co-teaching. As Butterfly is related to Co-teaching, we discuss their major differences here. Although Co-teaching (Han et al., 2018 1) applies the small-loss trick and the cross-update technique to train dcep networks against noisy data, it can only deal with one-domain problem instead cross- problem. Besides, we argue that Butterfly is not simple mixtrue of Co-teaching and ATDA for two reasons.
First, network structure of Butterfly is different with that of ATDA and Co-teaching: Butterfly maintains four networks; while ATDA maintains three and Co-teaching maintains two. We cannot simply combine ADTA and Co-teaching to derive Butterfly. Second, we have justified that the sequential mixture of Co-teaching and ATDA (i.e., two-step method) cannot eliminate noise effects caused by noisy source data (see Section 4). Specifically, two-step methods only take care of part of noise effects but Butterfly takes care of the whole noise effects. Thus, Butterfly the first method eliminate noise effects rather than alleviate it.
Relations to TCL. Recently, transferable curriculum learning (TCL) is a robust UDA method to handle noise Shu et al. (2019). TCL uses small-loss trick to train the domain-adte adversarial neural network (DANN) Ganin et al. (2016). However, TCL can only minimize (i) + (ii) + (iv), while Butterfly can minimize all terms in the right side of Eq. (9).
RESULTS ON
WUDA TASKS
Tables 5 and 6 report the target-domain accuracy of each method for 24 human-sentiment WUDA tasks. For these tasks, B-Net has the highest average accuracy. It should be noted that two-step method does not always perform better than existing UDA methods, such as for 20%-noise situation. The main reason is Co-teaching performs poorly when pinpointing clean source data from noisy source data. Another observation is that noise effects is not eliminated like classification results on digit WUDA tasks. The main reason is that these datasets provide fixed features and we cannot extract better features in the training process. However, in digit WUDA tasks, we can gradually obtain better features for each domain and finally eliminate noise effects.
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Table 5: Target-domain accuracy on 12 human-sentiment WUDA tasks with the 20% noise rate. Bold values mean the highest values in each
Tasks
DAN
DANN
ATDA
TCL
Co+TCL
Co+ATDA
B-Net
B D
68. 68.28%
68 68.08%
70.31%
71.40%
67.81%
66.70%
71.84
B-+E
63.78%
63.53%
72.79%
65.08%
60.54%
68.89%
75.92%
B K-*K
65.48%
64.63%
71.79%
66.80%
61.23%
66.51% %
76.32%
D-+B
64.63%
64.52%
70.25%
67.33%
65.22%
68.04%
70.56
D-+E 65.33%
65.16%
69.99%
66.74%
64.55%
67.32%
73.73%
D-* 65.68%
66.28%
74.53%
68.82%
67.98%
72.20%
77.97%
E- 60.41%
60.15%
63.89%
63.13%
61.18%
61.08%
62.22%
E- 62.35%
61.67%
62.30%
62.93%
60.81%
59.77%
63.53%
E-KK 72.05%
71.51%
74.00%
75.36%
72.65%
70.85%
78.96%
K-B 59.94%
59.40%
63.53%
62.77%
60.71%
61.22%
63.36%
K+D 61.46%
61.51%
64.66%
64.16%
64.15%
64.94%
66.98%
K+E 70.60%
72.23%
74.75%
74.14%
68.95%
69.69%
76.96%
Average
65.00%
64.89%
69.40%
67.39%
64.65%
66.43%
71.53%
Table 6: Target-domain accuracy 12 human-sentiment WUDA tasks with the 45% noise rate. Bold values mean the highest values in each row.
Tasks
DAN
DANN
ATDA
TCL
Co+TCL
B-Net Co+ATDA
B-+
52.43%
52.98%
53.56%
54.44%
53.21%
54.32%
56.59
B-E
52.17%
53.50%
55.14%
54.14%
53.98%
57.34%
55.74%
B-*
52.89%
51.84%
51.14%
53.32%
51.77%
53.28%
57.00%
D-BB 53.11%
53.04%
54.48%
53.27%
54.85%
55.95%
55.15%
D-+E 51.30%
53.04%
54.21%
53.77%
55.63%
56.08%
58.91 %
D 52.15%
53.17%
57.99%
52.45%
58.10%
59.94%
66.20%
E- 51.38%
51.08%
52.54%
52.14%
54.88%
53.30%
54.93%
E 52.83%
51.24%
49.02%
52.57%
50.03%
49.62%
52.88%
E-K 54.21%
53.58%
51.66%
55.04%
56.15%
52.10%
56.12%
K-B 50.44%
51.77%
51.96%
51.50%
53.81%
52.59%
51.39%
K-D 52.20%
51.45%
52.86%
53.19%
55.69%
54.52%
53.53%
K-E 54.72%
53.33%
52.11%
53.46%
51.26%
52.62%
53.71%
Average
52.49%
52.50%
53.65%
53.27%
54.11%
54.31%
56.01% %
F EXPERIMENTAL. SETTINGS
F.1 NETWORK STRUCTURE AND OPTIMIZER
We implement all methods on Python 3.6 with NIVIDIA P100 GPU. We use MomentumSGD for opti- mization in digit and real-world tasks, and set the momentum as 0.9. We use Adagrad for optimization in muman-sentiment tasks because of sparsity of review data (Saito et al., 2017). Fi. F2, F.i and F,2 are 6-layer CNN (3 convolutional layers and 3 fully-connected layers) for digit tasks; and are 3-layer neural networks fully-connected layers) for human-sentiment tasks; and are 4-layer neural networks (4 fully-connected layers) for real-world tasks. The ReLU active function is used avtivation function of these networks. Besides, dropout and batch normalization are also used. The network topology shown in Figures and with the same network and optimization method, different
10. As deep networks highly nonconvex, initializations can lead to different local optimal. Thus, following Malach and Shwaey-Shwartz (2017), we also take four networks with the same architecture but different initializations as four classifiers.
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DIR
10 unte Schtmx
F
CNN
DIR
Branch-1
FC 2045 units RaL.U
F
cooee Sc5ol4 ReUU
mac--pool 3x3 2d zirdo
canT ExDre4
man pool 3x3
coor Ox 128
FC 5072 units Ru
FC 2048 units RaLU
Fii
TSR
Branch-I1
FC 10 unto Befmmxx
ReUU
Figure 8: The architecture of B-Net for digit WUDA tasks SYND MNIST. We added BN layer in the last convolution layer in CNN and FC layers in Fi and F22. We also used dropout in the last convolution layer in CNN and FC layers in F1. F2, Fai and Fia (dropout probability is 0.5).
DIR
FC unita ReLU
Softmax
Branch-I
DIR
FC
FC 2 units Softmas
Input 5000
FC
FC 2 units Softmax
Fu
TSR
Branch-I1
FC unita ReLU
Softma
F2
TSR
Figure 9: The architecture of B-Net for sentimettt WUDA tasks. We added BN layer in the first FC layers in Fi and Fz. We also used dropout in the first FC layers in Fi, F2, Fu and Fie (dropout probability set to 0.5).
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DIR
FC 128 units RaLU
FC
units ReiL
Branch-I
DIR
FC 1024 units Rei.U
FC 128
Softmax
Fi
Input 4096
128 unils ReL.U
FC 40 units
unils ReiL
Fu
TSR
Branch-l1
FC 1024 units
FC 128 unis ReLU
FC Softree
ReLl
TSR
Figure 10: The architecture of B-Net for real-world WUDA tasks. We added BN layer in the first FC layers in Fi. F2, Fu and Frz. We also used dropout in the first FC layers in F1, F2, Fui and Frz (dropout probability set to 0.5).
F.2 EXPERIMENTAL SETUP
For all 35 WUDA tasks and UDA tasks, T& is set to 5, Tmaz is set to 30. Learning rate is set to 0.01 for simulated tasks and 0.05 for real-world WUDA tasks and UDA tasks, "/ set to 0.05 for simulated tasks and 0.02 for real-world WUDA tasks and UDA tasks. Confidence level of labelling function in line of Algorithm is set to 0.95 for 8 digit tasks and 2 UDA tasks, and 0.9 for 24 numan-sentimen tasks and 0.8 for real-world WUDA tasks. 7 is set to 0.4 for digit tasks, 0.1 for human-sentiment tasks, 0.2 for real-world WUDA tasks and 0.1 for UDA tasks. n² maa tasks and 4000 for real-world WUDA tasks. Nmaz is set to 1000 for digit tasks and UDA tasks, and 200 for human- sentiment and real-workd tasks. Batch size is set 128 for digit, real- world WUDA tasks and UDA tasks, and 24 for numan-sentimen tasks. Penalty parameter is set to 0.01 for digit, real-world WUDA tasks and UDA tasks, and 0.001 for human-sentiment tasks.
15, 000 for digit tasks and UDA tasks, 500 for human-sentiment
To fairly compare all methods, they have the same network structure. Namely, ATDA, DAN, DANN, TCL. and B-Net adopt the same network structure for each dataset. Note that DANN and TCL use the same structure for their discriminate networks. All experiments are repeated ten times and report the average accuracy value and standard deviation (STD) accuracy values of ten experiments.
F.3 LINKS TO DATASETS
Digit datasets (MNIST and SYN Digit (SYND)) can be downloaded from official code of ATDA. The link https: htttts://githen
Sentiment datasets (Amazon products reviews) can be downloaded from the official code of marginal- ized Stacked Denoising Autoencoder (mSDA). The link is ststps://wwet cse. wustl.edu/mmeeheeee.. Code/mSDA. tar
Real-world datasets (BCIS) can be downloaded from the website of the project "A Testbed for Cross-Datasel Analysis": https:/ / /sstes google. com/ site/ crossda sesessaaaaseeee watatttteettttee hww.a///attttttteeeeeeeeeaeoe files ("setup DENSE decaf7", 1.3GB, decaf7 features).
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G RUNNING TIME
Table 7 shows the average running time of each method the task SYND-MMNIST. Although B-Net trains four networks, its running time is still comparable to most baselines.
Table 7: Running time for each method on the task SYND- >MNIST (minutes).
Methods
DAN
DANN
ATDA
TCL
Co+ATDA
B-Net
Time
17.17
9.02
17.17
14.04
18.28
20.55
H PROOFS
This section provides proofs of theorems demonstrated in the supplementary.
H.1 PROOF OF THEOREM
Proof. We will fist prove Eq. (4) (Case 1) and then prove Eq. (5) (Case 2).
Case 1. According definition of (h),,, we have
R2(h) (.((((.))))))
K
((h(x.), Ds) (.. dar.
((h(xx), Ds)D8, (Faless)en Pe, (xa)
9.=1
s (x., ((((ss)))))) (x.))os
(10)
where E(h(x.)) = 1)).
1). ((((x)).))))))))))))))))))) K)J" and 7(x.) =
Pr, (K(x,)) Ac-
cording to definition of the transition matrix Q, we know that
(xx) (x.)).
(11)
where nTx,)) [py,,x, (1/x),, Pr,Ix, (K x TT Substituting Eq. (11) into Eq. (10), have
x (h) / nt (F(=))@((h((z))1p (x. (xx),r,
(xx) + " (x.) ()ee-(()e)))))))))) (xr))r. = (R) + E (=) - n)((h(x))).
-
Hence, Case 1 is proved.
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Case 2. According definition of (h) and Eq. (3), we have
(h) (x.. ..) (((((()))) (..( ū.)]
((((as), (1s Us)
1==1
/
Σ
((h(2.). ppp + Mal(
v==1
(1 p) Jxx Σ
(D) + P E
e(h(xr), No )a vadde
Na
= (1 p) Rb +
Σ
E(h(xe) v.).v............ (Ve 20 1x). (xr))dxa.
(12)
x yaml
Let 77 (2s) 10,,,x (1/2r)), ... Qv, 1x, (K] (x have
(b) (1 p) (h(h)) p (w.) (n.)
Hence, Case 2 proved.
H.2 PROOF OF THEOREM 2
Proof. For any labelling function h, have
(h, ft) = (h, fi) + (h) (b) + Rh,
it)(h) (h, St) (h) (h, ft) (h) + R.(h) (h)
+ Rz fi) Rg (h,
(13)
Since we do not know fe. we substitute following equations into Eq. (13),
Re fa) = Re fi) Rh, ft) Re fo), lo, ft) (h, f() + (h, fi) Ro,h, fi), Ro ft) RR(h, fi) + (h, fo) Ro,
Then, we have
fc) = (h) + Ra (h, (h, + R. fi) R (h)h)
+ (h) R2(h) + R, f() R, fi) (h, fe)
Re(h, fi)
< (h) + [h, j:) R,, f:) + [R, f() -R,
+ (h) - (h)) + (h, fi) - (h, fol (h, fi) - (h.
Hence, this theorem is proved.
H.3 PROOF THEOREM
H.3.1 PRELIMINARY
Before stating the proof, first present random variable below.
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Let (X,, Vi) be a m.r.v. defined on X x V with respective a density p (xz, 2t), where V {0, 13. V2 can be regarded as perfect-selection random variables. Namely, 1 = means fe((x)) = fe(xxe) and V, = 0 means fe(x)) * fe(z)). Let PV, (v)) be the marginal density of p. (2), It is clear that, higher value of pi, (V:11 1) means that Je is more like ft. In following, we use Pvx represent P 1).
Then, we will show 1) relation between (X Y,, V3) and (X,, Y,: U,), 2) relation between (Xe, Vi) and (X,, U2) and definitions of poi and Po1- Based on (Xe, V2) and (X,, Y,, V.) defined in Appendix A.2, the densities of YX,, U,) and (X,,U, can be expressed as follows.
Fx X.U. (Is, Vala) PooPP X. (1., vo|0) + PiN X.V (T., Wols).l),
Iu (z/1i) = Phi X.1V, (z, + pi. x.IV, (xx|1),
where Pj: = Pr(V, j|U, = i) represents the probability of the event: V, j given U, = i, i
Pr(V
j|U; = i) represents the probability of the event: V, = given U, = i (i.j = 0)1). Since p. (s( Us) Do
P',,,,IV, (Is. V,)) (1 U.) Y.Iv, (Ix: Ya (0), Px (2x(0) (x. = Px, (m))1
(A) = Uz, (1it)
and Px, (1x|1) = Pr, (xx)) 1 B (24) Pr, (B) = Vo, (2x) (A (x: fa(x) # f((x)), B = X/A), we have
Fx Y,U, (I, Us ()) = Po:g. (1 Uv)) + (F.,
(14)
1x, (xeli) Por (x1) + Pid'ss (x.).
(15)
Next, we give lemma to show relation between R.Th (h, u,) and (h).
Lemma 1. Given the multivariate random variable (X Y,, Uz) with the probability (I. Usi u.) and Eq. (14), we have
| (h, u.) (h)l S Pû1 max ( (1(hha)))))()()))))))))))))))))) y.)l R.(h))
(16)
Proof. According to definition of RP50 (h, us) in Theorem 3, we have
K
(h, Un) = - (1-Pu.)
Σ Σ
ug (.((h(z=). (I.: Vor U, )dx
X 0.
= -11- - Pu.) 11
(M(xs)).s)PP V., (T.. vall)(0, (1)))
X Va=1
(0) (1 Pu,) 1 - prn)) [ Σ ((h(xs), (Pin (o) + PiLPs (ee Uo)) das N1=1
K
Pún Eg, (u,, (r.. ((((((x)) No)l + Ro),,
where (a) is based on the definition of Pu. and Eq. (14). Thus, we have (ig (h, u.) R. (h)) = (((c))...)))(((())))))))))) (1 Rb))
< pi max
((()))
This lemma is proved.
Similar with Lemma 1, we can obtain Reg (h. Je,we) w.) (h, Jo)l s pbi (ex f((x,))), Ra, Jo)-
(17)
Then, give another lemma to show relation between R, fer u.) and R, fo).
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Lemma 2. Given the multivariate random variable (X,, U2) with the probability (2 ue) and Eq. (15), if By, (as) fi - R. (h, fi) + Pô1 Mc then we have
R Fo, un) - Rc, foll S poi m (s, (aa)), Ro + PhiP11 M,.
(18)
Proof. According definition of R2 (h. ue) in Theorem have
ue)
R (h, Fr, u2) = ((1 - (P.) Σ (u((((z)) (x,, ue uz)d
u1=0
= =(1 (1-Puc)) / x
puu))
(1 (1)dz,
(0) - (P.) (1 (1-
P Pu)) {
+ PIIP (oxl1))
Bo (z.) ((h(ss)))))) pin / ((Maa)) (ErVV 1)dx
( Poi
+ i / ((M(=s). ( = 1)dxx
Φi /
Ba, (1,
(x.)dr:
= Pbi Be. (2,
pi (a
(19)
where (a) is based the definition of Pv, and Eq. (14) and (b) is based on the definition of (fe(zx)) Fc(xx)
when V/2 = 1). Since Epg, Ep,,(..))(( (((((((())) - (2, fe) + Po1 M, we have
(h, Fr, uz) S pin Bg, (eN + A1 (Ro, + P01 Mc).
(20)
Thus, we have
R (h, fu, wi) Re(
Rehh, fol
S Beer
Mc) M.)
Ra(h, foll
+ Mel Jpb (et R. PinPo
S P61 max max (B
(2x) ((M))))))) R. J.)) + PiuPor M,.
This lemma is proved.
Remark In Lemma 2, the assumption Ey, (a) ((())) < Re(h, + P61 M₁ means that the expect risk restricted in B (i.e., Ep,, (=))(((((z))) f(()))) represent the true risk R₃ (h. when pôr is small, where B fa f(x) ).)). In Butterfly, it is equivalent that pseudo labels provided by noisy source data are more useful if we can select more correct data from noisy source data. this assumption fails, we cannot gain useful knowledge from f even when we can perfectly select correct data from pseudo-labeled target data (ph, 0).
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Inequalities (16), (17) and (18) show that if we can avoid annotate incorrect data as "correct" (Po: and Poi 0), we have (h, u.) = (h)h), R. (h, fc. u.) R, fi) and R (h. ft. uy) (t.))
(h, ft). Nonetheless, Pôi and phi never equal O, and Egg, (z.) ((((()(()))) [e(cr))] may equal +oo for some h. In next section, prove that, under the assumption Remarks 2 and 3, F (h, u.) + (h), Agg (h, ft, ue) - Ra fi) and (h, fi, ue) - Re if P01 and Pi1 O. Moreover, we give new upper bound of Re (h,
(xx))) and
H.3.2 PROOF OF THEOREM 3
Now, we prove Theorem 3 as follows.
Proof. We first prove upper bounds of [R u,) (.))-R,(h)) (h)l, R (h, fh, u2) -R,)- f.) and R.. (h, ux) (h, [t) under assumptions in Theorem 3.
Based Lemma 1, have
Tigghh u.) - R. (h)) = (( (1 (..))
I l (Ro(h) + M.) - Pūz (1))
pûr Ma.
Similar, we have
1Rg Fi, u.) - Ro,h, S phi Mr
[25 (h, fe, ue) [h, fo)l S Mr + pi Mc.
Since M, and Mr are positive constants, it is clear that R (h, u.) Rh( R (h, F we) + Roh fe) and RS (h, for u,) + (h, ft) when Pō: -> and Ph: - O. Specifically, Ve E (0, 1), let 5, e/M, and 6, = e/ m Ms, pi M.}. When Por < 6, and por < dr we have
R (h, u.) - (b)) + R (h, Fe, uz) - -R, foll < 2c
[2 fr, uz) Rh, fe)l 2E.
Hence, we prove the Eq. (8). In following, we give a new upper bound of R₂ (h, ft). Call back to Theorem 2, we replace 1) (h) with (h, u.), 2) Re(h, Fo) with R (h, fir uz). 3) R. (h, fo) with (h, fc, ue). Then, we have
(h, ft) S (h, u.) + R. (h, Fr, u.) Rg (h, Fr, u.))l + RR (h, f.) Ro(h)l
+ RR (h, un) (h)) + |R,0 (h, fc. ui) R. (h. fa) + [Re fo) - R (h, fe, uel-
Let pô1 x 6g and pbi S oz, we have
ft) < Re (h, us)
R (h, Jr, ue) Re. (h, Fr, u.)
Ra f.) - Ra
(4) risk noisy data
(i)) diserepancy between distributions
(668) domain dissimilarity
2c
2c
(30) noise effects from source A
(1) noise effects from target A
Hence, we prove this theorem.
25


Reviews:
[{"review_id": "rJeaTeMitr", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper proposes a new problem setting in the domain adaptation field. Since it is impossible to obtain perfectly clean labeled source data in the real world, existing UDA methods cannot well handle real-world data. However, in wildly unsupervised domain adaptation (WUDA), we do not need a perfectly clean source data, which means that WUDA problem is a more general and realistic problem than existing ones. \n\nTo address WUDA problem, the authors proposed Butterfly framework (based on dual checking principle) to simultaneously reduce the 1) noise effects in source domain and 2) distributional discrepancy between source and target domains. They tested the proposed method on simulated and real-world WUDA tasks (35 tasks in total), and the accuracy of proposed method is higher than those of representative UDA methods. They claim that Butterfly can eliminate noise effect, which is strongly supported by Figures 2, 4 and 5. They also present the ablation study to show that each part in Butterfly is meaningful. \n\nIn general, this paper is easy to follow and clearly presents the main idea and learning procedures of Butterfly. Since WUDA, as a new problem, could lead a new research direction in the domain adaptation field, this paper should be presented in ICLR 2020. Detailed comments can be seen below.\n\nPros:\n\n+ WUDA, as a new problem, is very important for the domain adaptation field.\n+ Butterfly, as a solution to WUDA, outperforms representative UDA methods on simulated and real-world WUDA tasks.\n+ All claims are strongly supported by experimental results, and ablation study shows that each part in Butterfly is a necessary component.\n+ Following Ben-David's paper, this paper also presents an upper bound of the target domain risk. This is 1) the first WUDA bound and 2) probably the first DA bound related to pseudo labelling function. The conditions in Remark 3 are very interesting.\n+ It is very nice to use noise effect \\Delta to explain the abnormal phenomenon in experiments.\n\nCons:\n\n- The color scheme of figures is not friendly to color-blind people. The authors should do different line styles or marker styles.\n- The interaction between DIR and TSR happens via shared CNN, right? The authors should explain this in the caption of Figure 3.\n- When T = 1, you directly use source data as the pseudo-labeled target data since there are no pseudo-labeled target data in the first step (based on Algorithm 1). Is that correct? If yes, the authors should explain this in Figure 3 and the description of Algorithm 1. If no, please give a detailed explanation.\n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly."}, "extra_text": {}}, {"review_id": "HylUhej6KH", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper presents a method for unsupervised domain adaptation. The problem is well known in literature and follows the setting of labeled source and unlabeled target set. This work proposes the “butterfly network” suitable to train on noisy data (labels) and assign pseudo-labels to the target set. The butterfly network consists in two branches one for source+target and one for target only data. Both use the same optimization objective and a “checking” mechanism has been devised for pseudo-labelling the data.\nDecision: weak reject\nMotivation: This paper has some merit but does not present the method in a clear way, it requires some additional effort to go through the method and retrieve from the appendix information useful for full understanding. For example algorithm 2 is a key component of the method and is in appendix, notation is not always clear nor explained (the loss in algorithm 2 is ), the networks F_1, F_2, F_t1, F_t2 could be added in figure 3 for more clear understanding and R(t) along with u_i could be more clearly defined (how to obtain u_i is still not clear to me after several re-reading of the paper). The introduced losses should be better justified. \nAnyway, as I said the paper has some merit, it provides many insights and extensive analysis on “butterfly” method for unsupervised domain adaptation. The experimental section is extensive and demonstrates improvement in performance using this method compared to state-of-the-art, even though for some \"real world\" datasets (e.g. SUN, Caltech, ImageNet) the improvement is not so significant as in the case of MNIST-SYND. Could the authors provide results on MNIST-SVHN to help compare with other papers in literature? Did the authors observe the same evolution of the accuracy (decreasing and increasing after a few epochs) also on the \"real world\" datasets as in MNIST-SYND?\nReplicability: as I said the method is not really clearly explained and therefore I am not confident I could implement and replicate the results. This not because I think the method is complex but because some key components that I pointed out previously about the method are not clear and I strogly believe these are key components to replicate the results.\n", "extra_scores": {"experience_assessment": "I have published in this field for several years.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "HJlcZBJLYH", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper introduces the idea of wildly unsupervised domain adaptation, where the source labels are noisy and the target data is unsupervised. To tackle this, the authors propose an architecture based one two branches: one acting on the mixed source-target data and the other on the target data only. During training, each branch is updated using the idea of co-teaching, by finding the samples with the lowest loss values. Pseudo-labeling is then applied to the target data, and the process iterates.\n\nOriginality:\n- In essence, the proposed method combines co-teaching (Han et al., 2018) and pseudo-labeling (Saito et al., 2017). While it goes beyond the naive two-stage approach, used here as a baseline, the technical novelty remains limited.\n- The main novelty consists of using two branches to model the two domains. However, the necessity for the second branch is not very clearly explained, and remains obscure to me, since the first branch already acts on the mixed source-target data.\n\nClarity:\nIn addition the fact that, as mentioned above, the design of the overall framework is not entirely well motivated, I found the paper somewhat hard to follow. In particular:\n- One has to go to the appendix to find Alg. 2, which describes one of the key components (the Checking method in Alg. 1). The steps performed by Alg. 2 are not explained anywhere.\n- In Alg. 1, it seems surprising that \\tilde{D}_T^l is initialized as \\tilde{D}_s, since, according to Fig. 3, the second branch should act on the target data only.\n- In Alg. 1, the authors do not explain how they initialize the values R(T) and R_t(T).\n- I would expect that, to obtain meaningful results from the Checking method, the parameters of the networks F_1, F_2, F_{t1} and F_{t2} should already be initialized to reasonable values. Can the authors comment on the initialization procedure?\n- In Alg. 2, how are the inner minimization problems solved? Are u_1 and u_2 truly enforced to be binary variables? How fast can one obtain the solutions to these problems?\n- In Fig. 1, it is not clear to me what the term Interaction between the two branches represent. From the text, I could not find any reference to explicit interactions between the branches.\n- In Eq. 1, the loss function \\ell() is not defined (although I imagine that it is the cross-entropy).\n\nExperiments:\n- The experiments show the good behavior of the method. However, while I understand the motivation behind defining the two-stage baseline using ATDA, which is used in the proposed method, there seem to be no strict constrain on using this specific method in the two-stage scenario. For example, based on the results in Table 1, one might rather want to use TCL as the second stage, i.e., have a baseline Co+TCL. \n- As I mentioned before, the motivation behind the second branch in the framework is not clear to me. I would appreciate it if the authors could explain the reasoning behind this branch and evaluate their method without it.\n\nSummary:\nThe novelty of the proposed method, relying on a combination of co-teaching and pseudo-labeling, is limited. Furthermore, the clarity of the paper could be significantly improved.\n", "extra_scores": {"experience_assessment": "I have published in this field for several years.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The authors proposed a new problem setting called Wildly UDA (WUDA) where the labels in the source domain are noisy. They then proposed the "butterfly" method, combining co-teaching with pseudo labeling and evaluated the method on a range of WUDA problem setup. In general, there is a concern that Butterfly as the combination between co-teaching and pseudo labeling is weak on the novelty side. In this case the value of the method can be assessed by strong empirical result.  However as pointed out by Reviewer 3, a common setup (SVHN<-> MNIST) that appeared in many UDA paper was missing in the original draft. The author added the result for SVHN<-> MNIST  as  a response to review 3, however they only considered the UDA setting, not WUDA, hence the value of that experiment was limited. In addition, there are other UDA methods that achieve significantly better performance on SVHN<->MNIST that should be considered among the baselines. For example DIRT-T (Shu et al 2018) has a second phase where the decision boundary on the target domain is adjusted, and that could provide some robustness against a decision boundary affected by noise.

Shu et al (2018) A DIRT-T Approach to Unsupervised Domain Adaptation. ICLR 2018. https://arxiv.org/abs/1802.08735

I suggest that the authors consider performing the full experiment with WUDA using SVHN<->MNIST, and also consider the use of stronger UDA methods among the baseline. 
Decision: Reject