Dirichlet-based Uncertainty Calibration for Active Domain Adaptation
Authors: Mixue Xie
Shuang Li
Rui Zhang
Chi Harold Liu
Venue: ICLR 2023 notable top 25% (2023)
Keywords: domain adaptation
active learning
uncertainty
Dirichlet

Abstract: Active domain adaptation (DA) aims to maximally boost the model adaptation on a new target domain by actively selecting limited target data to annotate, whereas traditional active learning methods may be less effective since they do not consider the domain shift issue. Despite active DA methods address this by further proposing targetness to measure the representativeness of target domain characteristics, their predictive uncertainty is usually based on the prediction of deterministic models, which can easily be miscalibrated on data with distribution shift. Considering this, we propose a Dirichlet-based Uncertainty Calibration (DUC) approach for active DA, which simultaneously achieves the mitigation of miscalibration and the selection of informative target samples. Specifically, we place a Dirichlet prior on the prediction and interpret the prediction as a distribution on the probability simplex, rather than a point estimate like deterministic models. This manner enables us to consider all possible predictions, mitigating the miscalibration of unilateral prediction. Then a two-round selection strategy based on different uncertainty origins is designed to select target samples that are both representative of target domain and conducive to discriminability. Extensive experiments on cross-domain image classification and semantic segmentation validate the superiority of DUC.

Published as a conference paper at ICLR 2023
DIRICHLET-BASED UNCERTAINTY CALIBRATION FOR ACTIVE DOMAIN ADAPTATION
Mixue Xie, Shuang L Rui Zhang, Chi Harold Liu Beijing Institute of Technology, China
(mxxle, e, shuangli i, zhangrui 2 edu. en, liuchi Liuchi02@gma 020 i com
ABSTRACT
Active domain adaptation (DA) aims to maximally boost the model adaptation on a new target domain by actively selecting limited target data annotate, whereas traditional active learning methods may be less effective since they do not consider the domain shift issue. Despite active DA methods address this by further proposing targetness to measure the representativeness of target domain characteristics, their predictive uncertainty is usually based on the prediction of deterministic models, which can easily be miscalibrated on data with distribution shift. Considering this, we propose a Dirichlet-bar basee Uncertainty Calibration (DUC) approach for active DA, which simultaneously achieves the mitigation of miscalibration and the selection of informative target samples. Specifically, we place a Dirichlet prior the prediction and interpret the prediction as a distribution on the probability simplex. rather than a point estimate like deterministic models. This manner enables to consider all possible predictions, mitigating the miscalibration of unilateral prediction. Then two-round selection strategy based on different uncertainty origins is designed to select target samples that are both representative of target domain and conducive to discriminability. Extensive experiments on cross-domain image classification and semantic segmentation validate the superiority of DUC.
INTRODUCTION
Despite the superb performances of deep neural networks (DNNs) on various tasks (Krizhevsky it al. 2012 Chen et al., 2015), their training typically requires massive annotations. which poses formidable cost for practical applications. Moreover, they commonly assume training and testing data follow the same distribution, making the model brittle to distribution shifts (Ben-David et al. (010)) Alternatively, unsupervised domain adaptation (UDA) has been widely studied, which assists the model learning domain (Ganin & Lempitsky 2015) Long et al., 2018). Despite the great advances of UDA, the unavailability of target labels greatly limits its performance, presenting huge gap with the supervised counterpart. Actually, given an acceptable budget, a small set of target data can be annotated to significantly boost the performance of UDA. With this consideration, recent works (Fu al. 2021 Prabhu et al. 2021) integrate the idea of active learning (AL) into DA, resulting in active DA.
unlabeled target domain by transferring the knowledge from a labeled source
The core of active DA is to annotate the most valuable target samples for maximally benefiting the adaptation. However, traditional AL methods based on either predictive uncertainty or diversity are less effective for active DA, since they do not consider the domain shift. For predictive uncertainty (e.g., margin (Joshi et al. 2009), entropy (Wang & Shang 2014)) based methods, they cannot measure of samples. As result, the selected samples are often redundant and less informative. As for diversity based methods (Sener & Savarese] [018 Nguyen & Smeulders 2004), they may select samples that are already well-aligned with source domain (Prabhu al. 2021). Aware of these, active DA methods integrate both predictive uncertainty and targetness into the selection process (Su et al., 2019 Fu et al.) 2021 Prabhu et al. (02I). Yet, existing focus is on the measurement of targetness, e.g., using domain discriminator (Su et al. 2019) or clustering (Prabhu et al. 202T). The predictive uncertainty they used still mainly based on the prediction of deterministic models, which is essentially a point estimate (Sensoy al.
the surgettropresentaaiveene..
2018) and can easily be
miscalibrated on data with distribution shift (Guo et al., 2017). As in Fig. [(a) standard DNN is wrongly overconfident most target data. Correspondingly, its predictive uncertainty is unreliable.

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Published as a conference paper at ICLR 2023
Parresttraa Sandard SKW
Expacted Crinpp of icchrrdaedddd
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(a) Standard DNN v.s. Dirichlet-based Model (b) Examples of different prediction distributions Figure I: (a): point-estimate entropy of DNN and expected entropy of Dirichlet- baaee model, where colors of points denote class identities. Both models are trained with source data. (b): examples of the prediction distribution of three "monitor" images on the simplex. The model is trained with images of "keyboard", "computer" and "monitor" from the Clipart domain of Office- dataset. For the two images from the Seal-World domain, the entropy of expected prediction cannot distinguish them, whereas Udi and Udota calculated based on the prediction distribution can reflect what contributes more to their uncertainty and be utilized to guarantee the information diversity of selected data.
To solve this, we propose a Dirichlet-based Uncertainty Calibration (DUC) method for active DA, which is mainly built on the Dirichlet-basee bassdd evidential deep learning (EDL) (Sensoy et al.) 2018). In EDL, a Dirichlet prior is placed on the class probabilities, by which the prediction is interpreted as distribution the probability simplex. That is, the prediction is no longer point estimate and each prediction occurs with a certain probability. The resulting benefit is that the miscalibration of unilateral prediction can be mitigated by considering all possible predictions. For illustration, we plot the expected entropy of all possible predictions using the Dirichlet-based model in Fig, [(a]] And we see that most target data with domain shift are calibrated to have greater uncertainty, which can avoid the omission of potentially valuable target samples in deterministic model based- methods.
Besides, based on Subjective Logic (Jøsang) 2016), the Dirichlet-bascd evidential model intrinsically captures different origins of uncertainty: the lack of evidences and the conflict of evidences. This property further motivates us to consider different uncertainty origins during the process of sample selection, so as to comprehensively measure the value of samples from different aspects. Specifically, we introduce the distribution uncertainty to express the lack of evidences, which mainly arises from the distribution mismatch, i.e., the model is unfamiliar with the data and lacks knowledge about it. In addition, the conflict of evidences is expressed as the data uncertainty, which comes from the natural data complexity, c.g., low discriminability. And the two uncertainties are respectively captured by the spread and location of the Dirichlet distribution on the probability simplex. As in Fig. [[b]] the real-world style of the first target image obviously differs from source domain and presents broader spread on the probability simplex, i.e., higher distribution uncertainty. This uncertainty enables us to measure the targetness without introducing the domain discriminator or clustering, greatly saving computation costs. While the second target image provides different information mainly from the aspect of discriminability, with the Dirichlet distribution concentrated around the center of the simplex. Based on the two different origins of uncertainty, we design two-round selection strategy to select both rereestrprreeentative and discrimmnabilltyyconee conducive samples for label query.
We explore the uncertainty miscalibration problem that is ignored by existing active DA methods, and achieve the informative sample selection and uncertainty calibration simulta- neously within a unified framework. 2) We provide novel perspective for active DA by introducing the Dirichlet-basee evidential model, and design an uncertainty origin-aware selection strategy to comprehensively evaluate the value of samples. Notably, no domain discriminator or clustering is used, which is more elegant and saves computation costs. 3) Extensive experiments on both cross- domain image classification and semantic segmentation validate the superiority of our method.
Contributions:
1)
2 RELATED WORK
Active Learning (AL) aims to reduce the labeling cost by querying the most informative samples to annotate (Ren et al. 2022). and the core of AL is the query strategy for sample selection. Committee- based strategy selects samples with the largest prediction disagreement between multiple classifiers strategy chooses a set of representative samples in the latent space by clustering core-set selection (Nguyen & Smeulders
(Seung et al.) 1992. Dagan & Engelson 1995). Representative-
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2004 Sener & Savarese, 2018). Uncertainty- strategy picks samples based on the prediction confidence (Lewis & Catlett 1994), entropy (Wang & Shang 2014 Huang et al. 2018). etc, to annotate samples that the model is most uncertain about. Although these query strategies have shown promising performances, traditional AL usually assumes that the labeled data and unlabeled data follow the same distribution, which may not well deal with the domain shift in active DA.
Active Learning for Domain Adaptation intends to maximally boost the model adaption from source target domain by selecting the most valuable target data annotate, given a limited labeling budget. With the limitation of traditional AL, researchers incorporate AL with additional criteria of targetness (i.e., the representativeness of target domain). For instance, besides predictive uncertainty, AADA (Su et al.] (019) and TQS (Fu et al. (021)) additionally use the score of domain discriminator to represent targetness. Yet, the learning of domain discriminator is not directly linked with the classifier, which may cause selected samples not necessarily beneficial for classification. Another line models targetness based on clustering, e.g.. CLUE (Prabhu et al. 2021) and DBAL (Deheeger et al., 2021 Differently, EADA (Xie et al., 2021 represents targetness as free energy bias and explicitly reduces the free energy bias across domains to mitigate the domain shift. Despite the advances, the focus of existing active DA methods is the measurement of targetness. Their predictive uncertainty is still based on the point estimate of prediction, which can easily be miscalibrated on target data.
Deep Learning Uncertainty measures the trustworthiness of decisions from DNNs. One line of the research concentrates on better estimating the predictive uncertainty of deterministic models via ensemble (Lakshminarayanan
al. 2017] calibration (Guo et al.. (017). Another line explores to combine deep learning with Bayesian probability theory (Denker & LeCun 1990; Goan & Fookes) 2020). Despite the potential benefits, BNNs are limited by the intractable posterior inference and expensive sampling for uncertainty estimation (Amini et al. (020). Recently, evidential deep learning (EDL) (Sensoy et al., 2018) is proposed to reason the uncertainty based on the belief or evidence theory (Dempster] 2008 Josang, 2016). where the categorical prediction is interpreted as distribution by placing a Dirichlet prior on the class probabilities. Compared with BNNs which need multiple samplings to estimate the uncertainty. EDI. requires only single forward pass, greatly saving computational costs. Attracted by the benefit, TNT (Chen et al., 2022) leverages it for detecting novel classes, GKDE Zhao et al. (2020) integrates it into graph neural networks for detecting out-of- distribution nodes, and TCL (Li et al. (022) utilizes it for trustworthy long-tailed classification. Yet, researches how to effectively use EDL for active DA remain scarce.
3 DIRICHLETT-BSED UNCERTAINTY CALIBRATION FOR ACTIVE DA
3.1 PROBLEM FORMULATION
Formally, in active DA, there are labeled source domain 8= {2 ; vf f2=1 and unlabeled target domain T { J 1. where yf E 21 , C} is the label of source sample æ; and C' is the number of classes. Following the standard setting in (Fu et al., 2021), we assume that source and target domains share the same label space y {1, 1, 2, ..., Cj but follow different data distributions. Meanwhile, we denote a labeled target set as T which is an empty set initially. When training reaches the active selection step. b unlabeled target samples will be selected to query their labels from the oracle and added into T Then we have target set. Such active selection step repeats several times until reaching the total labeling budget B.
T U TV, where T is the remaining unlabeled
To get maximal benefit from limited labeling budget, the main challenge of active DA is how to select the most valuable target samples to annotate under the domain shift, which has been studied by several active DA methods (Su et al., 2019 Fu et al.) 202 Prabhu et al., 2021: Deheeger et al.. 2021 et al. 2021). Though they have specially considered targetness to represent target domain characteristics, their predictive uncertainty is still mainly based on the prediction of deterministic models, which et al. 2017] Guo et al. 2017). Instead, we tackle active DA via the Dirichlet-based evidential model, which treats categorical prediction as distribution rather than point estimate like previous methods.
easily be miscalibrated under the domain shift, found in (Lakshminarayanan
3.2 PRELIMINARY OF DIRICHLET-BASE EVIDENTIAL MODEL
Let us start with the general C-class classification. X denotes the input space and the deep model f parameterized with 0 maps the instance X' into C-dimensional vector, i.e., f X -> RC, For
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standard DNN, the softmax operator is usually adopted the top of f convert the logit vector into the prediction of class probability vector A while this manner essentially gives a point estimate of and can easily be miscalibrated on data with distribution shift (Guo et al. 2017).
To overcome this, Dirichlet-based evidential model is proposed by Sensoy et al. (2018), which treats the prediction of class probability vector p the generation of subjective opinions. And each subjec- tive opinion appears with certain degrees of uncertainty. In other words, unlike traditional DNNs, evidential model treats p as a random variable. Specifically, a Dirichlet distribution, the conjugate prior distribution of the multinomial distribution, is placed over to represent the probability density of each possible p. Given sample z₁ the probability density function of p is denoted as
T and p(p|z;, 0) = Dir(pla,) = I ((ae)
Po
if PE
otherwise . aie > O, (1)
where or is the parameters of the Dirichlet distribution for sample æt, r(.) is the Gamma function and A C is the C-dimensional unit simplex: AC {pl Ee Pe and Vp., 0 S Pe S 1}. For Og it can be expressed as a = ( 0)), where g(-) is a function (e.g., exponential function) to keep a; positive. In this way, the prediction of each sample interpreted as a distribution over the probability simplex, rather than point on it. And we can mitigate the uncertainty miscalibration by considering all possible predictions rather than unilateral prediction.
Further, based on the theory of Subjective Logic (Jøsang) 2016) and DST (Dempster 2008), the parameters a, of Dirichlet distribution closely linked with the evidences collected to support the subjective opinion for sample Z;, via the equation e; a; 1 where e; is the evidence vector. And the uncertainty of each subjective opinion p also relates to the collected evidences. Both the lack of evidences and the conflict of evidences can result in uncertainty. Having the relation between or and evidences, the two origins of uncertainty are naturally reflected by the different characteristics of Dirichlet distribution: the spread and the location over the simplex, respectively. As shown in Fig. 1(b) opinions with lower amount of evidences have broader spread on the simplex, while the opinions with conflicting evidences locate close to the center of the simplex and present low discriminability.
Connection with softmax-based DNNs. Considering sample x;, the predicted probability for class c can be denoted as Eq. (2), by marginalizing over p. The derivation is in Sec. E.1 of the appendix.
Ply = cle,, 0) p(y = clp)p(ple. O)dp-
Oli
g(fa(Tre 0))
([[Dir(p:)a))) (2)
Ei 06k
Ee 2==1 (w, 0))
Specially, if g(.) adopts the exponential function, then deftmax-based DNNs can be viewed as predicting the expectation of Dirichlet distribution. However, the marginalization process will conflate uncertainties from different origins, making it hard to ensure the information diversity of selected samples, because we do not know what information the sample can bring.
3.3 SELECTION STRATEGY WITH AWARENESS OF UNCERTAINTY ORIGINS
In active DA, to gain the utmost benefit from limited labeling budget, the selected samples ideally should be 1) representative of target distribution and 2) conducive to discriminability. For the former, existing active DA methods either use the score of domain discriminator (Su al. [019 Fu et al. 2021) or the distance to cluster centers (Prabhu et al. [222 Deheeger et [2.2). As for the latter, predictive uncertainty (c.g., margin (Xie et al. [202]] }. entropy (Prabhu al. (021I) of standard
DNNs is utilized to express the discriminability of target samples. Differently, we denote the two
characteristics in a unified framework, without introducing domain discriminator or clustering.
For the evidential model supervised with source data, if target samples are obviously distinct from source domain, e.g., the realistic v.s. clipart style, the evidences collected for these target samples may be insufficient, because the model lacks the knowledge about this kind of data. Built on this, we use the uncertainty resulting from the lack of evidences, called distribution uncertainty, to measure the targetness. Specifically, the distribution uncertainty Udis of sample æj is defined as
C
C
Unio (zi 0) A 1y. p 2; 0
Σ
Pie
elaao + 1) - +0
aak +1)+11) Σ
-
Piclogpso (3) c=l
c=1
1=1
>= 12,,2, _ = IP(y = 1), Ply 2).... Ply C)) T. is vector of class probabilities.
p =
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add y Training Stage
Active Selection Stage
high
query labels
&
Ugis
datee
Gradie
lintt round
second round
sorted by Vax
sorted by Usata
Diriples
law
high
feature extractor
evidence head
?
top
labeled source sct
labelod target set uniobeled larget
selected target
cencee selected data round
labeled
labeled target
unlabeled
decision boundary
selected
Figure 2: Illustration of DUC. When the training reaches the active selection steps, the distribution uncertainty Udis and data uncertainty Udate of unlabeled target samples are calculated according to the Dirichlet distribution with parameter a. Then kb samples with the highest Udis are chosen in the first round. In the second round, according to Udata- we select the top b samples from the instances chosen in the first round to query their labels. These labeled target samples are added into the supervised learning. When reaching the total labeling budget B, the active selection stops.
where 0 is the parameters of the evidential deep model, (--) is the digamma function and Pjc [[ Here, we use mutual information to measure the spread of Dirichlet distribution on the simplex like Malinin & Gales (018). The higher Uais indicates larger variance of opinions due to the lack of evidences, i.e., the Dirichlet distribution is broadly spread on the probability simplex.
For the discriminability, we also utilize the predictive entropy to quantify. But different from previous methods which are based on the point estimate (i.e., the expectation of Dirichlet distribution), we denote as the expected entropy of all possible predictions. Specifically, given sample æ, and model parameters 0, the data uncertainty Udata is expressed as
Uduta (3j. 0) A Eplpl=,, [M[P(y]))]] Σ Pje +
E aak +1 - (lacc+))) +1)
(4)
Here, we do not adopt H [E[Dir(pla,))) i.c., i.e.. the entropy of point estimate, to denote data uncertainty, in that the expectation operation will conflate uncertainties from different origins as shown in Eq. (
Having the distribution uncertainty Udie and data uncertainty Udata. we select target samples accord- ing to the strategy in Fig. 2 In each active selection step, we select samples in two rounds. In the first round, top xō target samples with highest Udis are selected. Then according to data uncertainty Udata- we choose the top b target samples from the candidates in the first round to query labels, Experiments on the uncertainty ordering and selection ratio the first round are provided in Sec. D.T and See. 4.3
Relation between Udis. Udata and typical entropy. Firstly, according to Eq. 2). the typical entropy of sample I, can be denoted as [[ 0)] H[ = Pyclogeje. where ie = [[Dir(pela,)) Then we have (2 0) + Udata (z,, 9) H[P(y 0)). by adding Eq. (3) and Eq. 4 together. We see that method actually equals decomposing the typical entropy into two origins of uncertainty, by which our selection criteria are both closely related to the prediction. While the targetness measured with domain discriminator or clustering centers not directly linked with the prediction, and thus the selected samples may already be nicely classified.
Discussion. Although Malinin & Gales (2018) propose Dirichlet Prior Network (DPN) distinguish between data and distribution uncertainty, their objective differs from us. Malinin & Gales (2018) mainly aims detect ofiit--diitiiuuti (OOD) data, and DPN is trained using the KL-divergence between the model and the ground-truth Dirichlet distribution. Frustratingly, the ground-truth Dirichlet distribution is unknown. Though they manually construct a Dirichlet distribution as the proxy, the parameter of Dirichlet for the ground-truth class still needs to be set by hand, rather than learned from data. In contrast, by interpreting from an evidential perspective, our method does not require the ground-truth Dirichlet distribution and automatically learns sample-wise Dirichlet distribution by maximizing the evidence of ground-trute class and minimizing the evidences of wrong classes, which is shown
in Sec. 3.4 Besides, they expect to generate flat Dirichlet distribution for OOD data, while this is not desired on our target data, since our goal is to improve their accuracy. Hence, we additionally introduce losses to reduce the distribution and data uncertainty of target data.
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3.4 EVIDENTIAL MODEL LEARNING
To get reliable and consistent opinions for labeled data, the evidential model is trained to generate sharp Dirichlet distribution located at the corner of the simlpex for these labeled data. Concretely, we train the model by minimizing the negative logarithm of the marginal likelihood (Cnu) and the KL-divergence between two Dirichlet distributions (LxL). Lun is expressed as
Luul 1
Σ log (f p(u = (ippsppppppppp + 0,68
Σ ØGET!
log
(f -ys p 1slpippppass
Tio
log
Qic)
logase
Tj
log Σ aze)
-logaaa (5)
Ths 2:E8 c=1
T
ZJET
where T is the e-th element of the one-hot label vector Y; r of sample na/Uj. Luu is minimized to ensure the correctness of prediction. As for Lui, it denoted as
CkI C C. 0,68
Σ
(L
E KL(Dir(pla;)IDii(([]] (6)
C-ITI
where /; = x/i +1 (1- aty and O is the element-wist multiplication. ā.y can be seen as removing the evidence of ground-truth class. Minimizing Lai will force the evidences of other classes to reduce, avoiding the collection of mis-leading evidences and increasing discriminability. Here, we divide the Kl.ddiereeecee by the number of classes, since its scale differs largely for different C. Due to the space limitation, the computable expression is given in Sec. E.4 of the appendix.
In addition to the training on the labeled data, we also explicitly reduce the distribution and data uncertainties of unlabeled target data by minimizing Lun, which is formulated
B
Lum = BLus + ALUaato
Σ #LET
(EEk 0)
+ T
Σ ØTET"
Udaia (atkaaaKk O),
(7)
T
where B and À are two hyper-paramette to balance the two losses. On the one hand, this regularizer term is conducive to improving the predictive confidence of some target samples. On the other hand, it contributes to selecting valuable samples, whose uncertainty can not be easily reduced by the model itself and external annotation is needed to provide more guidance. To sum up, the total training loss is
Lrotal
Ledl Lun (Cnu + Lxa) + (BCua.. ACUssta)
The training procedure of DUC is shown in Sec. B of the appendix. And for the inference stage, simply use the expected opinion, i.e., the expectation of Dirichlet distribution, as the final prediction.
Firstly, Cutt, Lis actually widely used in EDL-inspired methods for supervision, e.g.. Bao et al. (2021): Chen et al. (2022); Li et al. (2022). ). Secondly, our motivation and methodology differs from EDI. EDL does not consider the origin of uncertainty, since it is mainly proposed for OOD detection, which is less concerned with that. And models can reject samples as long as the total uncertainty is high. By contrast, our goal is to select the most valuable target samples for model adaption. Though target samples can be seen as OOD samples to some extent, simply sorting them by the total uncertainty is not good strategy, since the total uncertainty can not reflect the diversity of information. A better choice is to measure the value of samples from multiple aspects. Hence, we introduce a two-round selection strategy based on different uncertainty origins. Besides, according to the results in Sec. D.5 our method can empirically mitigate the domain shift by minimizing Lt.... which makes our method more suitable for active DA. Comparatively, this is not included in EDL.
Discussion.
Time Complexity of Query Selection. The consumed time in the selection process mainly comes from the sorting of samples. the first round of each active section step, the time complexity is O([T]logg]77) And in the second round, the complexity is ((<b)logg<<b) Thus, the complexity of each selection step is O[TT" [")) logb)
Assuming the number of total selection (({b)logg( (og())))) where T is the unlabeled target set in the m-th active selection step. Since r is quite small (5 in our paper), and xb < [TH] < n4, the approximated time complexity is denoted as Onnlogn.).
steps is then the total complexity is Ei=n(0 (O [ [log]T.")

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Table 1: Accuracy (%) on miniDomainNeet with 5% target samples as the labeling budget (ResNet-S0)
Method
clp-ppo
cip-ttel
clg-tik
pat--cip
pat-trel
pm-tiki
rel-4ch
zei
zei-ipul
rel-+ak3
yel-
skt
skt-icip
ska
Ma-tpil
sla-ire)
Aag
Source-only
63.0
55.9
73.0
56.3
Random
616
78.7
61.6
64.0
78.7
63.7
60.5
64.3
61.1
64.8
58.1 7
75.2
BoSR
Inshi et al 2009
63.2
77.9
62.7
66.7
80.5
64.9
64.1
67.0
62.2
67.6
62.5
77.8
68.1
Entropy
Wante Scatn 2014
63.3
78.3
61.0
65.7
81.4
63.2
63.3
66.2
63.0
67.9
00.5
78.5
67.7
CoreSat
Nawrew
62.6
78.3
60.2
62.1
79.9
63.6
63.6
65.2
59.1
63.1
62.3
7k.1
66.5
WA
80.2
K0.3
62.9
654
66.9
80.8
65.2
80.2
65.9
66.7
79.2
68.5
AAIA
624
77.5
61.7
61.9
79.7
G1.1
65.6
06.0
60.8
65.1
02.1
80.0
67.0
DBAL
(Detreger ef 2021
62.9
79.2
60.8
64.6
78.1
62.5
65.6
65.2
59,2
66.3
61.3
80..
67.2
TUS
Firer 1014
67.8
82.0
65.4
67.5
84.8
66.1
63.8
67.2
62.5
71.1
64.4
81.6
70.4
CLUE
(Pyinn 2011
77.5
58.9
76.8
06.9
00.2
66.2
65.3
BADA
66.0
80.8
09.4
83,0
65.1
71.1
68.6
65.7
71.0
70.8
67.1
66.1
74.0-066
3 67.6
72.40
70.3+00
66.5+0
73.5
70.0
72.9H-0
Supty--eerriised
74.8
89.2
75.8
82.9
89.2
75.1
82.4
75.6
74.9
82.7
73.8
88.7
80.3
For miniDemaiiNee, since these compared besclines not report results on dataset, we report our runs based their open sounce code.
Table 2: Accuracy (%) on Haice-Homeaae and VisDA-200 with 5% target samples as the labeling
budget (ResNet-50),
Method
Vala-a017
Oflic-
1.1
65.2
42.6
75.6
55.3
Random
78.1 0.6
52.5
50.9
70.0
54.6
61.3
Bv5B Toshi atal. 2004
81.3 0.4
56.3
78.6
79.3
70.9
19.5
71.2
55.4
54.5
68.2
Untropy
82.7 0.3
58.0
78.4
54.2
71.3
58.0
83.6
68.9
Conseer
Sanger Store
81.
51.8
72.6
58.3
08.5
58.3
48.8
15.2
58.0
52.7
90.0
65.1
WART-
83. 0.4
55.7
17.1
79.3
61.1
74.7
72.6
60.3
52.1
78.1
70.1
56.6
82.5
68.3
BADGE Gotn 20:20
84.3 0.3
58.2
79.7
79.9
61.5
74.6
72.9
61.5
56.0
78.3
71.
60.9
84.2
09.9
AAJA SS 11i0
803 04
$6.5
7%
75.0
58.5
753
71.0
40.
33.1
77.0
70.6
37.0
64.
68.3
DBAL (Dehveer
2021
826 0.3
53.7
77.3
70.2
61.7
73.8
73.3
62.6
54.5
78.1
72.4
59.9
84.3
69.6
TQS DIEE 2ln KMM
85.1 0.4
58.6
$1.1
91.5
61.1
76.1
73.5
61.2
54.7
79.7
73.4
58.9
96.1
70.5
CLUBE
852 0.4
58.0
79.3
90.9
68.8
77.5
76.7
66.3
579
K1.4
75.6
6008
96.3
72.5
BADX
Se 2001
88. 0.1
61.6
84.4
83.5
70.7
83.7
80.
73.0
63.5
85.2
78.4
65.4
83.6
96.7
DDC
889 0.
68.8166
94,9:0
73.0
81.1
66.6
0
85.4
0.2
80.
780193
Fullp-epervies
93.3
95.6
99.5
90.5
99.3
99.6
99.5
99.3
95.8
99.5
99.5
95.6
90.5
98.5
EXPERIMENTS
4.1
EXPERIMENTAL SETUP
We evaluate DUC on three cross-domain image classification datasets: miniDomainNer (Zhou et al. (Peng et al. 2017), and two adaptive al. 2016) + Cityscapes (Cordis al. 2016).
2021), Office-Home (Venkateswara et al. 2017). VisDA-2017 2017 semantic segmentation tasks: GTAV (Richter
SYNTHIA (Ros et al.) 2016) + Cityscapes. For image classification, we use 50 (He et al. 2016) pre-trained on ImageNet (Deng et al., 2009) as the backbone. Following (Xie et al.) 2021). the total labeling budget B is set as 5% of target samples, which is divided into 5 selection steps, ie.. the labeling budget in each selection step is = B/3 = 1% x Thy We adopt the mini-batch SGD optimizer with batch size 32, momentum 0.9 to optimize the model. As for hyper- parameters, we select them by the grid search with deep embedded validation (DEV) (You et al., 2019) and use adopt DeepLab-
10 for image classification. For semantic segmentation, v2 (Chen et al. 2015) and DeepLab-v3+ (Chen et al. 2018) with the backbone ResNet- 101 (He et al., 2016), and totally annotate 5% pixels of target images. Similarly, the mini-batch SGD optimizer is adopted, where batch size is 2. And we set 8 = 1.0, X = 0.01, k = 10 for semantic segmentation. For all tasks, we report the std of 3 random trials, and we perform fully supervised training with the labels of all target data as the upper bound. Detailed dataset description and implementation details are given in Sec[iof the appendix. Code is available at htttps: thub. com BBAI//TTTDAAASS
1.0, À 0.05,
4.2
MAIN RESULTS
4.2.1
IMAGE CLASSIHICATION
Results on miniDomainNet are summarized in Table [ where clustering-based methods (e.g.. DBAL., CLUE) seem to be less effective than uncertainty-based methods (e.g., TQS, FADA) on the large-scale dataset. This may be because the clustering becomes more difficult with the increase of data scale. Contrastively, our method works well with the large-scale dataset. Moreover, DUC surpasses the most competitive rival EADA by 2.1% on average accuracy. This is owed to our better estimation of predictive uncertainty by interpreting the prediction as a distribution, while EADA only considers the point estimate of predictions, which easily be miscalibrated.
Results on Office-Home are reported in Table 2 where active DA methods (e.g., DBAL, TQS, CLUE) generally outperform AL methods (e.g., Entropy, CoreSet, WAAL), showing the necessity of
7

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Published as a conference paper at ICLR 2023
Table 3: mloU (%) comparisons on the task GTAV Cityscapes.
Methol
Iudget
will
oale
ug
VeL
per
Siunce-obh
25.5
20.1
MRRKD 2 20.9
33.7
21.
37.3
34.5
57.
246
56.1
30.1
TPLD
25.5
57.0
87.8
560
448
45.6
535
53.6
70.7
588
48.9
57.5
65.
HADA"
506
95.5
73.8
89.6
51.3
648
40.9
474
56.5
89
550
91
692
47.6
90.7
06.4
64.9
551
52.
65.
DDC
59g
96.8
76.2
89.2
53.2
66.0
42.5
48.5
5766
99
54.
92.1
72.
513
92.
62.8
722
48.5
528
70.3
67.0
Fully-anerised
100%
97.2
76
90.6
54.5
53.7
43.
54.
61.
W1.1
568
02.4
728
963
91.
740
713
676
56.3
76V
70.5
AADAY Sug
2019
59
91.2
50.9
87.3
36.4
45.7
66.1
30.6
59.1
13.1
44.5
002
69.
300
353
45
327
326
61.
19.3
MADA
Neag
5%
95.1
69.5
88.5
43.3
48.7
45.7
53.3
99.2
89.1
46.7
91.5
73.9
50.1
91
606
56.9
48
51.6
68.7
64.0
5/6
95.9
70.6
507
07.8
59.7
98.3
76.7
928
74X
634
59.5
71.6
698
Fully- Puparrisddd
1001
96.6
10.4
96.3
46.6
56.8
50.3
58.5
68.1
90.
59.4
95.3
75.8
54.
92.5
74.9
79.1
71.6
56.8
21.8
72.2
Muttrod wath haued Lheppaabbo
Chem 21 [20X]] other ore boaet Derpl.abet
Chem m1 2015 Matted with hadge
w0 or UIA metaods BARX deroess
scconding compopanding open
Table 4: mloU (%) comparisons on the task SYNTHIA + Cityscapes. mloU is reported according to the average of 13 classes, excluding the "wall", "fence" and "pole".
Method
budgee
cond
sile-
bull.
wall"
fono"
pule"
hight
sign
par- nlet
bike
mlaUi
mfft"
Spanse
7.0
21.7
07.6
103
31.9
MRKUD Zou et
73.9
10.7
50.5
1944
45.3
43.8
TPLD
Stin Brai
80.9
44.3
82.2
19.9
20.5
30.1
509
411
24.7
43.7
47.3
53.5
Seg- Ung-enerssinn
2021
87.6
41.9
83.1
14.7
1.7
36.2
31.3
816
30.6
63.0
218
56
407
23.6
53.1
47.9
54.9
ProDA
87.8
45.7
84.6
37.1
0.6
54.6
88
54.
74
24.1
51
40.5
45.6
55.5
62.0
DCC
3%
96.1
73.1
88.7
43.3
3900
42.2
19.9
55.5
90.7
92.
73.7
19.2
919
679
45.9
71.1
56.9
72.8
Fully supervised
100%
97.3
79.1
89.6
52.8
55.0
46.7
53.4
61.6
90.5
92.9
71.3
50.8
92.1
77.9
55.4
58.7
71.0
75.5
AADA Sa al, 2010
5%
91.3
57.6
86.9
37.6
48.3
45.0
50.4
56.5
88.2
90.
09.4
57.9
59.9
44.5
528
02.5
61.9
66.
MADA
96.5
74.6
88.3
45,9
43.8
60.3
52.4
69.4
68.1
73.3
74.6
78.9
75.6
Bully-supersisedd
100%
57.0
50.4
90.9
48.6
56.
52.1
58.5
67.4
93.4
54.2
92.3
78.5
56.1
71.3
72.7
77.4
Mothadk with hoacd on Deepl 2b
Chen
2018
and ohhons hoadd 2ho2
aho22 Chenet al 2015 Methoal with halges '57 the sceeco-only UTB maheos.
considering targetness. And our method beats EADA by 1.3%, validating the efficacy of regrading the prediction as a distribution and selecting data based on both the distribution and data uncertainties.
Results on VisDA-2017 are given in Table [ On this large-scale dataset, our method still works well, achieving the highest accuracy of 88.9%, which further validates the effectiveness of our approach.
4.2.2 SEMANTIC SEGMENTATION
Results on GTAV Cityscapes are shown in Table B Firstly, we can see that with only 5% labeling budget, the performance of domain adaptation can be significantly boosted, compared with UDA methods. Besides, compared with active DA methods (AADA and MADA). our DUC largely surpasses them according mloU: DUC (69.8, 10.5t) v.s. AADA (59.3), DUC (69.8, 4.91) v.s. MADA (64.9). This can be explained as the more informative target samples selected by DUC and the implicitly mitigated domain shift by reducing the distribution uncertainty of unlabeled target data.
are presented in Table 4 Due to the domain shift from virtual to realistic as well as a variety of driving scenes and weather conditions, this adaptation task is challenging, while our method still achieves considerable improvements. Concretely, according to the average mloU of 16 classes, DUC exceeds AADA and MADA by 8.4% and 2.2%, respectively. We owe the advances to the better measurement of targetness and discriminability, which are both closely related with the prediction. Thus the selected target pixels are really conducive to the classification.
Results on SETTHHAA-Citysaappp
Table 5: Ablation study of DUC on Office- -omee.
4.3 ANALYTICAL EXPERIMENTS
Loss
Active Selection Criterion
Method
Avg
Lu We..
random entropy Uas Unir.
Ablation Study. Firstly, we try EDL with dif- ferent active selection criteria. According to the results of the first four rows in Table 5 variant A obviously surpasses EDL with other selection criteria and demonstrates the superiority of eval- uating the sample value from multiple aspects, where variant A is actually equivalent to EDL. with our two-round selection strategy. Then, we study the effects of LUa., and LUaues The supe- riority of variant B over A manifests the necessity of reducing the distributional uncertainty of unla- beled samples, by which domain shift is mitigated. Another interesting observation is that Cu does not bring obvious boosts to variant A. We infer this is because the distribution uncertainty will potentially affect the data uncertainty, as shown in Eq. (2) It is meaningless to reduce Udata
EDL
61.5
EDL
71.1
EDL
73.3
Variant
74.1
Variant
/
76.6
Variant
74.2
Variant
/
68.6
Variant
/
75.0
Variant
76.7
Variant
77.1
Variant
76.9
DUC
78.0
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Published as a conference paper at ICLR 2023
CleAAr
Ar+
3.5
Sourte Targel
3.5
Source Targei
1.0
(ECE-L25)) (25)
3.
0.8
2.5
0.6
20 2.66
16
0.4
14
10
0.
0.5
06
-7
-6
-5 4
0.0
-7
-5
0.0
0.0 0.6. Confidence
0.0
0.4
log Uas
log Das
Confidence
(a) Distribution of logUais
(h) Expected calibration (ECF) of target data
Figure 3: (a): The distribution of logUais for source and target data task Ar + CI and CI - Ar. For clegancy, we apply logarithm to Udi.. (b): Expected calibration error (ECE) of target data, where the standard DNN with cross entropy (CE) loss and our model are both trained with source data.
when Udis is large, because opinions are derived from insufficient evidences and unreliable. Instead, reducing both Udis and Unnto is the right choice, which further verified by the 7.1% improvements of variant D over pure EDL. Besides. Even without LU... and LVaneu variant A still exceeds CLUE by 1.6%, showing our superiority. Finally, we try different selection strategies. Variant E to H denote only criterion is used in the selection. We see DUC beats variant F, G, H. since the entropy degenerates into the uncertainty based on point estimate, while Udie or Udata only considers either targetness discriminability. Contrastively, DUC selects samples with both characteristics.
Distribution of Udis Across Domains. To answer whether the distribution uncertainty can represent targetness, plot in Fig. ((a] the distribution of Udis. where the model is trained source domain with Leat- We see that the Uais of target data is noticeably biased from source domain. Such results show that our Udis can play the role of domain discriminator without introducing it. Moreover, the score of domain discriminator is not directly linked with the prediction, which causes the selected samples not necessarily beneficial for classifier, while our Udis closely related with the prediction.
Expected Calibration Error (ECE). Following (Joo et al. 2020), we plot the expected calibration error (ECE) (Neeini al. 2015) on target data in Fig. (b) evaluate the calibration. Obviously, our model presents better calibration performance, with much lower ECE. While the accuracy of standard DNN much lower than the confidence, when the confidence is high. This implies that standard DNN can easily produce overconfident but wrong predictions for target data, leading to the estimated predictive uncertainty unreliable. Contrastively, DUC mitigates the miscalibration problem.
Effect of Selection Ratio in the First Round. Hyper- Hyper-paramett parameter k controls the selection ratio in the first round and Fig. 4(a presents the results on Pffice-Home with different k. The performance with too much too small is inferior, which results from the imbalance between targetness and discriminability. When k = 1 or k = 100, the selection degenerates to the one-round sampling manner according Udis and Udata. respectively. In general, we find K E {10, 20, 30} works better.
Sensitivity. and control the tradeoff between Lia.. and LUaarn- test the sensitivity of the two hyper- pareeerrrrmeterrs on the Office-Homm dataset. The results are presented in Fig. 4(b)) where 3 E {0.01, 0.05, 0.1, 0.5, 1.0] and X {0.001, 0.005, 0.01, 0.05, 0.1). Accord- ing to the results, DUC is not that sensitive to 8 but is a little bit sensitive to A. In general, we recommend X E (0.01, 0.05, 0.1) for trying.
4615
(a)
(b)
Figure 4: (a): Effect of different first-round se- lection ration %% on Office-Homee Home. (b): Hyper- parameter sensitivity of B, X on Office-
5 CONCLUSION
In this paper, we address active domain adaptation (DA) from the evidential perspective and propose Dirichlet-based Uncertainty Calibration (DUC) approach. Compared with existing active DA methods which estimate predictive uncertainty based the the prediction of deterministic models, we interpret the prediction as a distribution on the probability simplex via placing a Dirichlet prior on the class probabilities. Then, based on the prediction distribution, two uncertainties from different origins designed in a unified framework to select informative target samples. Extensive experiments on both image classification and semantic segmentation verify the efficacy of DUC.

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ACKNOWLEDGEMENTS
This work was supported by National Key R&D Program of China (No. 202 YFB330113))))
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APPENDIX CONTENTS
A. Broader Impact and Limitations
B. Algorithm of DUC
C. Implementation Details
D. Additional Results
E. Derivations
A BROADER IMPACT AND LIMITATIONS
Our work focuses on active domain adaptation (DA), which aims to maximally improve the model adaptation from one labeled domain (termed source domain) another unlabeled domain (termed target domain) by annotating limited target data. In this paper, suggest new perspective for active DA and further boost the adaptation performances on both cross-domain image classification and semantic segmentation benchmarks. The advances mean that our method may potentially benefit relevant social activities, e.g., commodity classification, autonomous driving in different scenes, without consuming high labor cost annotate massive not anticipate adverse impacts, our method may suffer from some limitations. For example, our work restricted classification and segmentation tasks in this paper. In the future, will explore method in other tasks, e.g., object detection and regression, hoping to benefit more diverse fields. Besides, only try train the Birichlet-based model using the evidential deep learning in the paper. Yet, there may exist better training frameworks, c.g., normalizing flow-based Dirichlet Posterior Network which can predict a closed-form posterior distribution over predicted probabilities for any input sample. In the future, we may also explore to extend our approach into the training framework of normalizing flow-based Dirichlet Posterior Network.
data for different scenes. While do
B ALGORITHM OF DUC
The training procedure of DUC is shown in Algorithm
Algorithm Pseudo code of the proposed DUC
Input:
labeled source dataset S, unlabeled target dataset T, selection steps R, total annotation budget B, hyperparameters K. 33 A, total training steps T.
Output: learned model parameters O.
1: Initialize model parameters 0.
2: Define T = Ø and T =T, b B
3: for = 1 to T do
4: Update parameters 0 via minimizing Liotal-
5: it't E Rt then
6:
Vz, E TT...ompuuu compute its distribution and data uncertainties: (Zi 0). Udata 0). temp.Candi Candi <- select top xb samples with highest Udis from T Candi t- select top b samples with highest Uanta from lemp. Candp.i Query the labels of Candi from the oracle.
7:
8:
9:
10:
T ===10 TTW,Candi T = T U Candi.
11: end if
12:
end for
13: return Final model parameters 0.
13

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Published as a conference paper at ICLR 2023
miniDomainNNet
GTAV
Cityscapes
Figure 5: Image examples from dataset miniDomainNNt, Office- Homee VisDA-2017, Cityscapes,
GTAV and SYNTHIA.
C EXPERIMENTAL SETUP DETAILS
C.I DATASET DESCRIPTION
NiniDomainNNt (Zhou et al. 2021) is subset of DomainNet (Peng et al. 2019), a large-scale image classification dataset for domain adaptation. miniDomainNet contains more than 130,000 images of 126 classes from four domains: Clipart (clp), Painting (pnt), Real (rel) and Sketch (skt). The large data scale and multiplicity make the adaptation on this dataset quite challenging. And we build 12 skt -rel, by permuting the four domains, evaluate our method.
adaptation tasks: clp->pnt,
Office-Home (Venkateswara et al., 2017) collects 15,500 images of 65 categories from office and home scenes. And these images divided into four distinet domains: Art (Ar), Clipart (CI), Product (Pr) and Real-World (Rw), respectively with images from artistic depictions, clipart pictures, product pictures and cameras.
VisDA-2017 (Peng et al. 2017) is large scale dataset for cross-domain image classification. It collects images of 12 classes, including synthetic images rendered from 3D models and real images. Following Xie et al. (202T), we use 152,397 synthetic images as source domain and 72,372 real images as target domain, forming the adaptation task: Synthetic-Real.
Cityscapes (Cordts et al. 2016) gathers 5,000 images of urban street scenes from real world, where each pixel in the image annotated from 19 categories and the image resolution is 2048 1024. These images are divided into training, validation and test splits. Similar to (Ning et al. 2021). we use the training split with 2,975 images as target training data, where labels are not used, and the model is evaluated the validation split with 500 images by reporting the mloU of the common categories.
GTAV (Richter et al. 2016 is dataset of 24,966 simulated images with pixel level semantic annotation. These images are rendered by "Grand Theft Auto V game engine, with the resolution of 1954x1052. And this dataset shares 19 categories with the Cityscapes dataset.
SYNTHIA (Ros et al. 2016) consists of 9,400 synthetic images of street scenes, with the image resolution of x280 760. It contains diverse street scenes, such towns and highways, different weather conditions and seasons. There are 16 categories that are compatible with the semantic categories in Cityscapes.
The image illustration of different datasets is shown in Fig.
C.2 IMPLEMENTATION DETAILS
IMAGE CLASSIFICATION
All experiments are implemented via PoTocc (Paskee et al. 2019). For image classification, we use ResNet-50 (He al. 2016) pre- pre-trained ImageNet (Deng et al. 2009) the backbone, and the exponential function is employed to the model output to ensure a non-negative. Following (Xie)
et al. 2021 Fu al. 2021), The total labeling budget B is 5% of target samples, which is
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Table 6: Results with different total labeling budget B on Office-Home (ResNet-50). Total labeling budget
0%
2.5%
5%
7.5%
10%
12.5%
15%
17.5%
20%
Avg accuracy
68.6
72.9
78.0
80.2
82.4
84.8
86.4
88.0
88.9
Gain over previous one
4.3 f
5.1 f
2.2
2.2
2.4
1.6 f
1.6
0.9 f
Table Accuracy (%) on Office-Home with 5% target samples as the labeling budget (ResNet-50), when DUC is combined with semi-supervised learning method.
Method
Ar-
Ar
Ar- CT CI-+1 CI-Rw Pr-+Ar Pr Pr- Rw-+Ar Rw-s[]
Rw-
Avg
DUC
65.5
84.9
84.3
73.0
83,4
81.1
73.9
66.6
85.4
80.1
69.2
88.8
78.0
DUC w/ Lill
C.tematch
66.5
85.7
85.0
73.3
84.3
82.8
74.8
67.0
85.7
81.5
70.8
89.7
78.9
divided into 5 selection steps, i.e., the labeling budget in each selection step is b B/5 1% x ne- For data preprocessing, we use BandommHorizotaalF]] the training process and use CenterCrop during the test stage. For the optimizer, we adopt the mini-batch stochastic gradient descent (SGD) optimizer with batch size 32, momentum 0.9, weight decay 0.001 and the learning rate schedule strategy (Long al. 2018). ). The initial learning rates for mimannnmi,,et, Office-Home and VisDA-2017 are 0.002, 0.004 and 0.001. respectively. As for hyper-parameters, we select them by the grid search and finally use 1.0, À = 0.05, x 10 for miniDomainNet and Office-Homne datasets. We run each task on a single NVIDIA GeForce RTX 2080 Ti GPU.
RandomResizedCrop and ColorJitter during
SEMANTIC SEGMENTATION
For semantic segmentation, we also implements the experiment using Py (Paszke al. 2019) and adopt the DeepLab-v2 (Chen et al. 2015) and DeepLab-v3+ (Chen et al. 2018) with the backbone ResNet-101 101 (He et al. 2016) pre-trained on ImageNet (Deng et al. 2009). Regarding the total labeling budget B, we totally annotate 5% pixels of target images, which is divided into 5 steps. In other words, we annotate 1 % pixels for every image in each active selection step. For data preprocessing, source images
resized into 1280 720 and target images resized into x Similarly, the model is optimized using the mitc- SGD optimizer with batch size 2, momentum 0.9, weight decay 0.0005. The "poly" learning rate schedule strategy with initial learning rate of 3e-4 is employed. And we set 3 = 1.0, A = 0.01, 10 for the semantic segmentation tasks. For each semantic segmentation task, we run the experiment on single NVIDIA GeForce RTX 3090 GPU.
D ADDITIONAL RESULTS
D.1 EFFECTS OF THE ORDERING OF Udisi Udata IN TWO-ROUND SAMPLING
Since our selection strategy is a two-round sampling manner, there naturally exists the ordering of Unis and Udata in the two rounds. Table 8 explore the influence of dif- ferent orderings, where Udies Udata de- notes Udis and Udata are respectively used in the first and second round. We no- tice that Udis. Udata generally surpasses Udatay Udis. It shows that selecting pnaeriminabilityccodddde
Table 8: Analysis on the ordering of Udis. Udata-
Dataset
mimiDomaiNNet
Office-Home
Ordering
(Avg)
(Avg)
Udiay Udata
72.9
78.0
Udatar Udie
72.2
77.5
Dataset
samples from renget-representativ samples is better for active DA than the converse manner. Thus, we adopt Udis, Udata throughout the paper.
Ordering
(mloU)
(mloU mloU")
Usion Vdala
67.0
66.9772.8
Udata, Udio
66.2
/
D.2 PERFORMANCE GAIN WITH DIFFERENT LABELING BUDGETS
In T we present the performances on Office-Home dataset with different total labeling budget B. As expected, better performances can be obtained with more labeled target samples accessible.
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In addition, observe that the increasing speed of performance generally gets slower, the total labeling budget increases. This observation demonstrates that all samples are not equally informative and our method can successfully select relatively informative samples. For example, when labeling budget increasing from 17.5% to 20%, the performance gain much smaller, which implies that the majority of informative samples has been selected by our method.
D.3 COMBINATION WITH SEMI-SUPERVISED LEARNING
To further improve the performance, one can incorporate ideas from semi-supervised learning to use the unlabeled target data in training as well. Here, we consider one representative semi-supervised learning method: FixMatch (Sohn et al. 2020). Specifically, we apply strong and weak augmentations to each unlabeled target sample z,, obtaining two views x strong and 2; aeteak And we use the pseudo label of weakly augmented view aryeak as the label of strongly augmented view an ottrongg Then the model is trained minimize the loss efiamatch i.e., the negative logarithm of the marginal nil Cfammath is formulated as likelihood of strongly augmented views. Concretely, Lall
Fizmatcch nl
Σ
-log
(f ply = Dj p)p(pl strong 0)dp)
M ø guouk
Σ
rweek je
log
ajo
strong)
loga
je
strong
BJETTATCHaR, gweak
where 0f arg m graa arg (air (rjak))] and M Haylæ, TTAAT (week) H. r is hyper-parament denoting the threshold above which the pseudo label is retained, max. Pjo
and Tweek is the e-th element of the one-hot label vector Y, weak for pseudo label grreak
Table pressents the results on the Office-Home dataset when combining our method DUC with the sepi-supervised learning method FixMatch Sohn et al. (2020), where the arper-parameter T is set to 0.8. We can see that utilizing unlabeled target data indeed conduces improving the performance. Of course, other semi-supervised learning methods are also possible.
D.4 QUALITATIVE VISUALIZATION OF SELECTED SAMPLES
In the label histogram Fig. we plot the ground truth label distribution of the samples that selected by DUC, with the total labeling budget B 5% n,. For the Ar-CI task, "Bottle", "Knives" and "Toys" are the top classes that are picked, while "Bucket", "Pencil" and "Spoon" turn out to be the top 3 picked classes in the Cl-AA task. It shows that our method DUC can adaptively select informative samples for different target domains. Despite few categories are not picked, we still that the samples selected by DUC generally category-diverse. And, according the visualization of selected samples, the style of target domain is indeed reflected in theses selected samples. In addition, we also visualize the selected pixels for the task GTAV -TTVV-Cityscapes in Fig. 7 Overall, the selected pixels are from diverse objects that are hard to classify or are nearby together. Annotating such pixels can bring more beneficial knowledge for the model.
D.5 T-SNE VISUALIZATION FOR SHOWING EFFECTS OF Lias
To verify that reducing our distribution uncertainty Udis conduces to the domain alignment, we respectively train the model with Les! and Ceat + /BLu... where there no labeling budget. And the t-SNE (van der Maaten & Hinton 2008) visualization of features from source and target domains on task Ar + Cl and CI Ar shown in Fig. g Form the results, we can see that reducing the distribution uncertainty of target data indeed helps to alleviate the domain shift, which makes method more suitable for active DA, compared with EDL Sensoy et al. (2018). Besides, the results also verify that distribution uncertainty can measure the targetness of samples.
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Label Histogram
High
Priority
Low
Poller
Bust
5000
19
0000
Kasta
ScrEMSTIIN
Soda
Solterur
Gouch
Gorl Bruur
Tolephone
Scrowdiver
Botte
Monier
Toys
Kriwas
Ruler
Shade
TV
Selected arggeimmages (top 10 in each selection step)
Ar-CI
Label Histogram
Court
High
Prionty
Low
Fal
Can
Suitarica
KOTA
Soll
TA
Ctp
Naktbokk
Mantor
Holebosk
Sign
Printor
Selected target images (top 10 each selection step)
(b) Cl-Ar
Figure 6: (a) and (b) the label histogram and examples of selected instances by DUC Ar-CI and CI-AAr tasks, respectively. The total labeling budget is 5% of target images. For the visualization of selected samples, we present the top 10 selected instances in each active selection step.
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Ground
Figure 7: Visualization of selected pixels in the task GTAV with the total labeling
budget of 5% pixels. Here, we randomly choose ten images from Cityscapes for display.
(a) Ar CI ( (wo keys))
(b) Ar CI ( wi kegs
(c) Ar ( wlo )eggu)
(d) CI Ar (wl Egss)
Figure 8: The t-SNE visualization of features learned by the model trained with Lest and Ladl BLu., respectively, Red and blue dots represent source and target features, respectively.
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E DERIVATIONS
E.I
PREDICTIVE PROBABILITY P(y cla;, 0)
Given sample æ; and model f parameterized with 0, the predicted class probability for class c can be obtained as
Ply = c/ 0)
plu = -lpppppppppps)
Pc: ppppp., 0)
/ I ... Po papp,,p,... p
, pola; dpp..dp.................... dpc
= I pal [
11 plel. PC m, 0)dpıdp2 1dd---dpe1--- ... dpc)ddp
= / Pe: (ppolee, Oydpe
(10)
where Pe is the c-th element of the class probability vector p. According to (Ng et al. 2011 the marginal distributions Dirichlet is Beta distributions. Thus, given p(p 0) Dir(paa we ( 0)), = Σ k= agk and g(-) is
have p(pe|=;, 0, 0) ~ (eta(pp a:o ass)), where
a function (e.g., exponential function) to keep a; (i.e., the parameters of Dirichlet distribution for
sample æ;) non-negative. And according to the probability density function of Beta distribution, we further have
pppe x;, 0)
Po) Pe 0v- po) 000--
(II)
BlOtie Osi Oiie)
where (): is the Beta function and B(oser O.00 - (r,e)
Tlaso + tooo aasa) with r()) denoting the Gamma function. Based on these, we can further derive P(y cla,, 0) as follows:
I(ate)
P(y = c|z,, 0) = / Pe p(pela0,, O)dpe
/ Pe: Bloxies 0000 and)
Pe Die 0ie-1(1 (1 pe) aso- dpc
Blaie + 1,0 alse)
1e 10:e(1 pa) - ai -ao- -pe
Bloie, 0:0 ass))
Blasc + 1,0 - (zi)
B(aie + 1,000 asse).
Blaie a:u ass))
l'ase + 1)l((s))
T(aso + ())((n
afaTferi (ora)
Olic g(Sc(x;; 0))
(12)
k= Oik
R (ff((x 0))
= E[Dir(ppllss)]
(13)
Specially, if g() adopts the exponential function, traditional softmax-baad based models can viewed as predicting the expectation of Dirichlet distribution.
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E.2 EXPECTED ENTROPY Bptel=,,0) [H[((()))
Given sample z and model parameters 9, the corresponding expected entropy B) (H) formulated
Spcrla, [H[[(e]] = Eplolagio)== Σ log pcl
Spielmyio Pel
Σ / plplay; 0)p, log
EJ piel......... .poe.... 0)p, log pe dpidpz- dpc
(oclogpelf (.. ..../...... -...... pl.r. poleey polaa, dp: dp 1dpets Apc]dp.
ploeliy o sylee pel.
Combining the probability density function in Eq. (T). we can further derive Eppp (m ppo log pel
as
Epcolee, 8) log pc]
(pelogpe) B(aje, aço aze)
Pc 2o (1 (0) dpc
Blage 1,000 - aga)
/ (logpc) Blase + 1, ajo) 2 pc) aaj-- dpc
Bloje, 0'0 Ojjc)
Maae + 1)I((3)0)
Eg Retele to [logpc] [logpp)
(15)
T(a,0 ()j())
Oje (vi(aze + 1) (aaa + 1)),
(16)
ajo
where (-) is the digamma function, Oje is the c-th element of vector ay and ayu 2k=1 ajk- Finally, the expected entropy for sample is denoted as
Epeple, (H(((()))) =
1p log pel
Oje (N(aje + vba55 + 1))
ayo
Djc
1
Ajk + 1) Maze + +1)
(17)
k=1
where Pjo
Bis oso
E[Dir(pelaa)]
E.3 MUTUAL INFORMATION [[,, plz,, 0]
According to the definition of mutual information be expressed as
Kieffer
1994 Shannon 1948
Fl. play, 0 can
p(y play 0)
Ty. pla;, 0) =
Σ p(u c, pla,, 0) log
dp.
(18)
ply c|æ, 0)p(ppppp pl., 9)
Since the deep model induces the Markov chain (z. 0) - - y. we have y and (æ,, 0) condi-
tionally independent given p, i.e., p(y, play, 0) plv p) p)p(p 0). Then, Eq.. 18) can be further
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derived as
ply c)p) dp ply c/ 0)
Tly pla,, 0]
p(p|2z 0)
Σ ply= = clp) log
= f p(pla, 0) Σ (pe log Pc - Pc ply = cla.j 0))
- p(plzz
-/rlplz, 0)
>(pee (polog pp))
p(plzz, 0)
Σ
(pe log
O'jo
)d
(19)
2k Oik
cml
B 0) Dir(pla))
log pel
(log
ajo
k=
Ogk
Pe log pcl
Pjclogise
Σ Pjo (o(aae+1)
v1 2 ajk + +11
Σ
PiclogPje-
(20)
The derivation of Eq.
19 based on the conclusion from Eq.
12 i.e. P(y = c/a,, 0)
And Eq. 20 is based on the conclusion in Section E.2
E.4 KULLBACK-LEIBLER DIVERGENCE CRI
For p(p)a.) Dir(plā;), its probability density function is defined as
p(p(a;) ((ā;))
Il
Pa
dic-1
(21)
IT ((aee)
where B()) the multivariate Beta function, B(ās)
TQ2 dic) and [(-) is the Gamma func-
tion. The Kullback-Leibler Divergence between Dirichlet distribution Dir(plã,) and Dir(p)1) is formulated as
KL(Drr(pla))DDi(ool) p(pláz))oo log p(plā.)) dp
p(p]1)
= / (()a))
((1)
C
Pc
log
B(a))
Pe
die
dp
cml
log ((ā.)
B11
B(a.)
1
C
Pe
Esc
1 dp
(log II Pc
a(a)))
II
Pe
asc dp
log 2(1)
+ T.
Bp- [lo II
Pc G
2(a.)
((1)
log B (.)
(die 1)B 1) BetolBBll & [logp]]
1 - arc) IT [(āre)
C
= =oo
[ān 1) 11(((ār))) - 2 2 an))
(22)
c=1
k=1
Thus, the computable expression of LE given by
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CK C. Σ
1
E KL.Ditolas:(Diw(oD)))
T.IT4
0,68
m,en
r dic)
log
+
(aie - 1) (((dic) 10 dist)
C Th8
r(C) [(ate))
2,ES
1 age)
Σ log
(ase 1) ((āse) - 2 > astt)
(23)
C. IT
I[C) I(āje)
BJET!
km
22


Reviews:
[{"review_id": "tXwCzXcM1h", "reviewer": "Reviewer_Rp4n", "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": "This paper proposes a novel domain adaptation active learning scheme building upon evidential deep learning. Namely, it computes distributional (or epistemic) uncertainty as mutual information and data (or epistemic) uncertainty as the expected entropy.  Then it uses a two stage approach that selects  to label the largest data uncertainty samples from a pool of the largest distribution uncertainty samples. The EDL method is enhanced to minimize data and distribution uncertainty for the newly labeled target samples.  This helps to identify remaining gaps in the labeling of the target samples.  The paper demonstrates via extensive experiments that this new Dirichlet-based Uncertainty Calibration method is able to find a better set of target samples to label than state-of-the-art active learning and domain adaptation active learning methods.", "summary_of_the_review": "The paper proposes a novel approach that is sensible and validated in extensive experiments spanning two different applications.\n\nI have looked over the revised paper and the authors' response.  I think this is a good paper that should be accepted, and my recommendation reflects this.  I think the other reviewers may not have appreciated the significance of the changes to EDL so that it can be applied for active domain adaptation. I can attest that the contribution of the paper in that regard is significant. I also believe that the authors have significantly enhanced the experiments in response to the other reviewers. The experimental section is comprehensive and demonstrates an advancement relative to the SOTA.", "strength_and_weaknesses": "The strength of the paper is that is proposes a novel domain adaptation active learning method that is a significant modification of evidential deep learning in its use of distribution and data uncertainty in its training and its selection of the samples to label.  The experimental validation is done for domain adaptation in image classification and semantic segmentation applications. The experimental results also provides ablation and other studies demonstrating the effectiveness of various components of the proposed DUC method. The weaknesses are fairly minor.  It would be nice if the experimental sections explains that datasets represent different domains to serve as the source and target domains. Perhaps one could quibble that other single-pass Dirichlet-based methods should be studied. Nevertheless, the study is already very extensive.   ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "Mwyd4sODdg", "reviewer": "Reviewer_arzy", "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": "The authors propose an uncertainty aware active learning domain adaptation based on imposing a dirichlet prior over model predictions. This allows them to get a distribution over model predictions, which in turn enables them to compute 2 kinds of uncertainty measures for each target datapoint. 1) target distribution uncertainty 2) data complexity uncertainty. \nUsing these two measures of uncertainty the active learning is done in 2 steps, first they select data points with highest amount of target distribution uncertainty and then from those datapoints with highest data uncertainty are chosen for being assigned ground truth labels. \nThe results on 2 classification datasets and 2 segmentation datasets show promising results.  \n", "summary_of_the_review": "I think the novelty is limited in the theoretical sense but its been used in an interesting application. That being said, the experiments are sound and do confirm the merits of the approach.  ", "strength_and_weaknesses": "\nStrengths\n- simple yet effective method\n- active domain adaptation is a practical approach for domain adaptation. Probably you can improve results by incorporating ideas from semi-supervised learning to use the unlabeled data in training as well. \n- extensive experiments and calibration analysis\n- ablation studies are good\n\nWeaknesses:\n- there are no error bars on the results of the experiments. Its important to have error bars to know if the improved results are statistically significant .\n- I think experimenting on more datasets would add merit to the paper and give more credibility to the approach. large scale datasets like Vista could be good additional datasets. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and 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": "EefJ0uxhk24", "reviewer": "Reviewer_CH6i", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The authors propose a solution to the problem of active domain adaptation, where limited target data is annotated to maximally benefit the model adaptation. The proposed solution called \"Dirichlet-based Uncertainty Calibration (DUC)\" achieves both target representativeness and mitigation of miscalibration. The authors place a Dirichlet prior on the class probabilities which helps interpret it as the distribution over the probability simplex. There is a two-round selection strategy, uncertainty of distribution and uncertainty of data, to select the target samples for annotation. The authors show the superiority of their approach on cross-domain image classification and semantic segmentation tasks.  ", "summary_of_the_review": "Overall, the paper is well written, and the results show improvement over the baseline models. However, I feel the technical contribution and the novelty are limited.\n\n", "strength_and_weaknesses": "Strengths:\n\nActive domain adaptation is a new sub-track of domain adaptation and the authors have proposed a new DUC approach to solving it. \nThe authors dealing with this use of Dirichlet prior and probability space on simplex mitigate the issues of the point estimate and consider all possible predictions.\nThe authors provide a detailed analysis of their approach with the intuition behind the optimization. \nThe results on miniDomainNet and Office-Home show improvement over the state-of-the-art (SOTA) models. This is true for GTAV and SYNTHIA experiments as well.\nThe ablation study in Table 5 shows that having loss of distribution uncertainty and loss of data uncertainty with the selection process helped in improving other SOTA counterparts.\nAlso, the authors studied the effect of different first-round selection ratios κ% on the Office-Home dataset which remains almost the same except for k=1% , where it was lowest (Fig 4a).\n\nWeaknesses:\nTwo main contributions in this work are derived from previous works:\n\t1: Predictive uncertainty estimation via prior networks (Malinin & Gales, 2018).\n\t2: Evidential deep learning to quantify classification uncertainty (Sensoy et al., 2018).\nIn my opinion, the above two prior work have been put together in this area of active DA.\n\nWhy has the author not reported the result on the VisDA-2017 dataset used in the EADA paper, since EADA is the current SOTA model? Why has the author not included the EADA paper as a baseline for the GTAV dataset in Table 3?\nIt is not reported in the paper where these numbers in Table 1 for EADA on miniDomainet have come from. \nIt is not reported in the paper what is the performance gap between Active DA methods and the “Full Supervised\" on the target domain. \n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and 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": {}}]

Author rebuttal:

Decision: Accept: notable-top-25%