Distributionally Robust Learning for Uncertainty Calibration under Domain Shift
Authors: Haoxuan Wang
Anqi Liu
Zhiding Yu
Junchi Yan
Yisong Yue
Anima Anandkumar
Venue: ICLR 2022 Submitted (2022)
Keywords: Domain shift
uncertainty estimation
calibration
distributional robustness
unsupervised domain adaptation
semi-supervised learning

Abstract: We propose a framework for learning calibrated uncertainties under domain shifts. We consider the case where the source (training) distribution differs significantly from the target (test) distribution. We detect such domain shifts through the use of binary domain classifier and integrate it with the task network and train them jointly end-to-end. The binary domain classifier yields a density ratio that reflects the closeness of a target (test) sample to  the source (training) distribution. We employ it to adjust the uncertainty of prediction in the task network. This idea of using the density ratio is based on the distributionally robust learning (DRL) framework, which accounts for the domain shift through adversarial risk minimization. We demonstrate that our method generates calibrated uncertainties that benefit many downstream tasks, such as unsupervised domain adaptation (UDA) and semi-supervised learning (SSL). In these tasks, methods like self-training and FixMatch use uncertainties to select confident pseudo-labels for re-training. Our experiments show that the introduction of DRL leads to significant improvements in cross-domain performance. We also demonstrate that the estimated density ratios show agreement with the human selection frequencies, suggesting a match with a proxy of human perceived uncertainties. 

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DISTRIBUTIONALLY ROBUST LEARNING FOR UNCERTAINTY CALIBRATION UNDER DOMAIN SHIFT
Anonymous authors Paper under double-blind review
ABSTRACT
We propose framework for learning calibrated uncertainties under domain shifts. We consider the case where the source (training) distribution differs from the tar- get (test) distribution. We detect such domain shifts through the use of binary domain classifier and integrate it with the task network and train them jointly end- to-end. The binary domain classifier yields density ratio that reflects the close- ness of target (test) sample to the source (training) distribution. We employ to adjust the uncertainty of prediction in the task network. This idea of using the den- sity ratio is based on the distributionally robust learning (DRL) framework, which accounts for the domain shift through adversarial risk minimization. We demon- strate that our method generates calibrated uncertainties that benefit many down- stream tasks, such as unsupervised domain adaptation (UDA) and semi-supervised learning (SSL). In these tasks, methods like self teafninaining and FixMatch use uncer- tainties to select confident pseudo-labels for re-training. Our experiments show that the introduction of DRL leads to significant improvements in cross-domain performance. We also demonstrate that the estimated density ratios show agree- ment with the human selection frequencies, suggesting a positive correlation with a proxy of human perceived uncertainties.
INTRODUCTION
Uncertainty estimation is an important machine learning problem that is central to trustworthy AI (Tomsett et al., 2020; Antifakos et al., 2005). addition, many important downstream applica- tions rely on the correct estimation of uncertainties. This includes unsupervised domain adaptation (UDA) (Zou et al., 2019) and semi-supervised learning (SSL) (Sohn et al., 2020) where they are used solicit confident pseudo-labels for re-training. In these applications, reliable pseudo-labels help avoid error propagation and catastrophic failures in early iterations (Kumar et al., 2020).
Obtaining reliable uncertainty estimation is challenging. In contrast human annotation of labels, obtaining the ground-truth uncertainties from real-world data can be costly or even infeasible. It is also known that commonly used uncertainty proxies in deep neural networks, such as the soft- max output, tend to give overconfident estimates (Guo et al., 2a). This overconfidence is further amplified under domain shifts, where the target (test) domain and the source training domain differ significantly. Such distributional shifts tend to aggravate the existing issues in uncertainty estima- tion, leading wrong but overconfident predictions on unfamiliar samples (Li Hoiem, 2020).
Many methods have been proposed to calibrate the confidence of deep learning models so that the uncertainty level of model prediction reflects the likelihood of the true event (Guo et al., 2017a). Label smoothing is a popular approach to reduce overconfidence and to promote more uniform outputs (Szegedy et al., 2016). 'Temperatrre scaling is another method where the logit scores are rescaled by a calibrated temperature (Platt et al., 1999). Approaches such Monte-Carlo sampling (Gal & Ghahramani, 2016) and Bayesian inference (Blundell et al., 2015; Riquelme et al., 2018) model uncertainties from Bayesian perspective but are computationally more expensive. Even though these methods lead to more calibrated uncertainties, recent studies show that their results cannot be fully trusted under domain shift (Snoek al., 2019).
Our approach. To handle domain shifts, we characterize the "overlap" between the source training data and the test data. Intuitively, if the test sample is highly unlikely in the training distribution,

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P.(x) (x)
P(ylar) exp
0- solor
Source Domain
o(2, 9)
Pa(x)
Y
Representation Learning
Target Classilier
X
(x)
Disciminative Learning
Binary Classifier
Target Domain
P((0)
X
22
(a) The end-to-end framework of DRL
(b) Density ratios:
(a(a1)
= 2.232, ((
(x( 1.004 ((a)))
Figure 1: (a) Architecture for end-to-end training of the proposed DRI, framework (training details in Sec. 2.3). (b) Example images for category 'Train' in VisDA. The estimated density ratios for the easy and hard target images are shown, respectively. The DRL framework gives higher uncertain predictions for the harder example (x:2) that is more cluttered and hence not well-represented the source domain.
then the resulting confidence levels should be lowered. We incorporate this idea through the density ratio between the two domains and employ for confidence calibration.
To make our idea more concrete, recall that the probability output of a standard neural network for classification can be expressed as P(ylær) xx exp (0,, ((x:)), where æ is the predictor input, Φ(x)) is the data feature, and y is the model parameter of the y-th class. Instead, we propose the following predictive form for our neural network:
P.(2z)
P(ylæ)) or exp
0, o(z)) P((x)
where (x) and (a())) are the densities of a data sample under the source and target distributions, respectively. When target sample is close to the source domain (large P. (.(x)) the prediction confident. However, when target sample (.(x)//(())) the confidence is lowered and the prediction is closer uniform distribution. This intuition is analogous to incorporating sample-wise remperature to adjust the confidence according to the closeness of test sample the training distribution.
is far away from the source distribution (small
Eq. (1) is based on the distributionally robust learning (DRL) framework. DRL is an adversarial risk minimization framework that involves a two-player minimax game between predictor and an adversary (Grünwald et al., 2004). While many previous DRL. methods (Liu et al., 2020; Nakka al., 2020) operate in low dimensional spaces using kernel density estimators for the density ratio estimation, we develop DRL method to scale to real-world computer vision tasks, which is able to produce calibrated uncertainties under domain shift. Our contributions are:
I) We propose a DRL method for uncertainty estimation under domain shift. We introduce a binary domain classifier network which learns to predict the density ratios between source and target do- mains (See Fig. (a)). The domain classifier and the target classifier are trained simultaneously in an end-to-end fashion. We also introduce a regularized DRL framework further promote smoothed model prediction and improve the calibration.
2) We show that the estimated density ratio reflects the distance of a test sample from both training and test distributions (Fig. I(b)). Our experiments further empirically show that these estimates are also correlated with human selection frequency, based on the available ground-truth labels in Ima- geNetV2 (Recht et al., 2019a), which can be regarded as proxy of human uncertainty perception.
3) We empirically show that the top-1 class predictions of DRI. are more calibrated than the em- pirical risk minimization (ERM) and the temperature scaling Office31 (Saenko al., 2010), Office-Home ( (Venkateswara et al., 2017), and VisDA (Peng et al., 2017). We measure the level of calibration using expected calibration error (ECE), Brier Score and reliability plots.
4) We integrate our method as a plug-in in module downstream applications such as unsupervised domain adaption and semi-supervised learning, leading to significant improvements. For exam- ple, incorporating self-training (Zou et al., 2019) with DRL leads to -fate-of-the-arr performance on VisDA-2017 (Peng et al., 2017) and 6% improvement hard examples. Incorporating Fix-
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match (Sohn et al., 2020) with DRL improves the original Fixmatch by relative 17% increase in accuracy under the cross cross-domain setting.
DISTRIBUTIONALLY ROBUST LEARNING
In this section, we first review the preliminaries of DRL (Sec. 2.1), followed by a proposed variant of DRL with class regularization (Sec. 2.2). We then propose an instantiation of DRL with a dif- ferentiable density ratio estimation network (Sec. 2.3). Finally, we show the application of DRL in UDA and SSL tasks (Sec. 2.4).
2.1 PRELIMINARIES
Notations and definitions: We denote the input and labels by random variables X and Y. We also use I E RR and X' to represent the realization and sample space of X. Our goal is to find a predictor
F. R + RC A (f(x)) E X, (() E nR
close to the true underlying (Y(Y) Here, d, C' and A denote the input dimension, class number, and probabilistic simplex, respectively. We consider the problem with labeled data sampled from a source distribution P.(X, Y) and unlabeled data sampled from a target distribution Pi Pi(X). and use (X, Y) to represent the empirical source distribution. In this work, we consider an important form of domain shift with the covariate shift assumption (X( o P.X), P.( P. (X).
Traditional empirical risk minimization (ERM) frameworks tend to fail under covariate shift since ERM empirically learns a predictor (Y from the finite source data that usually fails to generalize to the target distribution. DRL was previously proposed to overcome this issue. DRL can be formulated as a two-player adversarial risk minimization game (Grünwald et al., 2004) with the predictor player minimizing loss, while the adversary player maximizing the loss. The adversary is allowed to perturb the labels, subject to certain feature- feature-matching constraints to ensure cata-compaiibility.
Motivation:
Formulation: Under covariate shift, DRL (Liu & Ziebart, 2014) deals with the mismatch between the expected loss and the training data, and is defined on the target data distribution:
X((Y|X)= = argmin max GE
(ff)))
where f(x).g(x) E RC are the conditional label distributions given an input x and F. G are the entire distribution over all the input. E,-r, [(-) is an expected log loss on the target input defined:
Rex) (x)
R(x) g(=) log f(r)).
(4)
F is the predictor player minimizing the loss function while G is the adversary maximizing the loss function. After solving this game, F our estimate of P.(Y)X), which we will use for the classification on the target domain.
Eq. defined on the target domain only. How could a predictor be properly trained while there are no target labels available? The answer is that the adversary G is implicitly constrained by the source features. We use the following constraints to make sure that G close to PY(Y(X):
Σ = = E. ((x.) E. = v) (xx)) Vy).
(5)
where D4 (X) and By is the y-th dimension of g. Eq. 5 is a necessary but not sufficient condition for G (Y))). thus serving as an implicit constraint for G' to be close to the true (X under the covariate shift assumption. Given a predefined feature function d, when the adversary perturbs the conditional label distribution, certain aggregate function of & on g should equal to the counterpart on the empirical source data.
From DRL to density ratio: When using the expected target logloss in Eq. 3, Eq. 1 is derived by solving the predictor F. Here we refer the derivation details to (Liu & Ziebart, 2014) but emphasize the important properties of the prediction: representation-lewe conservativeness.
Representation-level conservativeness: The predictions have higher certainty for inputs closer to the source domain when Pz(x)/P((s) is large. On the contrary, when Px(x)/P((x) is small, the prediction is more uncertain. This property reflects the model's ability to convey information about what does not know through the model uncertainty.
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2.2 CLASS- CEASS-REGULARIZED DISTRIBUTIONALLY ROBUST LEARNING
Inspired by label smoothing (Szegedy et al., 2016) and regularization of neural network outputs (Pereyra et al., 2017), we can further add class-regularization to the conservative predictions in Eq. I. Instead of doing it in a post-hoe way, we study how to incorporate class-regularization into the DRL framework. We propose to use weighted logloss to penalize high confidence in the adversary's 's label prediction:
X(( = argmin max R g(x) log f(x)] - rB R(X) ly 2 g(x) log f(x) (6)
F GEE
where y is the one-hot class vector, C is the element-wis product, and parameter that controls the level of regularization. E here is the same as in 3. We observe the whole loss function is convex-concane function in terms of f and g. According the strong duality, switch the order of the min and max. With a fixed g. I = is the optimal solution of the inner min problem. So we have the following lemma (we refer all the proofs appendix Sec. A):
[0. is hyper-
Lemma 1. Eq. 6 can be reduced regularized maximum entropy problem with the estimator constrained:
max
- log (a)] P((X)) y O (() log f(x)]
FEE
where E is the same as Eq. 5, meaning F should be close to the empirical source Px(()
Paiw) 0g (()))))))))))))))) Pite) r(())+1
Theorem 1. The solution of Eq. 7 for takes the form: fo.((ulx)) & exp
where A represents the model parameters and (ty) the yth dimension of the one-hot encoding y.
The proof of Theorem follows the same principles when Eq. I derived from Eq. The training process of this model also follows the same procedure in (Liu & Ziebart, 2014), except that we use Theorem to compute the prediction results. In training, we can compute the gradients using source labels where is the one-hot encoding of each class. In testing, we set y to be an all-one vector.
r adjusts the smoothness of g's label prediction in Eq. 6. It translates to the ry terms in the prediction form. Intuitively, this regularization increases the correct label's prediction result when small and decreases when it large, using a thresh- old of 1 to discriminate between 'large' and 'small'. This provides additional regularization and smoothness to the conservative prediction.
Class-level regularization: Hyper-parantn
2.3 DIFFERENTABLEE DENSITY RATIO ESTIMATION
Estimating P.(z)) (x) (Sugiyama et al., 2012) can be challenging, especially in high-dimensional spaces. Usually a plug-in estimator is used. But the plug-in estimates are usually sub-optimal for downstream tasks due to the different objectives. We propose end-to-end training procedure for DRL such that the density ratio estimator trained together with the target classifier. The key insight here is that we use two neural networks for classification and differentiating the two domains, respectively. See Fig. (a)). We now first introduce differentiable density ratio estimation before introducing joint training loss and the parameter learning of the two networks.
Differentiable density ratio estimation: Based on the Bayes' rule, (.x))/(((zz) can be computed Pi(=) P(a P(tæ)) P(s).
P.(=) P( P(s P(t) Concretely speaking, they can be estimated through binary classification using unlabeled source and target data
from conditional domain classifier (Bickel et al., 2007):
P(s) with P(U) as a constant relating to number of source and target samples. On the other hand, we observe that P.(=))/ (ax)) can be a trainable weight for each sample, and can receive gradients from the training objective of DRL. Therefore, we propose to train a discriminative neural network to differentiate the two domains, which receives training signals from both the target classification loss in DRL and the binary classification loss. The weights trained this way lost their original properties as density ratios, but still reflects the relation between the two domains.
Joint training loss: Assume ((x, w,)) is the representation learning neural network with parameter W,, We further define (x(X) as the joint distribution of both source data and target data with their domain labels D = {d(x) ( }. We denote T (x, wa) = (Tx, (where т, + 7, = 1) as the probability output of the source and target domains from domain classifier with parameter wa. Our joint
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training loss is defined as:
min Wr.C
P(xx)(() ga:)) log (a; wr, 0, wa)] + Px d(x)) : log wa))
(8)
where (x) P and f (x: w,, 0, ra) takes the form in Theorem 1:
f(x; wr: ra) x exp ((T)(2))))) wa) 0 Φ( w.) + rl(v)) /(r(())+ +1)
(e)
Parameter learning: Note that Jt in the first loss term of Eq. (8) concerns the conditional label distribution on target which assumed to be not available. However, with the DRL formulation, we can compute and evaluate the gradients of 0 and 6(x w,) directly with the change of measure in the derivation of the gradients (Liu & Ziebart, 2014), since the gradients are only associated with the source data and labels. We show this in Fig. (()) that the representation learning network ø only has source data as the input. We then update and w, using the computed gradients and also directly hack-propagate from the second loss term to update wa. Finally, treat the densities trainable variables and derive gradients for them from the first loss term (details shown in appendix Sec. B).
By the Bayes rule, P. T.P(s)' where P(t) and P(s) are the amount of unlabeled data from each of the domain during the training process. Since we usually the same amount of source and target P(a) 1. Then f Theorem reduced to Eq. data in each batch, they cancel out by following P(t)
P.(=) T_P(t)
9. Therefore, besides the binary classification loss, the parameter wh of the discriminative network is also trained with gradients from the first loss term. Algorithm summarizes the procedure.
DRL model Prediction
Unsupervised
Algorithm 1 End-to-end Training for DRL
X,
Pseudo- Labels
Losses
1: Input: Source data, target data, DNN &. DNN
T, SGD optimizer SGD1. SGD2, learning rate Y11 and 72, epoch number T. Initialization:
Target
Φ, + random initialization,
X, Y.
DRL model Training
DRL Lasses
epoch + 0
3: While epoch < T
Source
4: For each mini-batch
Figure 2: Formulation of the pseudo label based UDA or SSL methods with DRL. The unsupervised losses represent the loss function user can impose on the unlabeled target data. DRST conducts this procedure for multiple it- erations, while DRSSL minimizes the unsuper- vised losses on the augmented target data.
Update т by SGD1(m) using the combined gradients from both loss terms; Compute f using 8, w., and wa; Update 6,0 by SGDa(12) using de-
6:
rived gradients;
epoch +- epoch +1
9: Output: Trained networks Φb,
2.4 APPLICATIONS TO UDA AND SSL
We show how to incorporate end-to-end DRL within a framework that takes unlabeled data for training. We introduce the general setting with two examples: self-training UDA and cross-domain SSL, followed by new self-training algorithm DRST and new SSL algorithm DRSSL.
General settings: In many cases, the source domain where models are trained may have abundant labels but the target domain lacks enough labels. Typical problems under this setting include unsu- pervised domain adaptation and (Zou al., 2019) and semi-supervised learning (Sohn al., 2020). In both cases, common strategy is to treat the prediction results on the target data as pseudo labels train the model on target data. In these methods, model confidence (softmax output) often leveraged as the proxy to rank the reliability of pseudo labels, with the underlying assumption that there exists a positive correlation between model confidence and pseudo label quality. However, such assumption requires accurate uncertainty estimation to avoid false usage of wrong pscudo labels which may poison the training. To this end, we incorporate DRL into these frameworks with to provide calibrated uncertainties. An illustration of this setting is shown in Figure 2.
Distributionally robust self-training: In UDA, we are given labeled source data and unlabeled target data and aim to achieve adaptation from the source to the target domain. Self-training is an effective method for UDA (Zou et al., 2019), where the training procedure in Fig. 2 is conducted multiple times. Here we propose DRST to plug the class-regularized DRL. model into self-training.
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The idea is to regard each training epoch as new domain shift problem in DRL. After each train- ing epoch, we make predictions on the target domain and select more confident data and generate pseudo-labels for them to merge into the source training data. Then the labeled source data and the newly pseudo-labeled target data become the new source set for the next training epoch.
Distributionally robust semi-supervised learning: In cross-domain SSL,, we have few labeled source data and many unlabeled target data. We aim to utilize unlabeled data in the target do- main to help representation learning and save the effort needed for labeling. One simple and effec- tive strategy is to use pseudo-labels generated from weakly-augmented data to supervise strongly- augmented data (Sohn al., 2020). Here 'weakly' means simple flip-and-shin data augmentation while 'strongly' follows the same strategy with (Sohn et al., 2020). Using DRL's prediction, we propose DRSSL. which assigns pseudo-labe labels more conservatively. We plug DRL, into Fixmatch (Sohn et al., 2020). Here the unsupervised loss in Fig. 2 is the "consistency loss' in (Sohn et al., 2020): La 1 M the weakly-augmentte target data, z² and y represent the strongly-augmentt version of the same image data, and is threshold for generating pseudo-labels it""
Im=1 I[max(P(y) (x+")) > (Ú.", (x;)), where 2x and yr" represent
3 EXPERIMENTS
We evaluate our method on benchmark datasets. DRL is evaluated as a method providing more calibrated uncertainties (Sec. 3.1), DRST effective UDA method (Sec. 3.2) and DRSSL cross-domain SSL method. We show additional results and details in appendix Sec. D.
Datasets and methods: We use Office31 (Saenko et al., 2010). Office-Home (Venkateswara al., 2017) and VisDA (Peng et al., 2017) for evaluating DRL's uncertainties. We compare DRL with temperature scaling (TS), VADA (Shu et al., 2018) and source-only. We also train models using ImageNet (Deng et al., 2009) as the source domain and ImageNetV2 (Recht et al., 2019a) as the target domain to check the relationship between our estimated weights and the human selection frequencies (HSF). VisDA2017 is used to evaluate DRST, for which we compare with (1) tradi- tional UDA baselines: MMD (Long et al., 2015), MCD (Saito et al., 2018b) and ADR (Saito al., 2018a); (2) recent self-training UDA baselines: CBST (Zou et al., 2018) and CRST (Zou et al., 2019); (3) other uncertainty quantification or UDA methods combined with self-training baselines: AVH (Chen et al., 2020a) CBST and DeepCORAL (Sun & Saenko, 201 CBST.. In addition, we use CIFAR1O, STL10 (Coates et al., 20, MNIST (Lecun & Bottou, 1998) and SVHN (svh, 2011) to construct settings with few source labeled data and much unlabeled target data and show DRSSL's advantages in cross-domain SSL over Fixmatch (Sohn et al., 2020).
Evaluation metrics: Apart from accuracy, we also use Brier score (Brier, 1950), expected calibration error (ECE) (Guo et al., 2017a), and reliability plot (Dawid, 1982; Guo et al., 2017a; Nacini et al., 2015) to evaluate the performance of our proposed method and the base-
Table 1: ECE on ImageNetV2.
HSF
Source
Temp.Scal.
DRL (Ours)
[0.0,
0.2694
0.2624
0.0129
10.2.
0,1818
0.1745
0.0036
[..4.
0.1344
0.0012
[0.6,
0.0667
0,0601
0,0019
lines. Brier score measures the mean squared difference between the predicted probability assigned to the possible outcome and the actual outcome. Despite potential prob-
[0.8
0.0319
0.0246
0,0019
lems with ECE (Nixon et al., 2019), it is still the most prevalent metric for the top- I prediction. ECE is defined as the confidence bins (we use 15 bins in practice). For both the Brier score and ECE, the lower the score, the better the model is calibrated.
of average difference between prediction accuracy and confidence of different
High
For Office31 and Office-Honee tasks, we use ResNet50 (He et al., 2016) the backbone for all models to make the comparison fair. We train by SGD for 100 epochs and set the learning rate 0.001. For VisDA, we use the ResNet101 (He et al., 2016) backbone and also the SGD optimizer. During the 20 epochs of training, the initial learning rate set as 10-5 and the weight decay parameter is set as 5 x 10-4 For ImageNet, we follow the standard training process of AlexNet (Krizhevsky et al., 2012) and VGG-19 (Simonyan & Zisserman, 2014), where the initial learning rate is 0.01 and we decay the learning rate by a factor of 10 every 30 epochs.
Experiment setup:
Mensttyyaa Ratio
AlexNet Figure 3: Density ratios vs. HSF on ImageNet V2.
VGG-19

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Brier Score
Brier score
0.13
Source DRL
Brier
VADA
0211
Epochs
1o Wx 355 15 Epochs
Epochs
Confidence Accuracy 5
Confrdence Accuracy
Confidence Accuraty
Source
T5
(max prob)
Confidence
EXIL
SANE
Confidence (max prob)
(a) Office31 (A-*) (b) Hifice-Home (P-+A)
(c) VisDA
Figure 4: Brier score (upper) and reliability diagrams (lower) on Office31, Office-Home and VisDA.
DRL generates more calibrated uncertainties than source-only and temperature scaling and VADA measures the mean squared difference between the predicted prob- ability and the actual outcome. For fully calibrated classifier, the confidence should match the accuracy across the full range of confidence. Thus the closer the lines the dashed line, the more calibrated the method is. Our method gets more and more calibrated as confidence increases.
Shu et al. (2018). Brier
3.1 CALIBRATED UNCERTAINTIES FROM DRL
DRL's calibrated confidence: Fig. demonstrates our more calibrated uncertainty. DRL tends to be underconfident and conservative but still stays closer to the calibration line (dashed line). Table also shows our better ECE on ImageNetV2 in different human selection frequency (HSF) bins. Our additional results appendix Sec. C show that the accuracy of DRL. also competitive.
Density ratio v.s. human selection frequency: Fig. shows that the estimated weight is positively correlated with the human selection frequency (HSF) in ImageNetV2 (Recht al., 2019b) under different neural network architectures, Here we regard [O, 0.2] as low HSF and (0.2, 1] as high HSF. Images with low HSF have smaller weights, indicating that they are visually harder for humans.
3.2 UNSUPERVISED DOMAIN ADAPTATION
Initialization with ASG: The quality the source model has significant impact on the final performance. The recently proposed automated synthetic-to-real generalization (ASG) model using ImageNet pretrained knowledge can be used to improve synthetic training (Chen et al., 2020b). Initializing with ASG trained model leads to significant improvements in self-training. Hence, we use the ASG pretrained model as an initialization, with results shown Table 2's last four lines.
Accuracy and calibration: Fig. 5(a) and Table 2 show that DRST performs best in accuracy. Our vanilla version of DRST outperforms CRST by over 5% with ASG initialization. We improve the SOTA self-training accuracy VisDA by over 1%. In the rest of the results, represent DRST-ASG. Fig. 5(b) shows that DRST also achieves higher calibrated confidence.
DRST to
Table Accuracy comparison with different methods on VisDA2017. "Skate" denotes "Skateboard".
Method
Acro
Bile
Bus
Car
Horse
Knife
Mator
Person
Plant
Skate
Trann
Truck
Mean
Scurce (Saito et al., 2018s)
55.1
53.3
61.9
59.1
80.6
17.9
79.7
31.2
81.0
26.5
73.5
8.5
$2.4
MMD (Long al, 2015)
87.1
63.0
76.5
42.0
90.3
42.9
85.9
53.1
49.7
36.3
85.8
20.7
51.1
MCD (Suito et all 2018b)
87.0
60.9
83.7
64.0
88.9
79.6
54.7
76.9
88.6
40.3
83.0
25.8
71.9
ADR (Saito ot all 2018a)
87.8
79.5
83.7
65.3
92.3
61.8
88.9
73.2
87.8
60.0
85.5
52.3
74.8
CRST (Zou 2018)
78.8
79.2
77.7
CRST (Zou et 2019)
88.0
79.2
61.0
60.0
87.5
81.4
86.5
78.8
85.6
86.6
73.9
68.8
78.1
CBST-AVH (Chon 2020g)
93.3
80.2
78.9
60.9
88.4
89.7
89.5
81.5
CBST-DCORAL. (Sun Suenko, 20166
92.1
78.9
83.0
73.6
93.2
94.7
$9.0
83.0
89.8
$1.2
85.5
44.9
82.4
DRST (ours)
93.47
86.
65.74
68.03
93.99
95.08
87.34
$3.30
92.97
88.65
83.66
66.42
83.75
ASG (Chen al., 2020bb
88.81
68.5
65.31
78.06
95.78
9.11
$4.39
29.58
82.13
33.76
$6.00
12.04
61.17
CBST-ASG (Chen al., 2020b)
95.12
86.53
79.83
76.01
94.61
92.34
85.94
15.08
89,23
82.16
73.42
$6.49
82.23
CRST-ASG (Chen 20201b)
74.63
92.43
83.78
DRST-ASG (ours)
94.51
85.55
76.50
77.18
94.39
95.33
83.89
81.23
94,22
90.36
$1.75
63.10
65.25

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Under review as a conference paper at ICLR 2022
5300
231T
30000
DRL DMS!
E3551
DAST Radl
DEST nx
DIST
10
CBST
CMSI
15000
02.03
061
30
10 125
153 13
75
133 X00
Epoch
Epoch
Denaty bresnots
(d) Harder cases Figure 5: (a)-(b) Main results on VisDA-17 (5 random seeds) with the test accuracy and Brier score. The results show that DRST outperforms the baselines significantly. (c) Distribution gap P. (((((()))PP((((()))
(a) Test accuracy
(b) Brier score
(c) Covariate shift
P. (Φ(œ), u)/ (:((()),,)) as proxy of covariate shift. DRST helps to further reduce this gap over DRL with self-training. (d) Accuracy vs. estimated weights. The improvement from DRST increases harder examples (lower weights).
Ablation study: Fig. (()(b) include two ablation methods. In the first ablation, we set to 0 so that there is no class regularization DRI. ("r = 0").. The prediction then follows the form in Eq. (1). In the second ablation, method so that there is no representation level conservativeness ("R = 1"). DRST achieves the best performance when both components present.
set the weights to to mute the differentiable density ratio estimation in our
Covariate shift: Fig. 5(c) shows P. (()( (()(())))))) (o(()) y)) y)/P(((()) y) using discrim- inative density ratio estimators (per class). This serves proxy of covariate shift as it becomes O when covariate shift holds. We can see that the gap decreases with self-training, which shows that even though covariate shift may not hold in the beginning, self-training helps to promote this assumption with better aligned domains and more discriminative feature distributions.
Improvement hard examples: Fig. 5 (d) demonstrates that DRST achieves larger performance gain compared to the baselines on target samples with smaller weights. Recall that data is not well- represented in the source domain when (ar) (ax))) small (Fig. 1(b)). Therefore, DRST provides robust performance on harder examples in the target domain.
Density ratios: In Fig. 1(b), a harder example obtains lower density ratio due its vague shape. Our density ratios reflect the closeness of a sample to the two domains. More examples are in appendix Sec. C. Moreover, the magnitude of our estimated density ratios are modest general within the range [0.1, 10). This is due to the regularization by the other network's 's learning signals.
Improved attention: Fig. visualizes the network attention of DRST and the baselines using Grad- CAM (Selvaraju et al., 2017), where DRST renders improved attention with better object coverage.
Input image
CBST
CRST
DRST
Bus x
Truck v/
Figure 6: Model attention visualized using Grad-Cam (Selvaraju et al., 2017). We also show the predicted labels by different methods. Our method captures the shape features of the image better.
3.3 DISTRIBUTIONALI ROBUST SEMI-SUPERVISED LEARNING
We use two pairs of source and target domains in this experiment: Source: CIFARIO Target:
Table 3: Accuracies for cross- cross-domain SSL.
Test set
CIFARIO
STL10
MNSST
SVHN
STL10 and Source: MNIST Target: SVHN. Table show that DRL-powered SSL. method improves the original Fixmatch significantly in
Fixmatch (Sohn al., 2020)
91.60
99.43
26.50
cross-domain ceni-supervised learning tasks. Note setting is different from UDA where source labeled data is abundant. SSL focuses on using unlabeled augmented data to help learning from few labeled data. In the CIFAR10 to STL10 case, only have 4k labeled source data. For MNIST to SVHN, we have 40k labeled source data. The results show that DRL is beneficial for generating high-quality pseudo supervision for unlabeled data under the cross-domain SSL setting.
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4 RELATED WORK
Distributionally robust learning: Several different learning algorithms be derived from this framework (Liu & Ziebart, 2014; 2017; Chen et al., 2016; Fathony et al., 2016; 2018). One limitation of this line of work is that it is only suitable for low-dimensional data. The other inconvenience is that it requires the density ratio to be estimated beforehand. Our work instead deals with high- dimensional data and estimates the density ratio along with the learning process. Another line of work perturbs the covariate variable (Ben-Tap Tal et al., 2013; Shafieczadeh Abadeh et al., 2015; Sinha al., 2018; Hu et al., 2018; Najafi et al., 2019) and focuses on model robustness against adversarial perturbations. In our work, we make DRL practical in high-dimensional vision tasks by introducing an end-to-end trained domain classifier.
There is rich literature in UDA focusing on representation alignment between the source and target domains (Fernando et al., 2014; Pan al.,, 2010; Sun et al., 2016; Wang et al., 2018: 88; Baktashmotlagh et al., 2013; Na et al., 2021). It is also prevalent to use a discriminator network to differentiate two learned representations (adversarially) to locate such a feature space (Ganin et al., 2016; Tzeng et al., 2017; Ajakan et al., 2014; Long et al., 2018; Sankaranarayanan et al., 2018). Some other works focus on more specific shift assumptions, such as covariate shift (Shimodaira, 2000) and label shift (Lipton et al., 2018; Azizzadenesheli al., 2019). For the covariate shift case, even though various density ratio estimation methods were investigated before (Sugiyama et al,, 2012), only few works explore the possibility apply them high-dimensional data (Khan al., 2019; Moustakides & Basioti, 2019; Park et al., 2020). Recently, multiple self-training methods have been proposed for UDA (Zou al., 2018; 2019) and many theoretical understandings of self- training are also developed (Kumar et al., 2020; Chen et al., 2020c). Similarly, rich literature also exist in pseudo-labeling for SSL (Berthelot al., 2019; Arazo et al., 2020; Miyato et al., 2018: 8; Sohn et al., 2020). In this paper, we focus on utilizing DRL's model uncertainty to help with choosing better pseudo-labeled data from the target domain in UDA and cross-domain SSL.
UDA and SSL:
Uncertainty quantification with deep models: Bayesian methods largely contribute to comple-
menting deep learning with uncertainty quantification (Gal, 2016; Welling & Teh, 2011; 1; Kingma & &Welling, 2013; Louizos& & Welling, 2017; Blundell et al., 2015; Riquelme et al., 2018; 8018; Gal & Ghahramani, 2015; Gal et al., 2017; Kendall & Gal, 2017: Mandt et al., 2017). However, with a large number of parameters, Bayesian deep learning may suffer from computational inefficiency. Other calibration methods include temperature scaling (Platt et al., 1999; Guo et al., 2017b), deep ensembles (Lakshminarayanan et al., 2017), calibration regression (Kuleshov et al., 2018), quantile regression (Romano et al., 2019) and trainable calibration measure (Kumar et al., 2018). These methods do not apply to our setting because we do not have access to the target labels. Recent work on calibrating or uncertainties under domain shift either only focus on "using" but not "generating" the uncertainties (Han et al., 2019; Lee & Lee, 2020: Kurmi et al., 2019) or focus on the importance weighting setup (Park et al., 2020; Wang et al., 2020). In this paper, we generate more calibrated uncertainties using the DRL framework, where the density ratios are inherent.
CONCLUSION AND DISCUSSION
In this paper, we have studied uncertainty estimation under distribution shift using the distribution- ally robust learning framework. We demonstrate that density estimation can be integrated into the learning process by using a domain classifier. We propose differentiable density ratio estimation and develop end-to-end training techniques for our proposed method. Using DRL's more calibrated model confidence helps to generate better pseudo-labels for self-training in UDA and cross-domain SSL. We also empirically demonstrate that the density ratios learned from our domain classifier re- flect the hardness of image, showing positive correlation with the human selection frequencies. In the future, we are interested in relaxing the assumptions made and study different shifts in the DRL framework.
Density ratio estimation: Our density ratios are estimated from a differentiable domain classifier and is not guaranteed to match the true density ratios. Thus our density ratios should not be used in circumstances where true density ratios are absolutely required. However, we show that our density ratios do reflect the relation between the two distributions and benefit the downstream tasks.
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14


Reviews:
[{"review_id": "rRHgkAIWfmq", "reviewer": "Reviewer_St2k", "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": "The paper proposes an uncertainty ( density ratio) of source-target prediction to adapt for the target domain. The novelty is somewhat limited; other works also tackled the distributional shift using the confidence and prediction of domain classifiers.[d][f]. The paper is lacking in some of these aspects: \nClarifications: \nWhat is the $\\sum$ in Eq 3\nHow to present work different/related adversarial domain adaptation methods; this discussion will clarify the paper further.  using the Bayes theorem, the Differentiable density ratio estimation can be treated as the discriminator's prediction.( discussed in sec 2.3) \nDo source and target predictors share some parameters? \nIn Eq 6and  7, how to obtain y for unsupervised domain adaptation case. Is it a class label or domain label?\nPerformance: \nThe performance is not compared with recent state-of-the-art methods in domain adaption[a][b][c][d][f] in real workd dataset such as VisDA.\nRelated comparison:\nThe paper missed some of the useful references that tackle the domain adaptation using uncertainty.[d][e][f]. I suggest authors to compare their methods with these related works in terms of performance.\n\n\n[a] FixBi: Bridging Domain Spaces for Unsupervised Domain Adaptation, CVPR 2021\n[b]d-SNE: Domain Adaptation using Stochastic Neighborhood Embedding, CVPR, 2019\n[c]Self-adaptive Re-weighted Adversarial Domain Adaptation, IJCAI 2020\n[d]Unsupervised Domain Adaptation via Calibrating Uncertainties, CVPR workshop 2019\n[e]Model Uncertainty for Unsupervised Domain Adaptation ICIP 2019\n[f] Attending to Discriminative Certainty for Domain Adaptation, CVPR 2019", "summary_of_the_paper": "The paper proposes an uncertainty ( density ratio) of source-target prediction to adapt for the target domain. The methods also validated in the robust semi-supervised tasks.", "summary_of_the_review": "The paper is lacking in terms of performance on domain adaptation tasks as compared to state-of-the-art methods. Some more clarification about the method will increase the readability of the paper.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "rIwXoUM13RT", "reviewer": "Reviewer_xXg4", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "1. The paper studies an interesting and important research question: calibrate uncertainties under domain shift. And the authors proposed a novel method based on DRL and density ratio estimation. The proposed method can be seen as a plug-in tool for existing methods. \n2. The paper may overclaim in the abstract that the authors \"consider the case where the source distribution differs significantly from the target distribution\". The proposed method has a covariate shift assumption. Then how could the two distributions differ SIGNIFICANTLY? Does the proposed method still work when the support of the source and target domain are (largely) different?\n3. Density ratio estimation is known to be hard when the input data is complex/in high-dimension. I have some doubts about how well the density ratio is estimated in the proposed method. I think further investigation in the learned density ratios is necessary to understand how the proposed method works. Figure 3 shows a coarse study on this point but I'm not convinced by this simple result. The discussions and ablation studies may not enough to show this point. Also, the threshold of low/high HSF seems quite artificial. \n4. The proposed method is based on a strong covariate shift assumption, which is very likely to be violated in real-world applications. The authors show that self-training may help to relax this assumption. But how about the proposed method without self-training? Self-training is already a strong additive in weakly-supervised learning for achieving good performance. Perhaps it is the self-training part in DRST that makes the proposed method work? I hope to see more results for the proposed method without self-training. ", "summary_of_the_paper": "In the paper, the authors propose a framework for learning calibrated uncertainties under domain shift based on a distributionally robust learning (DRL) framework. As a plug-in module, the proposed method benefits downstream tasks of unsupervised domain adaptation and semi-supervised learning in experiments. \n", "summary_of_the_review": "The research question is important and useful but the writing of the paper may overclaim the usage of the proposed method. Also, it may be hard to conclude how the proposed method works under the current evidence. \n", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "O3N5tjy1XLf", "reviewer": "Reviewer_zkq9", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths:\n+ The authors incorporate the density ratio estimation method into the existing distributional robust learning (DRL) framework and successfully achieve a better calibration under domain shift.\n+ They further integrate their method as a plug-in module in downstream applications such as unsupervised domain adaption and semi-supervised learning, leading to significant improvements. This part is new to me and riveting. I appreciate the authors for not only making the predictions more calibrated but also achieving higher performance.\n+ Competitive performance on various tasks including Office31, Office-Home, and VisDA-2017 demonstrate the superiority of DRL over empirical risk minimization (ERM) and the temperature scaling method measured by expected calibration error (ECE), Brier Score and reliability plots.\n+ This paper is well-written and easy to follow.\n\nWeaknesses:\n+ My first major concern is the novelty of this paper. There are mainly two technical parts of this paper: the density ratio estimation method and distributional robust learning (DRL). However, density ratio estimation by a domain classifier is common practice in domain adaptation and transfer learning. Moreover, this technique has already been successfully tailored into calibration under domain shift [1][2]. As for the distributional robust learning (DRL) framework, it has been successfully proposed in Liu & Ziebart, 2014 as stated by the authors.\nThe differences between these related works with the proposed method should be fully discussed to make the contribution enough for this top-tier conference.\n+ Another major concern is the performance of FixMatch on CIFAR10. The reported number (91.60) is much lower than that reported in the original paper of FixMatch, which is about 95.7?\n+ What is the definition of human selection frequencies (HSF)? Why should the estimated weight match HSF? I highly encourage the authors to deeply analysis this topic to bring more insights.\n+ Why Brier Score of Temperature Scaling (TS) is missing in Figure 4?\n\n[1] S. Park, O. Bastani, J. Weimer, and I. Lee. Calibrated prediction with covariate shift via unsupervised domain adaptation. 2020.\n\n[2] X.Wang, M. Long, J. Wang, and M. Jordan. Transferable Calibration with Lower Bias and Variance in Domain Adaptation. In NeurIPS, 2020\n", "summary_of_the_paper": "This paper focuses on the problem of uncertainty calibration under distribution shift. By using a domain classifier in the distributional robust learning (DRL) framework, the authors estimate the density ratio between the source and target domain to achieve well-calibrated predictions under domain shift. A regularized DRL framework is further proposed to promote smoothed model prediction and improve the calibration. Experiments on Office31, Office-Home, and VisDA-2017 demonstrate the superiority of DRL over empirical risk minimization (ERM) and the temperature scaling method measured by expected calibration error (ECE), Brier Score, and reliability plots.", "summary_of_the_review": "A uncertainty calibration method under domain shift with a distributionally robust learning framework that show competitive performance on comprehensive experiments but lacks enough novelty.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "9vyJ_apDG5F", "reviewer": "Reviewer_6Mv8", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths:\n\n* The proposed use of density ratios makes an attempt to quantify the domain shift. This is an improvement over other works which take domain shift for a given. \n* Uncertainty is evaluated using both ECE and Brier score. (Usually papers choose only one of the two.) \n* Section 2.2 derives use of density ratios to scale (temperature of) uncertainty from theory in Distributionally Robust Learning, which is a novel combination of views. Subsequently, Figure 3 shows that the density ratios correspond to human interpretation of domain differences. This correspondence validates the design choice for density ratio. \n\nWeaknesses:\n\n* “Intuitively, if the test sample is highly unlikely in the training distribution, then the resulting confidence levels should be lowered”. I don’t agree with this intuition. Let’s say the training distribution is of synthetic renderings and the test distribution of real-life pictures, then confidence could still be high when the same object is depicted. What would be a counter-argument to this statement and how does that influence the results?\n\n* The human selection scores seem to be a major motivation of this paper, but the figure misses error bars. When the ratio estimates change from 2.2 to 2.6, what is the noise in these numbers? (In other words, how statistically significant is this observation?)\n\n* The calibration and training of density ratios is not well explained. Densities are known to be hard to interpret in high dimensions [3]. Could the relevance of these density ratios be shown via some experiment?\n\n* Question: From figure 4 it seems that DRL generally shows signs of underconfidence (C-A negative), while TS and VADA signs of overconfidence (C-A positive). Could this effect be explained?\n\n\nMinor comments,\n  * Section 3: why use 5 bins for ECE? A lower number of bins introduces more bias, especially for high accuracy models (where the last bin is most occupied) [4]. This makes the ECE results less reliable.\n  * Section 2.2: This section has many connections to the research in GANs, where a similar density ratio is estimated [1,2].\n\nNB: These are meant as suggestions and do not influence the review. Use of papers on arXiv is not part of the review procedure. \n\n[1] Goodfellow et al. \"Generative adversarial nets.\" NeurIPS 2014\n\n[2] Arjovsky et al. Wasserstein generative adversarial networks ICML 2017\n\n[3] Nalisnick, et al. \"Detecting out-of-distribution inputs to deep generative models using a test for typicality.\" arXiv 2019\n\n[4] Roelofs, et al. \"Mitigating bias in calibration error estimation.\" arXiv 2020\n", "summary_of_the_paper": "This paper proposes scaled uncertainty prediction in the context of unsupervised domain adaptation. The problem in unsupervised domain adaptation is to obtain predictions in a target domain where no (or few) labels are available. A secondary problem then is the calibration of predictive uncertainties in the target domain. This paper proposes a model of uncertainty proportional to the (log) of density ratios between domains. Results include ECE and Brier scores on two common Domain Adaptation datasets. ", "summary_of_the_review": "This paper derives a new scaling for predictive uncertainty in unsupervised domain adaptation. Motivated by Distributionally Robust Learning theory, the scaling, density ratios, are verified against human frequency scores. Results show better calibration under similar (slightly better) predictive performance. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper investigates the problem of uncertainty calibration under distribution shift. Based on a distributionally robust learning (DRL) framework, the paper estimates the density ratio between the source and target domains to achieve well-calibrated predictions under domain shift. 
As a plug-in module, the proposed method benefits downstream tasks of unsupervised domain adaptation and semi-supervised learning in experiments on Office31, Office-Home, and VisDA-2017, demonstrating the superiority over empirical risk minimization (ERM) and the temperature scaling method measured by expected calibration error (ECE), Brier Score, and reliability plots.

After extensive interactions and discussions on the paper, the final scores were 6/5/5/5. AC considered the paper itself, and all reviews, author responses, and discussions, and reject the paper from the following concerns:
+ *Overclaimed Novelty*: This paper is mainly based on the well-established competitive distributionally robust learning (DRL) framework. The contribution of the newly-proposed regularization form that can further promote smoothed prediction and improve the calibration performance is relatively trivial. The designs of the resulting predictive form and the learning using new gradients, mentioned by the authors in the rebuttal, need further exploration and elaboration to verify its contributions.
+ *Lack of Clarifications*: Some key points mentioned by several reviewers are still not clear. For example, how well the density ratio is estimated, especially in high dimensions? Further, a positive correlation between HSF and density ratio is not enough to prove the main argument of the paper.
+ *Some statements are not well-supported*: For example, the statement that "the harder the examples are, the farther away the examples are from the source domain", claimed by the author in the rebuttal, is untenable.

In summary, this paper studies a promising research direction of uncertainty estimation, but the work cannot be accepted before addressing the reviewers' comments. I suggest the authors to substantially revise their work by incorporating all rebuttal material as well as addressing the remaining concerns.
Decision: Reject