Natural Attribute-based Shift Detection
Authors: Jeonghoon Park
Jimin Hong
Radhika Dua
Daehoon Gwak
Jaegul Choo
Sharon Li
Edward Choi
Venue: ICLR 2022 Submitted (2022)
Keywords: attribute shift
out-of-distribution detection
distribution shift

Abstract: Despite the impressive performance of deep networks in vision, language, and healthcare, unpredictable behaviors on samples from the distribution different than the training distribution cause severe problems in deployment. For better reliability of neural-network-based classifiers, we define a new task, natural attribute-based shift (NAS) detection, to detect the samples shifted from the training distribution by some natural attribute such as age of subjects or brightness of images. Using the natural attributes present in existing datasets, we introduce benchmark datasets in vision, language, and medical for NAS detection. Further, we conduct an extensive evaluation of prior representative out-of-distribution (OOD) detection methods on NAS datasets and observe an inconsistency in their performance. To understand this, we provide an analysis on the relationship between the location of NAS samples in the feature space and the performance of distance- and confidence-based OOD detection methods. Based on the analysis, we split NAS samples into three categories and further suggest a simple modification to the training objective to obtain an improved OOD detection method that is capable of detecting samples from all NAS categories.

Under review as a conference paper at ICLR 2022
NATURAL ATTRIBUTE-BASER SHIFT DETECTION
Anonymous authors
Paper under double-blind review
ABSTRACT
Despite the impressive performance of deep networks in vision, language, and healthcare, unpredictable behaviors on samples from the distribution different than the training distribution cause severe problems in deployment. For better reliabil- ity of neural-network-Be based shift (NAtS) detection, to detect the samples shifted from the training dis- tribution by some natural attribute such as age of subjects or brightness of images. Using the natural attributes present in existing datasets, we introduce benchmark datasets in vision, language, and medical domain for NAIS detection. Further, we conduct extensive evaluation of prior representative out-of-distribution (OOD) detection methods on NAtS datasets and observe an inconsistency in their perfor- mance. To understand this, we provide an analysis on the relationship between the location of NAtS samples in the feature space and the performance of distance- and confidence-basee baseed OOD detection methods. Based on the analysis, we split NAtS samples into three categories and further suggest a simple modification to the training objective to obtain an improved OOD detection method that is capable of detecting samples from all NAIS categories.
classifiers, we define a new task, natural attribute-
INTRODUCTION
Deep learning has significantly improved the performance in various domains such computer vi- sion, natural language processing, and healthcare (Bojarski et al. 20066] Mikolov et al., 2013 Esteva al. 2016). However, it has been reported that the deep classifiers make unreliable predictions on samples drawn from a different distribution than the training distribution (Amodei et al. 2016 Hendrycks Gimpel| 2017 Nguyen al.] (015). Detection of unreliable predictions is important to build a robust model but it is relatively hard when the test distribution is gradually shifting due to a natural attribute since it is difficult to determine whether the classifier fails when the shift is not significant. These shifts occur in the real-world as a result of change in specific attribute. For exam- ple, a clinical text-based diagnosis classifier trained in 2021 will gradually encounter increasingly shifted samples as time flows, since writing styles change and new terms are introduced in time. Detection of such samples is a vital task especially in safety-critical systems, such as autonomous vehicle control medical diagnosis, where wrong predictions this end, we take a step forward by proposing a new task of detecting samples shifted by a natural attribute (e.g., age, time) that can easily be observed in the real-world setting. We refer to such shifts as Natural Attribute- baase Shifts (NArS), and the task of detecting them as NAIS detection.
lead to dire consequences. To
Detection of NAIS is both different from, and also more challenging than -iittiidiitiiitoinnn (OOD) detection (Hendrycks & Gimpel Liagg et al. 2018 Lee et al. 2018 Chandramouli & Sageev 2020), which typically evaluates the detection methods with clearly distinguished in-distribution (ID) samples and OOD samples (e.g., CIFARIO as ID and SVHN as OOD, which have disjoint labels). In contrast, we aim to detect samples from a natural sttribute-based shift within the same label space. Since NAIS samples share more features with the ID than the typical OOD samples do, identifying the former is expected be more challenging than the latter. Although OOD detection has some relevance NAIS detection, comprehensive evaluation of the existing OOD detection methods on the natural attribute-based shift is an unexplored territory. Therefore, in this paper, we perform extensive evaluation of representative OOD methods on NALS samples.
Depending on the task environment, NAtS detection can be pursued in parallel to domain generaliza- tion (Seo et al. 2020 Gulrajani & Lopez-Paz) 2020 Carlucci et al. 2019), which aims to overcome domain shifts (e.g., image classifier adapting to sketches, photos, art paintings, etc.). For example, an X-ray-based diagnosis model should detect images of unusual brightness so that the X-ray ma-

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Under review as a conference paper at ICLR 2022
chine can be properly configured, and the diagnosis model can perform in the optimal setting. In other cases, domain generalization can be preferred, such as when we expect the classifier to be deployed in a less controlled environment (e.g., online image classifier) for non-safety critical tasks.
In this paper, we formalize NAIS detection to enhance the reliability of real-world decision systems. Since there exists standard dataset for this task, create new benchmark dataset in the vision, text, and medical domain by adjusting the natural attributes (e.g., age, time, and brightness) of the ID dataset. Then we conduct an extensive evaluation of representative confidence- and distance-based OOD methods on our datasets and observe that none of the methods perform consistently across all NAtS datasets. After a careful analysis on where NAtS samples reside in the feature space and OOD detection performance, we identify the root
its impact on the distance- and confidence-base cause of the inconsistent performance. Following this observation, we define three general NAIS categories based on two criteria: the distance between NAIS samples and the decision boundary, the distance between NAtS samples, and the ID data. Finally, we conduct an additional experiment to demonstrate that simple modification to the negative log-likelihood training objective can dramat- ically help the Mahalanobis detector (Lee et al. 2018), a distance-based OOD detection method, generalize to all NAtS categories. We also compare results with various baselines and show that our proposed modification outperforms the baselines and is effective across the three NAIS datasets.
In summary, the contributions of this paper
follows:
We define a new task, Natural Attribute Atribbutebassd Shift detection (NArS detection), which aims to detect the samples from distribution shifted by some natural attribute. We create a new bench- mark dataset and provide them to encourage further research on evaluating NAIS detection.
To the best of our knowledge, this is the first work to conduct comprehensive evaluation of the OOD detection methods on shifts based on natural attributes. and discover that none of the OOD methods perform consistently across all NAIS scenarios.
We provide novel analysis based on the location of shifted samples in the feature space and the performance of existing OOD detection methods. Based on the analysis, we split NAIS samples into three categories.
We demonstrate that a simple yet effective modification to the training objective for deep classi- fiers enables consistent OOD detection performances for all NAIS categories.
2 NATURAL ATTRIBUTE-BASHE SHIFT DETECTION
We now formalize a new task. NAIS detection, which aims enhance the reliability of decision systems by detecting samples from NAtS. We address this task in the classification prob- lems. Let Dj (X denote the in-distribution data, which is composed of N training samples with inputs X' = {..,..., .N) and labels y = [yi...., yN Specifically, x; E R represents a d-dimensional input vector, and y; E K. represents its corresponding label where K. -1,-.. K) is a set of class labels. The discriminative model fo X + y learns with ID dataset Dj to assign label y for each x;. In the NAIS detection setting, we assume that an in-distribution sample consists of attributes, and some of the attributes can be shifted in the test time due to natural causes such as time, age, or brightness.
When a particular attribute A (e.g., age), which has a value of a (e.g., 16), is shifted by the degree of 8, the shifted distribution can be denoted as D = {x",'") X" = (e1....,'',, } and y" (y',.., 3/r represents the M shifted samples and labels respectively. Importantly, in the NAIS setting, although the test distribution is changed from the ID, the label space is preserved as K., which the set of class labels in Dj In the test time, the model fa might encounter the sample r' from a shifted data D DA==+6 and it should able to identify that the attribute-shifted sample not from the ID.
3 NATS DATASET DESCRIPTION
In this section, we describe three benchmark datasets which have controllable attribute for sim- ulating realistic distribution shifts. Since there exists no standard dataset for NAtS detection, we create new benchmark datasets using existing datasets by adjusting natural attributes in order to flect real-world scenarios. We carefully select datasets from vision, language, and medical domains containing natural attributes (e.g., year, age, and brightness), which allows naturally split the
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12
21
22
26
UTKFaae
Age +
RSNA Bone
Age
Brightness
Figure 1: Facial images from the UTKFace dataset to show the variation with age. X-ray images with different levels of brightness created from the RSNA Bone Age dataset.
samples. By grouping samples based on these attributes, we can induce natural attribute-based dis- tribution shifts as described below.
Image. We use the UTKFace dataset (Zhang et al. 2017) which consists of over 20, 000 face images with annotations of age, gender, and ethnicity. observe that the facial images vary with age. Therefore, we set the 1, 282 facial images of 26 years old age as Dj- For creating the NAtS dataset, we vary the age of UTKFace dataset. To obtain an equal number of samples in the NAIS dataset, the age groups that has less than 200 images merged into one group until it has 200 samples. Finally, 15 groups DS are produced for the NAIS datasets, varying the ages from 25 to 1 (i.., De 25
shown in Figure [ we can visually
Text. We use the Amazon Review dataset (He McAuley, 2016 McAuley et al. 2015) which contains product reviews from Amazon. We consider the product category "book" and group its reviews based on the year to reflect the distributional shift across time. We obtain groups with each group containing reviews from the year between 2005 and 2014. Then, the group with 24, 000 reviews posted 2005 is set as Dj, and the groups with reviews after 2005 as D3 (i.e. D3 year= negative reviews. We observed that as we move ahead time, the average length of a review gets shorter and it uses more adjectives than previous years. Due to the space constraint, provide detailed analysis of the dataset in the Section B of the Appendix.
DS 2 ....,, D...,,Dsaar D Each DiSaa group contains 1500 positive reviews and 1500
Medical. We use the RSNA Bone Age dataset (Halabi et al. 2019), real-world dataset that contains left-hand X-ray images of the patient, along with their gender and age (0 to 20 years). We consider patients in the age group of 10 to 12 years for our dataset. To reflect diverse X-ray imaging set-ups in the hospital, we varied the brightness factor between O and 4.5 and form 16 different dataset Dhrighmess (i.e., Di Drrigghnnss=0O.. Drrighhnees==0.2 ..... Dhrightness=44./ and each group contains X- ray images of 200 males and 200 females. Figure presents X-ray images with different levels of brightness with realistic and continuous distribution shifts. In-distribution data Dj is composed of 3, 000 images brightness factor 1.0 (unmodified images).
4 CAN OOD DETECTION METHODS ALSO DETECT NATS?
In this section, we briefly discuss about OOD detection methods and conduct an extensive evaluation of OOD detection methods on our proposed benchmark datasets.
4.1 OOD DETECTION METHODS
In this work, use three widely-used post-hoc and modality- aggnosicc OOD detection methods. We use maximum of softmax probability (MSP) (Hendrycks Gimpell 2017) and ODIN (Liang et al. 2018) confidence-basee 2018 as distance-based OOD detection baseline. Note that ODIN and Mahalanobis detector as- sume the availability of OOD validation dataset to tune their hyperparameters. However, for all our experiments, we use variants the above methods that do not access the OOD validation dataset as Hsu et al. 2020). The exact equations and details of how each OOD detection method assigns OOD score to a given sample is provided in Section A of the Appendix.
OOD detection baselines, and Mahalanobis detector (Lee et al.
4.2 EXPERIMENTS AND RESULTS
We systematically evaluate the performance of the three OOD detection methods under NAtS. We report the AUROC of all OOD detection methods averaged across five random seeds, evaluated for all NAIS datasets. The details of the implementation described in Section Of the Appendix.
Experimental Settings. image domain, we train a gender classification model on our UTKFace NAIS dataset using ResNet18 8 model and the cross-entropy loss. We use Amazon Book Review
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(a] UTK Face
(b) A mazon Book Review
(c) RSNA Bone Age
DBIN Nahilanniis
Aj100
2011 250
301
254
14
34
Brighinees
Figure 2: Comparison of well-known distance-based and confidence-based OOD detection methods for the CE model on our benchmark datasets. Age '26', year '2005', and brightness '1.0" are in- distribution data in UTKFace, Amazon Review, and RSNA Bone Age dataset, respectively. The NAIS detection performance of these methods is inconsistent across different datasets.
NAIS dataset in text domain and train 4-layer Transformer with the cross-entropy loss for the sentiment classification task. Lastly, in medical domain, we use our RSNA Bone Age NAtS dataset and train ResNetl8 8 with cross-entropy loss to predict the gender given the hand X-ray image of the patient. We then evaluate the trained model on the corresponding test set in image, text, medical domains, respectively. Further, we evaluate the NAIS detection performance of representative OOD detection methods in image, text, and medical domains on their corresponding NAtS datasets, which gradually shift with age. year, and brightness, respectively.
Results. We present the classification accuracy of the trained models on the ID test set in Table I We observe that the models trained using the cross-entropy loss obtain high accuracy and perform well on their corresponding tasks. We further demonstrate the effectiveness of the existing represen- tative OOD detection methods on our benchmark datasets in Figure 2 The higher AUROC indicates that more NAIS samples are distinguished from the ID samples using OOD detection methods. To provide the reference point, we calculate the AUROC values where there is no shift in the attribute. We observe that in the UTKFace NAIS dataset, samples are detected by ODIN and MSP, which are confidence- based methods, but not by Mahalanobis detector (Figure 24). In the Amazon Re- view dataset, NAIS samples are detected only by the Mahalanobis detector, while MSP and ODIN fail (Figure (b)). Moreover, the scores of confidence-basee methods are lower than 50 in AUROC. Lastly, Figure 2 shows that inputs from NAIS in the RSNA Bone Age dataset are detected well by all three methods.
5 ANALYZING INCONSISTENCY OF OOD DETECTION METHODS
In this section, we first study the behavior of NAtS samples in three datasets using PCA visualization. Then we analyze the inconsistent performance of the OOD detection methods by considering them in two categories, namely confidence- based and distance-bart based methods. Lastly, based on the analysis, we conclude this section by defining three NAIS categories.
5.1 ANALYSIS OF THE LOCATION OF NATS SAMPLES
As illustrated in Figure 3 we apply principal component analysis (PCA) on the feature representa- tions obtained from the penultimate layer of the models to visualize the movement of NAtS samples as we monotonically increase the degree of attribute shift (i.e.. age, year, and brightness). Further, Figure I presents the model's prediction confidence across varying degrees of the attribute shift.
Image. By gradually changing the age, NAIS samples move toward the space between the two clusters of ID samples (i.e., the decision boundary) as can be seen in ( Further, Figure 4 demonstrates that confidence decrease as we increase the degree of attribute shift, which indicates that NAIS samples move close to the decision boundary. Note that the majority of the NAtS samples still overlap with ID sample clusters as we change the age.
Text. As shown in Figure [Middle]. NAIS samples gradually move away from the ID samples (and away from the decision boundary) as the year changes. contrast to the UTKFace dataset, the confidence gradually increases, as shown in Figure 4p, since the NAIS samples are getting far away from the decision boundary.
UTKFace
Amazon Review
RSNA Bone Age
CE
Ours
CE
Ours
CE
Ours
Accuracy 94.6100.
94.1
85.3
84.0109
93.0
92.3+1033
Table 1: In-distribution classification accuracy on three datasets with cross-entropy loss and our
proposed loss.
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Confidence-based methods. Figure 2 and Figure 3 illustrate that confidence-based methods achieve high AUROC when the NAtS samples are near the decision boundary due to their low confidence. In the image and medical domain, we observed the NAIS samples moving towards the decision boundary with increasing attribute shift, thus they are detected by the confidence-basel methods. contrast, the text domain, the high prediction confidence of the shifted NAtS samples causes the degradation in the AUROC of the confidence-bll based methods. Therefore, that to effectively utilize the confidence-based methods in all three NAIS datasets, it is necessary to the Under review as a conference paper at ICLR 2022
ID
NAIS
ID class
ID class2
NAS
UTKFacc
17-18
12-14
7-8
3-4
Amazon
Book Review
2005
2007
2009
2010
2011
2012
2013
2014
RSNA Bone Age
3.5
Figure 3: PCA visualization to demonstrate the movement of NAtS samples as we vary the age, year and brightness in UTKFace, Amazon Review and RSNA Bone Age dataset respectively.
(a) UTKFace
(b) A mazon Book Review
(c) RSNA Bone Age
0.96
Confidsape
Confiidappe
Confidaacee
0.05
0.94
0.93
0.32
0.86
Age
Year
Brightness
Figure 4: Impact prediction confidence varying age, year, and brightness in UTKFace, Ama- zon Review, and RSNA Bone Age dataset, respectively.
Medical. Figure [Bottom] demonstrates that when increase the brightness, NAIS samples move to the middle of the two classes and also move towards the outer edge of the ID sample clusters. Furthermore, as shown in Figure the relatively decreased confidence indicates that NAtS samples are placed near the decision boundary as we increase the brightness of the images.
5.2 COMPARISON BETWEEN CONFIDENCE- BASED AND DISTANCE- -ASSE OOD DETECTION
conclude
reduce the confidence of samples outside the ID), namely, enforce NAIS samples decision boundary, which is not always possible (e.g., Amazon Review dataset).
Distance-based methods. From Figure 2 and Figure we observe that the distance-based OOD detection method (i.e., Mahalanobis Detector) achieves high AUROC when NAIS samples are suf- ficiently away from the ID samples. In the and medical domains, the Mahalanobis detector worked well since NAIS samples moved sufficiently away from the ID samples as the shift in- creased. However, in the image domain, the method fails detect NAIS samples because instead of deviating from the ID, they move intermediately between the classes.
Prior works (Luo et al., 2020 Liu et al. 2017) report that the cross-entropy loss cannot guarantee sufficient inter-class distance. In other words, representations do not need to be far from the decision boundary to lower the cross-entropy loss. this regard, we assume that the performance degradation of the Mahalanobis detector is caused by the cross-entropy loss learning latent features that are not separable enough to detect the NAIS samples located between the classes (e.g., Figure [Top]). Specifically, if some classes are located nearby in the feature space, samples moving between classes (i.e., the case the UTKFace dataset) will not be far from the ID. Even though NAtS samples move away from one of the ID class cluster, they will gradually get closer another ID class cluster.
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5.3
NATS CATEGORIZATION
0.50
0.
0.33
0.334
Figure 5: ID score landscape (brighter region means higher ID score) of the existing OOD detection methods (left: MSP, middle: ODIN, right: Mahalanobis). We use synthetic 2D dataset train 4-layer ResNet. The Red points represent the ID samples; Purple Stars, Gray Diamonds and Orange Triangles indicate samples from different NAtS categories. A sample regarded NAIS when has a low ID score.
Considering the performance of confidence-based and distance-based detection methods, we now divided NAIS into three categories based on two criteria: 1) whether the dataset is near the decision boundary not; 2) whether they are close or far from the in-distribution dataset. Since dataset (i.e., samples) far from the decision boundary and overlapping with the in-distribution dataset is not distributionally shifted dataset, possible scenarios of NAtS. Without loss of generality, we use a classification task with three classes motivating example depicted by Figure
work focuses the remaining three cases that cover all
NAtS category 1: This category comprises of NAIS samples that located near the decision boundary, and between ID samples of different classes. Purple Stars in Figure [ represents samples from this category. Such samples are easily detected by confidence-based methods, MSP and ODIN, but harder to be detected by Mahalanobis Detector, which is a distance-based method.
NATS category 2: This category consists of NAIS samples that placed away from the decision boundary and the ID data. For example, Gray Diamonds in Figure 5 Mahalanobis detector regards such samples NAtS, whereas confidence-
methods fail to detect them since NAIS samples have a higher prediction confidence (ie., higher ID score) than ID samples.
NAtS category 3: This category mainly comprises of NAIS samples located anywhere near the decision boundary but away from data. For example, Orange Triangles in Figure Such samples are easily detected by both distance-based and confidence-based OOD detection methods.
Category 1
Category
Category 3
Decision Boundary
Near Near
Far
Near
In-distribution
Far
Far
Confidence based methods works?
V
Distance- methods works?
X
Table 2: Comparison between different categories of NAIS based the location of samples in the features space and performance of confidence-based and distance-based methods.
METHOD FOR CONSISTENT NATS DETECTION PERFORMANCE
In this section, we suggest modification in the training objective for deep classifiers to encourage consistent NAtS detection performance on all NAtS categories. Then we provide experiment results where proposed method was compared against diverse OOD detection methods on the three NAIS datasets (UTKFace, Amazon Review, RSNA Bone Age).
6.1 METHOD
For generally applicable OOD detection method to all NAIS categories, we suggest new train- ing objective for deep classifiers comprised classification loss (LcE), distance loss (Cais) and entropy loss (Cennopy). The proposed objective improves the performance of the Mahalanobis de- tector on NAIS samples from category without sacrificing performance on NAtS samples from other categories. We focus improving the distance-batt based OOD detection method rather than the confidence- based method since it is not always possible to enforce NAtS samples to be embedded near the decision boundary, as discussed in Section 5.2

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The proposed training loss is defined as:
Luwi Les Ldist + Lentropy
Note that for classification loss, focal loss can also be used. The distance loss is used to increase the distance between distinct class distributions of ID samples that NAIS samples have larger space move around without overlapping with ID clusters, especially in NAtS category 1:
the standard cross-entropy loss, but other losses such as
I M 12 VD
Ldist A1
K
where A < is a hyperparameter, is the number of target classes, D is the dimension of feature representation in the latent space (typically the penultimate layer), and 14 is the mean vector of the features of samples with label Since the value of the vector norm increases as the dimension of the feature space increases, normalize the distance by the square root of the feature dimension.
As will be discussed in Section D of Appendix, we discovered after some initial experiments that the distance loss often made the model use very limited number of latent dimensions to increase the distance between class mean vectors, which degraded the NAtS detection performance. In other words, adding only Ldist LCE caused the latent feature space to collapse into very small num- ber of dimensions (i.e. rank-deficient). which caused all NAtS samples to be embedded near the ID samples. Therefore, we add entropy loss to increase the number of features used represent samples.
The entropy loss detined as:
D Centroy X2 E, Var(z,) + ΣΣ jfi
where \2 > and À3 > are hyperparameters, z E IR. is the feature representation in the latent feature space, Var(.) is variance, and Ciz is the correlation coefficient between ith and jth dimension of the feature space. Specifically, Cij described as:
Cov (z, Cjj = oZz))(ZZ)
(4)
where Cov(-) and (-) are covariance and the standard deviation, respectively.
Intuitively, the first term in equation 3 encourages each latent dimension to have diverse values, therefore preventing the latent feature space from collapsing into confined space. With the first term alone, however, all latent dimensions might learn correlated information, thus making the latent space rank-deficient. Therefore, we use the second term in equation 3 to minimize the correlation between different latent dimensions. Note that minimizing the feature correlation was also used in previous works under different contexts such as self-supervised learning (Zbontar al. 202I).
6.2 RESULTS AND DISCUSSION
To demonstrate the effectiveness of the suggested method, we train all classifiers using the standard cross-entropy loss and our modified loss and compare post-hoc OOD detection methods across three NAIS datasets. Specifically, we present the results of the confidence-bees basedd (i.e., MSP and ODIN) and the distance-based methods (i.e., Mahalanobis distance). We also include recently proposed OOD detection method (Chandramouli & Sageev 2020) which computes channel-wise correlations in CNN with the gram matrix and estimates the deviation of the test samples from the training samples to detect the OOD samples. D Although this method uses the distance in the channel correlation space, expect it behave more similarly the Mahalanobis detector than confidence-basee methods, namely MSP and ODIN. We also compare with another recent baseline which exploits the energy score to detect OOD samples (Liu al. 2020). As the method leverage the logit layer to calculate the energy score, and the softmax score is based on the logit values, we conjecture that the energy score demonstrates detection ability similar to the confidence- based methods.
'oweeerr, in the text domain, the notion of gram matrix is vague, and hence do not compare against this baseline.

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CE
Ours Mahalanobis
Distribution
Age
MSP
ODIN
Mahalamobis
Gram matrix
Energy score
ID
26
25
49.7+18
46.8405
50.0+12
$1.5100
49,3
50.1
24
12.6
51.3+007
50.6428
52.0+111
12.4+15
53.3+1.3
23
50.1
48.5
47.9424
52.3113
49.8112
52.7:11.2
22
12.5
49.7
51.2417
53.2411
$2.34111
56.5+1.3
21
53.8
51.3+10
49.5+24
$2.51:5
$3,41117
55.3:110
UTKFace
19-20
55.9
518&10
52.2
52,41:16
55.7118
57.9
17-18
1.
56.7+10
52.9416
$4.0+0.7
62.0+13
61.0#111
NAIS
15-16
69 1.5
60.1420
59,9429
$6,6116
68.7.111
70.7:
12-14
76.1
69.2422
57.7126
57.7116
75.5
75.3:10.9
9-11
77.9=077
77.4226
56.0138
$5.9426
T14415
80.5=009
7-8
77.6220.
78.7+21
53.3144
$6.111A
77.0
82.1
5-6
79.6
80.5+26
53.2+24
55,4+24
79.2+
1.
3-4
79.8
85.5+24
56.4+322
$5,4
79.0
88.6
2
79.3=
88.1#177
53.3428
$3.5+08
78.64
18
80.7
90.7:+0.9
51.2+44
52.942.1
79.9
90.3++2.
CE
Ours
Distribution
Year
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
ID
2005
2006
49.6 09.04:0
49.6460.4
31.4011
49,5402
31.41.11
Amazon Review
2007
49.0=a14
49.0+114
56.8+02
47.7400
56.5.001
2008
48.4=1.1
48.4+111
S5.2403
47.5
54.9=0.1
2009
48.5
48.5+L.
53.7:002
47,8405
53.6=10.
NAIS
2010
48.1
48.7+112
54,0+05
47.9+06
53.6200.
2011
48.1
47.3
55.610.7
45.7104
54,9
2012
45.7+
45.5+22
63.3400
42.0+09
62.6#t0.1
2013
38.2:10.6
43.0:13.
75.5:00
38.2409
75.1:000
2014
38.92008
43.7.33
76,8102
38.8
76.7.0.1
CE
Ours
Distribution Brightness
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
0.0
93.9=4.2
100.0=000
99.9+t02
99.8+t0.5
92.2+4.1
100.0=0.0
0.2
71.7433.
89.1 19.11
93.7:11.8
68.7.12.
71.0141
98.0:1.0
NAIS
0.4
55.7:22.2
64.5444
79.54445
54.61333
55,24:26
89,8+122
0.6
52.321.5
53.4::3.1
64.51:5
$1.3419
$2.11166
74.6:225
0.8
50.211.1
48.9
53.3:24
49.91110
50.11:10
56.3:118
RSNA Bome Age
DD
T.00
T.2
31.6112
$4,9117
$831119
$1,4110
ST,411
$5.00124
1.4
54.7=22
63,5:330
69.013.1
54,81:1.5
54,4123
65.1:33.1
1.6
58.5233
71.7240
76.9440
59.8+119
$7.9433
75.5=19
1.8
61.1239
80.1144
82.14:511
62.61200
60.5137
82.3:443
NAIS
2.0
62.5+4.3
87.1+41
85.8+155
61.24355
61.8442
87.0=140
2.5
66.5+13.
95.0:t21
91.9
69.5+44
65,8+33
93.7=29
3.0
75.1
98.210.
95,4133
76.414.0
74.6.336
96,6
3.5
80.1+25
99.240.4
96.8+227
80.3+5..1
79.64:19
97.8+11.
4.0
83.4+25
99.6+t03
97.7421
84.74377
82.9411
98.4=1099
4.5
85.14335
99.7.10.3
98.2416
87.81499
84.5128
98.7.00.8
Table 3: NAIS detection performance on distributional shifts in three datasets measured by AUROC.
For fair comparison, we use only the penultimate layer for evaluating the Mahalanobis detector and Gram matrix since our method is developed based on the analysis of the NAIS samples in the penultimate layer feature space. We also provide results of the ensemble version that utilize all layers in Section of of the Appendix. We describe the details of experiment setups and selecting the values for A₁ A2 and X in the Appendix Section where the three values can be reasonably chosen without any explicit NAtS validation datasets. We also present an ablation study to investigate the effect of different terms the proposed loss in Section [] the Appendix. We also compare with other recent baselines that suggest other training objective for OOD detection in Section E of the Appendix.
As shown in Table the in-distribution classification accuracy of the model trained with our sug- gested loss is comparable to that the model trained with the cross-entropy loss. Further, we present the NAtS detection performance of the baselines and our method in Table As expected above, the gram matrix achieves performance similar to the Mahalanobis detector, demonstrating the low AUROC in the UTKFaaee dataset. Interestingly, even though the energy score is calculated based
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the logit values, which are more tempered than the softmax score, it shows NAtS detection perfor- mance similar to that of MSP, which is a confidence- based method. These results show that similar to MSP, ODIN, and Mahalanobis, Gram matrix and Energy- baaegy-based methods also have performance inconsistency on NAtS datasets. We report the additional NAIS detection performance on four other metrics, which are often used in the OOD detection community in Section (Foo Appendix.
Also, it is readily visible that our proposed training objective makes the Mahalanobis detector a ro- bust NAIS detection method for all NAIS categories. In UTKFaae, we can see the dramatic NAIS detection performance increase for Mahalanobis detector. And for the other two datasets, the pro- posed loss does not decrease the NAIS detection performance of Mahalanobis detector. Note that ODIN is more sensitive to OOD samples than Mahalanobis detector for some brightness levels in the RSNA Bone Age dataset, but shows inconsistent performance across all three datasets.
RELATED WORK
Extensive evaluation on distribution shifts. Recent works have leveraged the distribution shifts for OOD detection and uncertainty estimation. Rabanser et al.] (2019) primarily focus on detecting the entire shifted distribution, not on detecting single shifted sample. Yaniv et al. (2019) quan- tify the predictive uncertainty and investigate the quality of the calibration under the dataset shift. Engkarat & Takayuki (2019) aims to predict the classification accuracy of shifted distribution by utilizing the average OOD score of the distribution. HHsu et al. (2020) also consider the distribution shift with preserved label space. However, [ss et al. (2020) focus on the shifted distribution from different domain (e.g., real images vs. sketches ). To the hest of our knowledge, none of these works conduct an in-depth analysis on the performance of existing OOD detection methods on samples shifted based on natural attributes.
OOD detection methods. Post-hoc OOD detection methods (Hendryeks & Gimpel 2017 Liang et al. 2018: Lee et al. 2018 Chandramouli & Sageev 2020) that utilize the classification models to obtain the OOD scores have achieved remarkable performance. All of these works aim to detect shifted sample which might affect decision making system in terms of confidence and hidden rep- resentation. Other OOD detection approach is to train the generative model (Ren et al. 2019; Choi et al. 2018: Mahmood et al., 2020) on the training distribution and estimate the density of OOD samples in test time. While these approaches are viable, it is not directly related with the down- stream task but aims detect features which is different from training distribution. In this paper, we mainly focus on methods that utilize the classification models to detect OOD samples since we are mainly interested in samples that affect decision maainn systems.
Model uncertainty. A number of previous works measure model uncertainty using various methods such as Bayesian neural networks (Blundell et al. (0155). Monte Carlo dropout (Gal & Ghahramani] 2016). and deep ensembles ([akshminarayanan et al. 2017). Note that technically, model uncertainty can be used to detect NAIS samples, especially for NATS categories and 3, since sampling model weights from the function space can be seen as redrawing the decision boundary, and NAIS samples in categories I and 3 will be affected heavily by this process. Model uncertainty, however, aims to capture the uncertainty in the model weights rather than detecting OOD samples, making the two rather independent research directions.
CONCLUSIONS
To enhance the reliability of preision-making systems, we define a new task, Natural Attribute- based Shift (NAtS) detection, that aims to detect the samples shifted by natural attribute. We introduce NAtS detection benchmark datasets by adjusting the natural attributes present in the ex- isting datasets. Through extensive evaluation of existing OOD detection methods on NAIS datasets, we observe inconsistent performance depending on the nature of NAIS samples. Then, we analyze the inconsistency by probing the relationship between the location of NAIS samples and the perfor- mance of existing OOD detection methods. Based on this observation, we suggest a simple remedy to help Mahalanobis OOD detection method to have consistent performance across all NAtS cate- gories. We hope our dataset and task inspire fellow researchers to investigate practical methods for identifying NAtS, which is erucial for deploying the prediction models in real-world systems.

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ETHICS STATEMENT
We believe this is not applicable to us.
REPRODUCIBILITY STATEMENT
We describe the implementation and training details along with the details on computation resources in Section[]oo of the Appendix. We submit our source codes along with the instructions reproduce our results in the Appendix.
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Table of Contents
Details of OOD detection methods
Maximum of Softmax Probability (MSP)
ODIN
Mahalanobis Detector
B
Analysis on the Text Dataset
14
C
Implementation Details
15
Training Details and Computing Infrastructure
16
Hyperparameter Tuning
16
Links for Datasets
17
D Ablation Studies on Distance and Entropy Loss
17
E Comparison with Additional Baselines
19
Quantitative Results with Other Metrics
20
Additional PCA Analysis
25
Quantitative Results
26
Experiments Multi-class Synthetic Dataset
27
A DETAILS OF OOD DETECTION METHODS
In this section, describe the three post-hoc and task-agnostic OOD detection methods in de- tail, focusing mainly on their formulation and how each method assigns an OOD score to an input sample.
A.1 MAXIMUM OF SOFTMAX PROBABILITY (MSP)
In this method, the maximum of softmax probability is considered confidence score (Hendrycks) & Gimpel 2017). Formally, we calculate the maximum softmax probability as follows:
exp (z(5
SMSP(() max
Σf=1 exp (z(i))
where C' is the number of target classes, e is the index of a class, and z(6 denotes jth attribute of the feature the logit layer.
A.2 ODIN
ODIN (Liang et al. 2018) utilized two well established techniques, namely temperature scaling and input preprocessing to increase the difference between softmax scores of in-distribution and OOD samples. Temperature scaling was originally proposed Hinton et al. (2015) to distill the knowl- edge in neural networks and was later adopted widely in classification tasks to calibrate confidence of prediction(Guo et al., 2017). In addition to temperature scaling, the input preprocessed or- der to increase the softmax score of given input by adding small perturbations which obtained by back pack-propggating the gradient of the loss with respect to the input. More specifically, ODIN is computed as follows:
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exp (z!o) (2lo)/T)
((x; 7) max Σラ=1 exp ((D/TT)
where T' It is the temperature scaling parameter, C' is the number of target classes, c the index of class, and z(d) denotes jth attribute of the logit layer features of input x. During training, T is set to 1.
For OOD detection, the input is first pre-processed as follows:
x = x - e sign (~Va æ log S(x; 7)),
where e represents the magnitude of perturbation.
Next, the network calculates the calibrated softmax score of the preprocessed input follows:
exp
SODIN T) = max
2 exp 2 (
where 2 denotes jth attribute of the logit layer features of the preprocessed input x
Lastly, the modified softmax score is compared to threshold value 6. If the score is greater than the threshold, then the input is classified as ID sample and otherwise OOD, Originally, T, E, and are hyperparameters and selected such that the false positive rate (FPR) true positive rate (TPR) 95% minimized on the validation OOD dataset. However, the performance saturates when T is greater than 1000 and therefore, in general, large value of T is preferred. Following this, in this paper, we fix T 1000 for our experiments.
A.3 MAHALANOBIS DETECTOR
To obtain Mahalanobis distance-based OOD score (Lee et al. 2018) of a sample, we calculate mahalanobis distance from the clusters of classes to the sample. Then, the distance from the closest class chosen as the confidence score.
Specifically, the Mahalanobis score of an input is defined
Smahata (x) Σ, au max (f's (x) Me,1) Ej (x) Mo,.),
where e and are the class and layer index, respectively, f is the 4th layer's feature representation of an input Me.t and E, are their class mean vector and tied covariance of the training data, correspondingly.
Note that ODIN and Mahalanobis Detector assume the availability of OOD validation dataset. However, some recent works (Shafaei et al. 2019, Techapanurak et al.) (020) report that this as- sumption limits the OOD detection generalizability since a model biased towards OOD valida- tion set. In response, this paper validate the performance of OOD methods in the version that does require tune with OOD validation dataset. We perform the performance of ODIN as Hsu al. (2020). We do not perform Mahalanobis Detector ensembling over on all layers with the optimal linear combination which requires explicit OOD data. Instead, we perform two version that use only the penultimate layer of hidden representation and sum uniformly over all layers. Therefore, for all our experiments, we use modified OOD detection methods that do not require the OOD validation dataset.
B ANALYSIS ON THE TEXT DATASET
In this section, provide detailed analysis of the text dataset. We use the Amazon Review (He & McAuley 2016 McAuley et al. 2013) dataset. We consider the product category "book" and conducted an analysis to see the impact of time on product We then performed analysis to see the impact of time on the length of the reviews.
a comparison between density plot of review length for each year from 2006 to 2014. We observe that move ahead in time,
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the length of the reviews gradually reduces. Further, Figure presents the distribution of the average ratio important words in sequence by year. First, we train a model to classify sentiment polarity using Catboost (Prokhorenkova et al. (017) using document term frequency vector. We then extract top-100 important words using feature importance. Lastly, we manually select important words over 100 words. We find that the distribution of ratio of important words in sequence gradually increase over time. Based on this analysis, we figure out that the feature related with downtream task is shifted by time.
2005
2007
2005
2005 Vs 2009
2005 VS 2010
2005 vS 2011
2005 vs 2012
2005 VS 2013
2005 vs 2014
22
Figure 6: The density plot of sequence length per year. The x-axis represents the length with log scaling.
2005 2006
2005 vs 2008
2005 vs. 2009
2005 vs 2010
2005 VS 2011
2005 vs. 2012
2005 vs. 2013
2005 vs 2014
Figure 7: The density plot of the ratio of important words per sequence.
C IMPLEMENTATION DETAILS
In this section, describe the training details. Followed by it, describe the algorithm used to select the hyperparameters our suggested modification to the loss function. Then, we provide the links download the datasets.
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C.I TRAINING DETAILS AND COMPUTING INFRASTRUCTURE
Image. We used ResNet18 (He et al. 2016) that is pretrained with ImageNet (Degg et al. 2009) to train gender classifier using a UTKeaaee NAtS dataset. After the average pooling layer, we trained fully-connected network composed of 2 hidden layers which have 128 and 2 units respectively with relu activation. The network is trained for 100 epochs with a batch size of 64. We used stochastic gradient descent with Adam optimizer (Kingma & Ba, 2014) and set learning rate as 3e - 5. For data augmentation, the technique of SimCLR (Chen al. (020) used for all the experiments.
Text. We perform experiment with Transformer network with 4 layers. The network is trained for 10 epochs with batch size of 128. We used Adam as an optimizer and set the learning rate as 3e 6.
Medical. We use ResNet18 (He et al. 2016) model, pretrained on ImageNet (Deng et al. 2009), and add two fully-connected layers containing 128 and 2 hidden units with relu activation. We train the network to classify gender given the x-ray image. Each model is trained for 30 epochs using SGD optimizer with a learning rate of 0.01 and momentum of 0.9, using a batch size 64.
All the experiments are conducted on single GeForce RTX 3090 GPU with 24GB memory. The re- sults are measured by computing mean and standard deviation across trials upon randomly chosen seeds.
C.2 HYPERPARAMETER TUNING
Our suggested modification the training loss mainly comprises of distance loss (Luisa) and tropy loss (Centopy). More formally, the training loss is given by:
Littal = LeE + Lais + Lentropy-
(5)
The entropy loss comprises of two terms and is defined as:
D Centroy X2 E, Var(z,)
+ Aa (2) jfS
ΣΣ o
(6)
where A2 > 0 and Ag >> are hyperparameters, z E TRD is the feature representation in the latent feature space, and Ct3 is the correlation coefficient between ith and jth dimension of the feature space. For more details, please refer to Section 6.1
For simplicity, in this section, we will refer the first term of entropy loss variance loss, and the second term as correlation loss. To obtain the hyperparameters of different terms in our loss function, explore the value of X in [0.01, 0.1, 1.0, 10. and A in [0.0001, 0.001, 0.01, 0.1, 1.0]. The hyperparameter corresponding the distance loss, X1 is set as 1, and then the hyperparameters of the variance loss and the correlation loss are chosen by a simple algorithm.
Algorithm: We now describe the algorithm we used to find the hyperparameters of variance and correlation loss. First, we calculate the harmonic mean of the variance loss and correlation loss using our training dataset. Next, we select the hyperparameters with the lowest value of harmonic mean. Then, to ensure that entropy loss prevents the feature space collapsing problem, we apply the singular value decomposition (SVD) in the penultimate features and test if the sum of singular values except the two largest values is improved by the entropy loss not. Concretely, to prove the enhancement, we compare the values with those of the model trained with the Ler + X Cdist If the selected hyperparameters do not improve the values, we reject them and investigate the hyperparam- eters that have the next lowest harmonic mean. The hyperparameters satisfying the above steps selected as the hyperparameters our loss function.
Note that we reject the hyperparameters if they significantly degrade the classification accuracy. In image domain, we applied the algorithm and obtained 0.1, 0.1, 0.0001 as hyperparameters of λ1, Ag. and Ag. respectively. In the medical domain, we obtain the hyperparameter corresponding to Xa as 1.0, and the other hyperparameters are the same as those of the image domain. In the text domain, 10. and 1.0 are used for the X2 and Xg. The distance loss is set by 0.1.
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C.3 LINKS FOR DATASETS
In our work, we use the openly available datasets, namely, FTKeaace datase datasef and RSNA Bone Age datase
Amazon Review
D ABLATION STUDIES ON DISTANCE AND ENTROPY Loss
In this section, conduct ablation study to investigate the effect of each proposed term in the loss function in equation [ Table 4
presents an ablation study to find the effect of the entropy loss and distance loss the proposed modification
training loss. In UTKFaae, when training with solely attaching Ldist or Lencopy to LCE, the NAIS detection performance using mahalanobis OOD detection method improves compared training with only Lev, but the performance does not monotonically increase in both cases along with the variation of Age. However, when both Las and Centroy are used, there a large improvement in performance with the results being monotonically increasing as move from ID towards NAIS, which implies that these two losses are mutually beneficial. In the text and medical domains, although there is little degradation AUROC when only Ldist is added, the performance is improved by using Leatopy in the training objective.
Further, to analyze the impact of each loss term to the feature-level representations, we perform a singular value decomposition (SVD) in the penultimate layer of ResNet18 trained the UTKFace dataset, similar to Verma et al. (201)). When trained with Lex only, the sum of the two largest singular values was 617.47, while the sum of the remaining singular values was 785.54. When trained with LCF + Ldist. the sum of the two largest singular values increased (4481.88), while the sum of the remaining singular values decreased (371.86).
As discussed in Section 6. in the main paper, this indicates that the addition of the distance loss is likely to collapse the latent feature space (i.e. rank-deficient), thus possibly decreasing the model's sensitivity to NAIS samples. For example, if model is trained to classify apples and banaNAtS based only on the color, will not be able tell that a firetruck the classifier with Ceatopy added, the problem is effectively alleviated. The sum of the two largest singular value is reduced from 4481.88 2960.63, and the sum of the remaining singular values increased from 171.86 to 513.13.
NAtS sample. When we train
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Distribution
Age
LCB
LCe Ldia
LeR + Lemmoyy
Les. Lais + Lentropy
ID
26
25
50.01112
30.3+1.0
56.8124
30.1417
24
50.6+28
50.8
54.611.7
53.3
23
47.9+224
48.8+1.2
58.1
52.7
22
51.2+117
53.4+100
61.5+28
56.5
21
49.5+224
51.7422
56.0+3366
1..
UTKFace
19-20
52.2+1.5
54,8+2.0
56.613.1
57.9
17-18
52.941.6
58.5424
62.0+4.5
61.0+1.1
NAIS
15-16
59.9
70.0434
66.614.2
70.7
12-14
57.7=2.
67.4+5.5
65.2+5.6
75.3
9-11
56.0
66.5+7.6
67.7+5.8
80.5
7-8
53.3+44.
64.1+799
69.3+7.3
12.1
5-6
53.2+2.4
63.048&0
64.3+5..1
83,5
3-4
56.41332
64.3
65.815.1
88.611.0
53.3128
58.6210.1
57.714.2
1..
51.2.44.
10.2
55.615.7
90.3+2.0
Distribution
Year
LeB
LCB Laiss
LOx. + Cemmpy
Les. Laist + Lentrgy
ID
2005
2006
31.110.1
3T.140.1
31.410.1
31.4400.1
Amazon Review
2007
56.81002
56.3+0.1
56.610.1
56.5
2008
55.2.10.
54.840.1
54.940.1
54.9
2009
53.7110.
53.620.1
53.640.1
53.6#t0.1
NAIS
2010
54.0+10.5
53.62t0.1
53.6+0.1
53.6::0.1
2011
55.6+10.7
54.810.1
54.940.0
54.940.0
2012
63.3108
62.540.1
62.6410.1
62.611011
2013
75.5
74.740.1
75.1
15.0
2014
76,8+0.2
76.3+0.1
76.8+0.1
76.7
Distribution
Brightness
Les
LCe Lais
LOE Lemnoyy
Les Laist + Leninoyy
0.0
99.9+002
99.9
100.0+0.0
100.0+0.0
0.2
93.7+1.8
94.0.1..3
96.9+1.2
98. 08.0+110
NAIS
0.4
79.514.5
74.4166.3
88,4433.6
89.8+122
0.6
64.5
60.944.1
74.5
74.6412.5
0.8
53.3++2.
51,9:11.
56.742.3
56.3
RSNA Bone Age
ID
1.0
1.2
58.5119
57.8428
57.4418
35,04423
1.4
69.0.a3.1
67.1+4.4
68.6+117
65.1
76.944.1
75.415.00
78.541.9
75.5
1.8
82.1
81.4488
84.31:19
82.3+4..3
NAIS
2.0
85.8+5.5
86.3433
88.2+1.6
87.0++.00
2.5
91.9+
93.3+1..1
94.0+1.3
93.7
3.0
95.4-33.
96.8+16
96.3+10
96.6+188
3.5
96,8+2.7
98.41100
97,4108
97.8+11.
4.0
97.7+2.1
99.0+1.7
97.940.
98.4+10.9
4.5
98.2+1.6
99.2+0.6
98.2+0.8
98.7+008
Table 4: NAIS detection performance on three NAtS datasets measured with Mahalanobis OOD detection method using AUROC.
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E
COMPARISON WITH ADDITIONAL BASELINES
Dataset
CE
GODIN
Scaled Cosine
SSD+
Ours
UKTFaae
94.6=106
94.7+10.8
94.4110.7
94.2:10.5
94.1
Amazon Review
85.3
85.7
85.4
83.8
84.0=10.
RSNA Bone Age
93.0100.6
92.0+114
93.111100
71.9
92.3
Table 5: Classification accuracy of the in-distribution in three NAtS datasets.
Distribution
Age
Buselines
Mohalanobis
Gram matrix*
GODIN
Scaled Cosine
SSD+
Mahalanobis
Mahalanobis
ID
26
25
50.3005
49, 49.9203
30.511
$1.9219
48.7
50.11 10.3
49.8110
52.4
50.9199
48.91118
50.9
52.8111
13.3
54.41:10
23
50.2
51.7#06
4:.1
49.3=222
19.3
52.7+12
54.3+005
51.2+07
16.5
58.2+007
21
$1.8+13
$1,3:09
51.81:13
51,9=311
50,3:00
$5,3
$6,8+05
UTXFace
19-20
55,7
56.619.
47.9111
$4.821.
56.7107
57,9
58.810.
17-18
$6.9211
61.3
46.6:120
28.1
18.2
61.021.1
61.8100
NAIS
15:16
65.7
63.340.5
45.9
66.5=125
67.1
70.7
7..7
12-14
61.611.1
67.7+007
45.1+28
69.5-443
71.5114
75.340.9
75.9
9:11
63.7
70.8
43.8+22
71,3=55
73.4
80.5+000
80
72.5
82.1+19
3-6
61.8
70.610.
44.1+:30
68.9:59
74.7
83.5
83.0
3.4
68.421.0
75.3106
44.31:17
68.1
80.8111
88.6110
89.41:11
2
63.5
74.4+11
44.2
65.4::109
79.5
88.3
88.9
65.8
80.3409
43.3427
63.2#104
79.7&18
90.3+20
91.5+11
Buselines
Distribution
Year
Mohalanobis*
Gram matrix*
GODIN
Scaled Cosine
SSD+
Mahalanobis
Mahalanobis
ID
2005
20006
31,4300
50.5ET
09.4
51.3103
"1.4
31,4000
Amszon Reviow
2007
56.640.1
50.91:05
49.2=0.6
55.41:17
$6.5
56.61000
2008
54,9:00
50.8t:11
49.4=0.5
53.82:02
54.920.1
54.8+001
NAIS
2010
53.6400
50.5
48.8=06
52.6111
53.620.1
53.64001
201
55.0a001
50.5105
47.4
53.0115
54,9 9100
54.8100
2012
62.4
50.8100
45.9=113
58.2426
62.620.1
62.5
2013
75.0
51.2+111
45.2=1.5
67.4
75.0
75.0+0.1
2014
76.5
51.1486
45.8=15
69.1472
76.740.
76.740.
Baselincs
Ours
Distribution
Brightness
Mahulanobis
matrix*
SSD+
Mahalanobis
Mahalanohix
0.0
100.0:0.1
100.0:0.0
97.8206
97.5=2.1
100.0:00
100.0:00
100.0:a.
0,2
93.9+225
100.0:0.0
48.94110
72.9=9.3
96.1459
98,0+110
89.3+:123
NAIS
0.4
77,8
99.0a0.
51.8112
59.9=334
92.12:7
89.8112
67. 14.22:14.2
61.9#35
50.7+16
81.9274
74.6#2.
58.4+:22
0.8
$4,2+336
37.9+11
51.1+13
50.8-12
62.3a36
$6.3
$2.0a6.1
ID
1.0
1.2
65.8
6:000
$3.5236
66.6132
35.02234
61.21:15
1.4
79.
6.
49.24:06
58.4:4.5
83.8
65.1
73.4:22.6
1.6
88.4+24
69.1
49.1
62.9=56
92.7154
75.5
83.1
RSNA
NAIS
1.8
93.5219
74,9111
49.7114
66.627.3
96.2144
82.314.
89.4150
96.61111
80.8116
50.1
97.6132
87.0:440
93.2:154
2.5
99,5+002
91.3+114
48.2+20
75.4
99.3+111
93.7+29
98. 98.1
99.9.0.1
99,8103
99.34:10
3.5
99,9.0.1
97.6210.5
50.14330
87.3=52
99.9202
97.8
99.7403
4.0
100.0sa.1
98.4404
51.2435
89.3=17
100.0=0.1
98.4009
99,940.1
4.5
100.0200
98.9402
51.6433
90.2=15
100.0
98.7405
99.940.1
Table 6: NA1S detection performance on distributional shifts three NAtS datasets measured by
AUROC. Mahalanobis and Mahalanobis indicate using penultimate layer only ensembling all layer respectively. Gram matrix also denotes the ensembled version.
In this section, investigate NAIS detection performance using additional baselines, including recent work, and compare them with those of the model trained with our modified loss on three NAIS datasets. Firstly, entropy loss with ensembled version Mahalanobis detector (Lee et al. 2018)) and the method that utilizes the gram matrix in OOD detection (Chandramouli & Sageev 2020).
mentioned in the main paper, evaluate the model trained with cross-
We also consider the other recent baselines for the comparison. Recently, Sehwag et al. (2021) propose unified framework leverage self-supervised learning for OOD detection. We set the
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method our baseline and denote this baseline as SSD The experiment SSD* + requires data augmentation strategy. In the Image domain, we augment the training dataset as Chen et al. (2020). We construct augmented training dataset using back-trand trekssstanll model for text experiments as (Fang et al. 2020; Gunel et al. 2020). We train SSD+ for 100 epochs for UTKFaae and RSNA Bone age dataset and 50 epochs for Amazon Review dataset.
2020 Techapanurak et al. 2020) exploit the cosine similarity to 2020) suggest decompose confidence scores and to modify input Liang et al. 2018). For OOD detection, they calculate the cosine similarity between the features from the penultimate layer and the class specific weights and use the maximum value as an OOD score. [Techapanurak et al.] (2020) also propose to compute cosine similarity between the class weight vector and the penultimate layer feature of each input to obtain OOD scores. Specifically, they train the model with cross entropy loss as standard classification model, but logit value is set by the scaled cosine similarity value. After training, the cosine similarity values between the penultimate layer feature of the input and the weight vector for each class are calculated. The maximum cosine similarity value is used as the OOD score for the samples. We name the methods as GODIN and Scaled Cosine in Table 6 respectively.
Some recent methods (Hsu et al.
detect OOD samples. Hsu et al.
preprocessing method in ODIN
NAtS detection performance of our method and other baselines are provided in 6 In UTKFace dataset, GODIN, Scaled Cosine, and ensembled version of Mahalanobis detector have relatively low detection performance than the other baselines. Although Gram matrix shows reasonable detection performance in UTKFace and RSNA Bone Age NAIS groups, this method is hard applied the Amazon Book Review dataset because the notion of gram matrix is vague in the text domain. In three NAIS categories, SSD+ has the most robust detection performance among the five baselines, however, our simple remedy in training loss help Mahalanobis detector to demonstrate improved performance particularly under the UTKFace NAtS dataset. In conclusion, when compared with the five more recent baselines, our method shows robust and high detection performance in all the three NAtS datasets, regardless of the domains. Scaled Cosine, which compute logit based on cosine similarity, have similar tendency with confidence- methods.
F QUANTITATIVE RESULTS WITH OTHER METRICS
We report the NAIS detection performance of baselines and our method based on four other metries: Detection Accuracy, AUPR-In, AUPR-Out, and @95% TPR, which are often used the OOD detection community. We present the detection performance measured by Detection Accuracy AUPR-In, AUPR-Out, and TNR @ 19% in Tables 7 9 10 respectively. The results indicate that simple modification in the training objective improves the performance of the Mahalanobis detector, thus making it a robust NAIS detection method for the three NAIS categories presented in the paper. Specifically, in UTKFaae, we observe that using our suggested training loss results in a significant increase in NAIS detection performance using the Mahalanobis detector. At the same time, the suggested method effectively detects the NAIS samples in the other two datasets. In summary, based on the results obtained using five different metries (AUROC, Detection Accuracy, AUPR-In, AUPR-Ou Out, and TNR 100095%TTBB TPR), our suggested modification makes the Mahalanobis detector general NAIS detection method for all three NAIS categories.
NAIS datasets in three domain
and
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CR
Ours Mahalanobis
Distribution
Age
MSP
ODIN
Mahalanobis
Gram
Energy
25
6.34311
6.1
5.5113
3,5418
6.0223
7.1226
24
6.0.1.5
4.120.8
5.11117
6.6.1:55
5.5120
4,62:122
23
5.3:1.9
0.8
4.61112
7,0119
5.4122
5.3
22
7.2422
4,5=09
5.0+17
6,9+20
6.74:17
8.6#26
5.743.1
5.7=12
6.0119
6,2413
5,9427
7,9+188
UTKFaace
19-20
6.7123
4.8
4,8109
7.6.155
6,2115
8.1
17-18
9.8424
7.5=04
5.2118
8,9211
10.1=19
11.1333
NAIS
15-16
15.2+577
9.42211
6.742.11
11.7=20
14.2=445
17.1+44
12-14
19.2+49
17.7
4,5+19
10.9=35
17.2=112
21.7+447
9-11
19.1
23.943.6
4.34117
10.7=32
18.4:5.9
26.54:5
7-8
17.9+45
27.4553
4.9413
10.4=4.3
18.2+5.7
29.34774
5-6
19.2+60
28.5439
10.0=27
18.4260
29.84995
3.4
16.3+50
31.9131
6.7222
12.5=32
13.523.1
41.5488
2
10,6+35
37.6162
4.9416
9,0422
10.9
39.4+116
12.7+4.1
47.5+27
4.9426
10.8=4.1
10.5
46.0+15.6
CE
Ours
Distribution
Year
MSP
ODIN
Mahalanohis
Gram matrix
Energy score
Mahalanobis
ID
2005
2006
5.1.0.6
5.1
5.4103
4.810.4
5.410.2
Amazon Review
2007
4.8.10.4
5.1=0.5
8.24033
4.8
8.5
2008
4.4410.
4.9=0.8
8.14033
4.5+0077
8.740.22
2009
5.0:21.0
4.7=0.5
7.7+03
4,9+09
8.4+0.4
NAIS
2010
4.7.0.55
4.9=0.8
7,8102
4.8.00.7
8.1
2011
4.440.
4.4=0.6
7.410.4
4.6+:07
8.3+00.2
2012
3.74004
4.7=0.7
14.2##0.6
4.1+1.1
16.440.
2013
3.74002
4.5=0.7
25.92108
4.5+15
30.9
2014
3,840.5
5.4
25.8:10.9
4.3413
30,2407
CR
Ours
Distribution
Brightness
ODIN
Mahulanobis
matrix
Energy soure
Mahalamobis
0.0
40.0
100.0=0.0
100.0100
100.0100
40.0=54.8
100.0:0.0
0.2
12.1
59.34144
50.2=18.8
17.426.2
10.3
93.6455
NAIS
0.4
7.2+2.7
13.2433
15.448.
7.6422
6.1433
36.04:37
0.6
5,312.0
4.8
8.71433
5.111.3
4.9.2:6
14.411.
0.8
5,1414
4,2=1.1
5,911
5.0108
4.41.19
6.7
RSNA Bone Age
ID
T.0
1.2
5.64119
8.4-088
7.94166
5.7412
5.542.1
6.7211
1.4
7.3415
18.1435
13.0.14.3
9,3415
7.4119
13.4426
1.6
10,2+35
29.3149
20.8
13.3=29
10.5
22.8:440
1.8
11.5+35
41.8+72
29.0=9.6
16.9=4.0
10.9=25
29.7+7.4
NAIS
2.0
11.5+3.7
$5.2490
36.0=1222
18. 18.2=446
11.1=27
17.8
2.5
11.5+2211
77.749.6
53.3+2204
24.4
10.4#21
61.6+139
3.0
13.3+3.1
92.1453
72.3=23.2
31.7=9.7
11.9=32
12.5
3.5
81.5=2488
37.7=108
13.8-28
91.8447.
4.0
16.8166.
99,3108
85.6.2229
44.0=11.6
14.62441
96.1438
4.5
18.9478
99.61005
89.9=18.3
50.2=1388
16.0=544
97.9+26
Table 7: NAtS detection performance on three NAtS datasets measured by TNR TPR 95%.
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Distribution
Age
CE
Ours
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
ID
26
25
53.1
51.6+08
53.0+00
52.4+08
$2.8+04
53.4
24
13
53.6.10
53.7
$2.810.7
54.0109
54.9
23
53.4
52.3
52.3+113
53.0+0.7
53,2409
54.8:00.5
22
53.7=08
52.8115
53,4:1.
53.7111
54.0
57.3:11.5
21
55.2
53.8
52.8418
53.01111
55.21111
55,6:108
UTKFace
19.20
56.5+13
53.9
54.6
53,2409
$6.2409
57.2-007
17-18
60.8
56,7+05
55.6#188
$4,41007
60.2+110
59.3:00
NAIS
15-16
66,3
59.5:008
59,4120
$6,9113
65.8t115
66.4:11.0
12-14
70.4+13
65.1:114
58.242.
57.8118
70.0
69.220.5
9-11
72.5=14
71.6:11.9
$7.2429
$6.212.7
12.1+14
74.2:009
7-8
72.8+100
72.5+116
55.4+22
56.416
72.6+11
15.2+1.
5-6
74.0=116
74.8:220
54.8+22
55.8122
73.8+18
76.2
3-4
75.6
80,5#25
57.2422
56,0107
74.9116
81,5
2
76.0
83.3+2.1
55,9
54.1+03
75.2+18
81.6
76.9
84.6:112
54.0122
54.1120
76.2411
83.0
CE
Ours
Distribution
Year
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
ID
2005
2006
50.6
50.6
51.7+0.1
50.5
51.6
Amazon Review
2007
50,2.00.1
50.14022
54.940.1
50,2410.1
55.020.1
2008
50.1
50.3
54.4:002
50,2402
54.5+10.2
2009
50.420.4
50,4102
53.61001
50,3103
53.6:10.1
NAIS
2010
50.2
50.310.3
53.3100.1
50,240.1
53,4:10.1
2011
50.2=0.1
50.140.1
54.5#0.1
50.3402
54.6=10.1
2012
50.0=0.0
50.2:102
60.3::0.1
50.3
60.4:10.1
2013
50.0
50,2:10.1
70.3:102
50.4100
70.4:102
2014
50.12001
50.5:103
70.24n
50.4
70.220.1
Distribution Brightness
CE
Ours
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
0.0
97.0=2.1
100.0:0.0
99.910.1
99,91002
96.1121
100.0:0.0
0.2
68.3428
82.8.6.3
89.6
68.5
68.0433.4
96.1
NAIS
0.4
55.2+112
62. 1231
74.9:444
$4,81332
55,3+11
84.5:22.6
0.6
52.9.111
54.0:1.6
61.9144
$2.11117
53.0:110
70.5::3.0
0.8
51.5
51.1209
53.9+1.7
$1.0104
$1.6405
56.0=11.5
RSNA Bone Age
DD
T.00
122
33.27077
5444166
57.3E1
52.1199
53.2405
55.5322
1.4
55.8
60.4+211
65.14:22
55.2+
55.4+08
62.5+227
1.6
58.62099
66.3430
71.1230
59.7.118
58.7409
70.8::100
1.8
60.8+111
73.1:44.
75.7444
62.4+20
60.741.1
76.5+22
NAIS
2.0
61.2+1.0
79.4:44
79,2+5.0
63.943.5
61.241.1
80.8+1100
2.5
63.4
88.513.7
86.615.2
68.414.5
63.1429
87.7+39
3.0
70.4+229
94.3++2.5
91,4:40
74.8+33
70.3422
92.3#22
3.5
75.8
96.9:114
94,0:13.4
78.4149
75.5
94,8:2.3
4.0
78.9
98.3:10.9
95 15.4222
82.1
78.6111.
96.4-117
4.5
80.9+2.5
98,8440.8
96.0+20
85.0444
80.74224
97.1
Table 8: NAIS detection performance on three NAIS datasets measured by detection accuracy.
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CE
Ours
Distribution
Age
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
ID
26
25
48.2
46.3
49.0=0.6
319
48.1
4.
24
51.7+12
50.6207
10.1
32.2:004
51.5+11
51.9=1.9
23
51.2
49.7=005
47.2
32.3=006
50,8+09
51.2+1.4
22
$1.7+1.0
49.2=007
49.7
32.7=0.5
51.6+08
$3.7=2.4
21
54.7
13.7
48.7
32.4
54.5
53.9=0.9
UTKFace
19-20
$6.3111
53.1
$1.2-099
32.3=004
56.0114
$6.5=2.
17-18
61.8118
57.5
51.5=099
33.0=0.8
61,4118
1.8
NAIS
15-16
69.2+13
63.1-17
60.0=19
34.3-0.7
68.5+18
70.2=0.9
12-14
77.2415
7..5
$7.8#29
34.9
76.5+
76.4
9-11
19.2
78.6+2.
55.1=29
34.0=1.6
78.9+23
81.6
7-8
78.7
80.2+2.00
53.6227
34.1=1.2
78.2420
83.3
5-6
82.1
81.7-2A
52.1=18
33.7=1.5
81.9+15
85.1
3.4
83.7+11
87.4226
56.623.3
33.6=008
83.012.1
89 99.9-007
82.7+00.
88.7+11.
54.5=33
32.8=004
82.3+11
88.9=0.9
85,2100.6
92.0=0.9
53.02444
32.5=111
84.61114
91.6=1.3
CE
Ours
Distribution
Year
MSP
ODIN
Mahalanohis
Gram matrix
Energy score
Mahalanobis
ID
2005
2006
49.9
493204
50.7
49.8403
$0322.11
Amazon Review
2007
47.91103
48.4
54.3=0.1
4
$4.620.1
2008
47.8+10.3
48.1
52.7=0.1
47.8+03
52.9=0.1
2009
48.0100
48.5
51.7:001
48.11003
$1.9=0.1
NAIS
2010
48.5
49.02:.66
51.920.1
48.5
52.2=0.1
2011
46.91002
47.7-08
52.920.1
47.0100
53.2:0.1
2012
43.6100.
45.1
57.9=0.1
43.8+004
58.2+0011
2013
40.610.3
42.4=111
68.820.11
40.8104
70.3:0.1
2014
41.2+0.3
42.7=
72.3
41.3404
74.3
Distribution
Brightess
CE
Ours
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
0.0
96.81:2.1
99.9=0.0
99.8
99.722.3
95.9:22.
99.9=00.0
0.2
13.4
88.826.4
95.4
43.5=20
72.2+5.1
98.5=006
NAIS
0.4
55.7
64.5
81.8246
34.4=20
54.8135
92.2
0.6
$2.3+117
$3.3229
65:264
32.8=1.1
52.2+16
77.4=29
0.8
49.9
19.1
53.4=229
32.2:10.6
50.0108
56.6::1.6
ISNA Bone Age
ID
1.2
5T.0ETS
$4.2117
58.5116
32.8110
50.64116
54.8
53.0+3.5
61.5233
69.4
34.4=0.9
52.243.1
65.8
55.51555
69.31419
77.5
37.0=14
54.41:1.7
77.5
1.8
18.1
78.3258
83.0223.
38.7=1.6
56.9155
84.8=3.3
NAIS
2.0
60.6+7.0
86.2=50
87.0=58
39,8=2,5
59,4164
89.2=330
2.5
66.4+788
94.9+24
92.8+5.11
43.8=39
65.4+82
94.8=2.4
3.0
77.3+5.4
98.2=0.9
96.1=28
50,5
76.61159
97.2=1.5
3.5
83.5
99.2+0.4
97.5#20
55.7=7.4
83.0429
98.3
87.3118
99.5=:02
98.2:144
63.52109
86.9415
98.8=007
4.5
89.012.4
99.6:0.2
98.621.1
69.4211.0
88.6422.1
99.0=005
Table 9: NAtS detection performance on three NAIS datasets measured by AUPR-In.
23

---

Under review as a conference paper at ICLR 2022
CE
Ours Mahalanobis
Distribution
Age
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
ID
26
25
51.7119
1..
51.2#0.9
41.
51.2
52.2=2.1
24
12.5+16
50.1
50.9=27
42.5=12
52.3+12
$2.9=1.5
23
50.9
47.9=0.
49.6#23
1..8=1.
50.2
12.4+177
22
$3.4
49.3-09
51.9224
43.6215
52,9+12
$6.9=1.1
21
$3.5
50.610.6
51.3#28
42,6=112
53.0
55.5
UTKFace
19-20
55.2+2.1
50.5=09
$2.7=13
43.1=122
54.7413
17.5
17-18
60.72119
55.2=1.0
53.0=188
4..
60,5109
60.9=2.0
NAIS
15-16
67.842.6
58.0=2.0
56.9228
49.1-15
67.2414
69.5-0.5
12-14
73.24225
67.2#222
54.5#24
49.5
72.3420
13.4
9-11
74.2+22
74.6#28
53.8=38
47.6-40
73,6+22
1..2
7-8
74.0#22
76.1
52.12455
48.2-3.2
73,412.
79.9=2.7
5-6
75.2+2.3
77.7=30
52.7=23
47,2-32
74.4421
80.7=30
3.4
73.9124
81.42.11
$4,7=32
48.1=1.
72.7416
86.5
71.81:16
84.6#22
52.1
45.0=0.9
71.0427
35.8
73.3117
88.0a1.4
51.144.1
44.7=4..
71,822
88.2#34
CE
Ours
Distribution
Year
MSP
ODIN
Mahalanohis
Gram matrix
Energy score
Mahalanobis
ID
2005
2006
49.8
4933203
ST4
49.7403
Amazon Review
2007
48.91104
49.4-06
56.0=0.0
48.8
56.4-0.1
2008
47.91:0.5
48.4+0.7
54.4
48.0+05
54.9=0.1
2009
48.71007
48.9=002
53.7:000
48 48.61106
54.1::0.
NAIS
2010
48.2410.4
48.920.8
53.6::0.0
48.4:10.7
54.0=0.1
2011
46.91004
47.3208
53.92000
47.1406
$4.5:000
2012
44.81.0.6
46.8
62.2#000
45,4+:12
63.4=0.11
2013
43.610.5
46.0=110
73.9=0.1
44,4
75.9=0.1
2014
44.0.007
46.6
74.4
44.5
76.2=0.1
Distribution
Brightess
CE
Ours
MSP
ODIN
Mahalanobis
Gram matrix
Energy score
Mahalanobis
0.0
83.8
99.9=0.0
99.12111
99.0=2.0
80.2+72
99.9=000
0.2
67.2
88.1
89.2144
64.0=2.
65.7+552
96.1
NAIS
0.4
54.7
62.2#3.9
73.1
46.4=4488
53.9
84.9=2.7
0.6
$2.0#1.3
$2.1
60.3448
42.3=29
51.5+11
68.9=115
0.8
50.31:09
48.9=115
52.3=144
40.8=116
50.0+:111
$4.3=11.
ISNA Bone Age
ID
1.2
51.6110
$4.7115
16.5
42.5111
51,6111
53.99224
55.0
64.4229
65.8
47.3=24
55.1114
62.9=338
58.9128
73.2=:36
73.8
$4.0=29
58.9122
72.41:19
1.8
61.3132
81.0=39
79.423.5
58.123.2
60.9
78.8=5.4
NAIS
2.0
61.9+3.5
87.2=36
83.226.0
60.1
61.3426
83.6=5.0
2.5
63.9+3.
94.7=222
89.9-3.6
66.7=6.1
63.1+:30
91.6=36
3.0
69.94:3.0
97.9#1.
93.8224.3
74.6=15.5
69.14:24
95.0=2.5
3.5
73.8433.
98.9+0.5
95.4
79.0=55.
72,9420
96.5+2.1
76.61440
99.3-:044
96.5=3311
83.7=6.5
75,4+2.1
97.2=1188
4.5
78.214.7
99.4-004
97.3-22
86.9-199
76.54:5
97.6
Table 10: NAIS detection performance on three NAtS datasets measured by AUPR-Out.
24

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Under review as a conference paper at ICLR 2022
G ADDITIONAL PCA ANALYSIS
In this section, we provide the additional PCA visualization results. Figure presents PCA plots applied on the penultimate features obtained from the model trained with our loss. We observe that the shifted samples in the image domain move in between the two ID classes, and the majority of the NAtS samples do overlap with the clusters. This helps in effectively detecting the shifted samples as NAtS.
Furthermore, we present the PCA visualization on a model trained with a cross-entropy loss in Figure 9 We categorize NAIS samples based on their grouth-truth labels as opposed to Figure 3 which we do not segregate NAIS samples based on their ground truth labels. the main paper, we intentionally do not categorize (and colorize) the NAtS samples because the ground truth class labels are not available at the inference time. an ideal situation, the class labels should be predicted with the trained model only if the samples are not classified as NAIS, otherwise, they should be rejected for human assessment. Note that the PCA visualization cannot be used to infer the real increase in the distance between two classes since PCA compresses the original feature space into dimensions.
ID
NA
ID classi
ID clas2
NAIS
Face
26
23
21
17-18
12-14
7-8
3-4
A mazon
Book Review
2005
2007
2009
2010
2011
2012
2013
2014
RSNA Bone Age
2.0
2.5
3.0
3.5
4.0
4.5
Figure 8: PCA visualization to demonstrate the movement of NAIS samples after training models with our proposed loss. We vary the age, year and brightness in UTKFace, Amazon Review and RSNA Bone Age dataset respectively.
ID
NA is
ID clasi
ID class KAIS class
NAAS class2
UTK Face
26
23
17-18
12-14
7-8
34
mazon
Book Review
2006
2007
2008
2010
2011
2012
2013
2014
RSNA Bone A Age
4.0
Figure 9: PCA visualization to demonstrate the movement of NAIS samples as we vary the age, year and brightness in UTKFace, Amazon Review and RSNA Bone Age dataset respectively.
25

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Under review as a conference paper at ICLR 2022
H QUANTITATIVE RESULTS
FaKe
MSP
Gram matrix
0.8
ODIN
Energy
ARROC
0.7
Mahala
Ours
19.20
17.18
15.16
12.13.14
9.10.11
7.8
34
Age
A mazon Book Review
AUROC
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Year
RSNA Bone Age
AUROC
0.4
0.6
0.8
1.0
Brightness
Figure 10: NAtS detection performance on distributional shifts in three datasets measured by AU- ROC.
26

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Under review as a conference paper at ICLR 2022
I EXPERIMENTS ON A MULTI-CLASS SYNTHETIC DATASET
We conduct additional experiments on a multi-class classification dataset show that the three NAIS categories can exist in different tasks and datasets. In order to determine the NAtS category to which a shifted sample belongs, we need to train the model for a task on a dataset, evaluate the performance of existing OOD detection methods, and analyze the location of samples in feature space. However, we would have to conduct series of experiments on numerous tasks and datasets until we encounter sam- ples from each of the three NAtS categories. (There no way to know the NAtS category of given dataset until we run experiments on it.) To this end, we synthesized 2D multi-class dataset with 8 classes and conducted experiments on it.
10
Cless 1
Class 3
Class 4
Class
Class 6
Class
Class 8
-2
-0
-6
Figure 11: Visualization of synthetic dataset with 8 distinct classes. Each class label is defined by using the first two dimensions of each sample.
We synthesized the 2-dimensional vectors for train- ing dataset with classes, and those samples are vi- sualized as red points in the 2D plane in Figure 12 In particular, we create samples in each class by ran- domly sampling from a gaussian distribution with a random mean and variance. Deep neural networks are primarily useful in complex datasets with high dimensional inputs. Therefore, for training, we increase the input dimensions by adding 8- dimensional vector which are filled with the Gaussian noise which have mean of zero and variation of 0.1. The network would focus the 2 important input features which corresponds and coordinates to classify the classes and ignore others.
We train the feed-forward classifier using the standard cross-entropy loss and modified loss. The classifier comprises linear layers, and each hidden layer consists of 10 units, and the output layer consists of 8 units (one for each class). We then evaluate the performance of MSP, ODIN, Mahalanobis under NAIS for model trained using CE loss in Figure 12 (a), (b), and (c) respectively. Purple Stars, Gray Diamonds and Orange Triangles indicate samples from NAIS categories 1, 2 and 3 respectively. We observe that MSP and ODIN detects samples from NAIS category and but fails detect from NAIS category 3. Mahalanobis detects samples from NAIS category (Gray Diamonds) and 3 (Orange Triangles), but fails to detect samples from NAIS category 1 (Purple Stars). We then evaluate the performance of Mahalanobis under NAtS for model trained using our proposed loss in Figure 12 (d). We observe that Mahalanobis (on model trained with our loss) effectively detects samples from NAIS categories. This demonstrates that our proposed training objective makes the Mahalanobis detector a robust NAIS detection method for all NAIS categories.
27

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Under review as a conference paper at ICLR 2022
0133
0132
2
08
0128
(a) CE/ MSP
(b) CE/ ODIN
10
05
00
45
4
(c) CE/ Mahalanobis
(d) Ours/ Mahalanobis
Figure 12: ID score landscape (brighter region means higher ID score) of the existing OOD detection methods in multi-class classification task. We use a synthetic 2D dataset with 8 distinct classes. The Red points represent the ID samples; Purple Stars, Gray Diamonds and Orange Triangles indicate samples from different NAIS categories. sample regarded as NAIS when it has a low ID score.
28


Reviews:
[{"review_id": "z2Wjynwl12", "reviewer": "Reviewer_czxP", "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": "strengths\n* The idea is novel.\n* The writing is easy to understand.\n* This work improves the generalizability of the distance-based Mahalanobis method for NAS under different tasks.\n\nweaknesses\n* Some assumptions lack theoretical support. Why do the natural properties of age and image brightness make unreliable predictions **more severe**?\n* The experiment setting is weak. It is not convincing to support the claim with just three OOD methods and three binary classification tasks.\n* The acronym for the new task should be distinguished from the abbreviation for the Neural Architecture Search.\n* Table 2 is too far from the paragraph where it was first cited.\n* The formulation in Section 4.2 lacks explanation, making it hard to be reproduced.\n* To make sure the NAS could be detected, the model must be trained by adding extra loss, making the proposed method inefficient. Though the performance has not shown significant degrades, the time cost can not be ignored.\n* The study on different NAS situations is not thorough enough.\n* The authors should also visualize feature distribution after improving the Mahalanobis method using PCA.", "summary_of_the_paper": "The authors propose a new task named NAS (natural attribute-based shift), which is a sub-task of OOD (out of distribution). Three datasets are designed from existing datasets for the NAS experiment. By visualizing the distribution of category features produced by the model under different datasets using PCA, the authors find three categories for NAS distribution. Total three OOD methods are tested on NAS datasets and show an inconsistency in their performance. Finally, the authors propose to use distance loss and entropy loss to retrain the models to improve the distance-based OOD methods.\n", "summary_of_the_review": "Overall, I like the idea of this article, the proposed new task is valid. However, there are some weaknesses, especially the experiments that are not comprehensive and convincing enough.", "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": "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": "IiKQ3UaJ9_b", "reviewer": "Reviewer_KqWM", "summary": "", "questions": "", "limitations": "", "rating": 8, "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": "The strengths of the paper are the following:\n1. Present and analyze a new problem that OOD detection will fail to detection such NAS samples. Then categorize those samples into three categories.\n2. Extensive experiments to demonstrate the ability of OOD detection methods to detect NAS.\n3. New loss functions to improve classifiers so that OOD detection method, i.e. Mahalanobis, can detect NAS samples better.\n\nThe weaknesses of the paper are the following:\n1. There is inconsistent in the setting of adjusting natural attributes between image, text and medical datasets. NAS samples in image and text datasets are from the real images while NAS samples in medical dataset are from synthetic images, i.e. changing brightness factor.\n2. The proposed loss was used with Mahalanobis detector. How about the proposed loss with confidence-based OOD detectors?", "summary_of_the_paper": "The paper defines a task called Natural Attribute-based Shift detection (NAS detection) to identify shifted samples on some natural attributes, e.g. age, time and lighting. \nThe authors create three benchmark dataset from existing datasets in three domains, i.e. vision, text and medical.\nTheir contributions are in three aspects: evaluation and analysis of out-of-distribution detection (OOD) methods on those NAS benchmark datasets, classify NAS samples as three different categories and present a modification to training objective of deep classifiers to improve an OOD detection method.", "summary_of_the_review": "The paper is well written with extensive experiments. I think if the author could address my concern in the weakness listed above, the paper is good enough to publish in ICLR.", "strength_and_weaknesses": "", "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": "EGGNX69EXoc", "reviewer": "Reviewer_bsNT", "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": "STRENGTHS\n1. I like the the idea of Natural Attributed-based Shift as an important subset of Out-of-Distribution problems we can face in DL systems. I think it is sufficiently different from typical OOD problems studied in literature (different label space - CIFAR vs ImageNet or different support - images vs sketches). I don't completely buy the argument that one is harder or easier compared to the other (paragraph 2 of Section 1) but I think a systematic study of this problem is important.\n2. The three proposed datasets of: (1) Different grouping of UTKFace, (2) Different grouping of Amazon Review and (3) RSNA Bone Age dataset at different brightness settings, are good examples of interest that capture different domains (image, test and medical diagnosis).\n3. Identification of 3 types of NAS scenarios based on whether the dataset is close to decision boundary (or not) and if it is close to the in-distribution data (or not) is helpful especially since it identifies which OOD methods are expected to work for a particular scenario.\n4. The additional loss terms help enforce the constraints identified in the paper to enable better detection of OOD samples for the Mahanalobis model. The paper empirically demonstrates that they get comparable performance to the original model (even with the new terms) and are able to show good performance in the UTKFace dataset where the Mahanalobis model was not doing well earlier.\n\nMAJOR COMMENTS:\n1. I think NAS is studied implicitly in many circumstances related to pose for example, how to handle side faces for a DL system trained on frontal faces or similar pose problems in 3/6-dof object pose or medical image pose where registration followed by applying the system is an imperfect solution. Studying the NAS problem explicitly is expected to provide better solutions but I don't see any discussion of such a dataset or problem in the paper. I'd like the authors to comment on if they consider such a problem to be a NAS problem and if their proposed solutions apply to this NAS setting? One dataset of interest might be the [3D Object Dataset](https://ieeexplore.ieee.org/abstract/document/4408987) where a certain range of viewpoints is D_I and the others are D_S.\n2. Table 3 is very dense and not easy to parse. I strongly recommend converting it to the same format as Figure 2 for (a) easy comparison with Figure 2 to measure the impact of additional loss terms and (b) Visual Interpretation of the results.\n3. It is unclear how this method scales to say the ImageNet dataset with 1000 categories and a ResNet-101 model with penultimate layer of size 2048. The additional terms might be too expensive at such scale for training. Any thoughts/comments?\n\nMINOR COMMENTS:\n1. NAS in Deep Learning Literature has been commonly used for Neural Architecture Search. I would recommend not using NAS for Natural Attribute-based Shift as well.\n2. In Introduction: \"benchmark datasets in vision, language, and medical for NAS detection\". The word \"medical\" is incomplete here. I think you mean medical domain?\n3. In Section 4.2, paragraph \"Experimental Settings\", why use ResNet-18 instead of the more common ResNet-50?\n4. In Figure 2, add a note saying Higher is better? Also, for all the figures (a), (b) and (c), the AUROC is at 0.5 for D_I. I could not find any text explaining if some normalization was done for the results or if these are raw AUROC values.\n5. In Section 5.1, why use PCA instead of something like t-SNE?\n6. In Figure 3, can you change it to show NAS_class1 and NAS_class2 as well please? That will be more informative compared to just NAS shown right now.\n7. Why not include Gram matrix and Energy score in Figure 2 analysis?", "summary_of_the_paper": "The paper identifies the problem of a Natural Attributed-based Shift (NAS) in the data distribution affecting Deep Learning (DL) systems designed for the task of interest. An example may be a DL system for X-ray based diagnosis being able to handle a different brightness that it was trained for. The paper argues that it is similar to Out-of-Distribution (OOD) data but instead of the difference being in the label space (CIFAR vs SVHN) the label space is similar but the test data distribution is shifted due to a systemic shift in an important data attribute (brightness of image in the X-ray example above). The paper claims the following contributions:\n- A new task of NAS detection and datasets to study it.\n- A comprehensive evaluation of OOD methods on the NAS dataset and demonstration that none of them perform consistently across all NAS scenarios.\n- A novel analysis based on the location of shifted samples in the feature space and performance of existing OOD methods.\n- Demonstrate that a simple modification to training objective for deep classifiers enables consistent OOD performance on all NAS scenarios.\n", "summary_of_the_review": "Correctness: 4\nTechnical Novelty and Significance: 3 (I am debating between 3 and 4 for the final review. I think the NAS problem is clearly identified and the datasets curated for it are novel but the problem itself, of OOD, is not novel. There are more empirical insights than theoretical ones for the paper. I might change this rating based on the other reviews / discussions).\nEmpirical Novelty and Significance: 4 (I am debating between 3 and 4 for the final review. I think the total sum of contributions: detailed analysis, identification of the NAS scenarios, and additional loss terms to Mahanalobis detector make it novel & significant even if some parts may not be. I might change this rating based on the other reviews / discussions).\n\nOverall Rating: Weak Accept\nGiven the strengths and weaknesses of the paper mentioned above, I recommend an Weak Accept for the paper. It has good contributions with the NAS problem & relevant datasets to test it. It also presents a good analysis of existing OOD methods, their flaws and a potential improvement in one (for the Mahanalobis detector). My main concerns are about the Pose component of NAS and scalability of the proposed modification (new loss terms) which if addressed/responded to in the rebuttal discussion will help me change to an Accept.", "strength_and_weaknesses": "", "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": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper offers "natural attribute" methods for shift detection.  Several reviewers are positive, but reviewer czxP is the most authoritative in the eyes of the area chair.  In particular the AC is concerned that the task that this paper defines is artificial and not useful. Naturally occurring shifts are real, happen all the time and meaningfully affect model performance... Natural shifts should be defined over distributions not singular instances. The authors create artificial instantiations of natural shifts to illustrate a well known flaw in OOD detection algorithms.
To demonstrate the usefulness of this approach to "natural shifts" the authors should should show how this algorithm performs in settings like "WILDS"... where the shift are meaningful and not artificial, in the opinion of the AC.  The paper should cite and contrast WILDS (https://arxiv.org/abs/2012.07421) and Mandoline (http://proceedings.mlr.press/v139/chen21i.html) in a future revision.
Decision: Reject