Consistency Training with Learnable Data Augmentation for Graph Anomaly Detection with Limited Supervision
Authors: Nan Chen
Zemin Liu
Bryan Hooi
Bingsheng He
Rizal Fathony
Jun Hu
Jia Chen
Venue: ICLR 2024 spotlight (2024)
Keywords: Graph anomaly detection
consistency training
learnable data augmentation
Primary area: learning on graphs and other geometries & topologies

Abstract: Graph Anomaly Detection (GAD) has surfaced as a significant field of research, predominantly due to its substantial influence in production environments. Although existing approaches for node anomaly detection have shown effectiveness, they have yet to fully address two major challenges: operating in settings with limited supervision and managing class imbalance effectively. In response to these challenges, we propose a novel model, ConsisGAD, which is tailored for GAD in scenarios characterized by limited supervision and is anchored in the principles of consistency training. Under limited supervision, ConsisGAD effectively leverages the abundance of unlabeled data for consistency training by incorporating a novel learnable data augmentation mechanism, thereby introducing controlled noise into the dataset. Moreover, ConsisGAD takes advantage of the variance in homophily distribution between normal and anomalous nodes to craft a simplified GNN backbone, enhancing its capability to distinguish effectively between these two classes. Comprehensive experiments on several benchmark datasets validate the superior performance of ConsisGAD in comparison to state-of-the-art baselines. Our code is available at https://github.com/Xtra-Computing/ConsisGAD.

Published as a conference paper at ICLR 2024
CONSISTENCY TRAINING WITH LEARNABLE DATA AUGMENTATION FOR GRAPH ANOMALY DETECTION WITH LIMITED SUPERVISION
Nan Chen', Zemin Liu"; Bryan Hooi', Bingsheng He Rizal Fathony?, Jun Hu', Jia Chen National University of Singapore, "GrabTaxi Holdings Pte. Ltd.
fchennan, bhooi, hebs wttp://commuuc.c..m edu..edu.soo (zeminliu, jun. hu edu. sg, [rizal.fathony fathony, jia. chen Shenn@grab... com
ABSTRACT
Graph Anomaly Detection (GAD) has surfaced as significant field of research, predominantly due to its substantial influence in production environments. Al- though existing approaches for node anomaly detection have shown effective- ness, they have yet to fully address two major challenges: operating in set- tings with limited supervision and managing class imbalance effectively. In re- sponse to these challenges, we propose a novel model, CONSISGAD, which is tailored for GAD in scenarios characterized by limited supervision and is anchored in the principles of consistency training. Under limited supervision, CONSISGAD effectively leverages the abundance of unlabeled data for consis- tency training by incorporating a novel learnable data augmentation mechanism, thereby introducing controlled noise into the dataset. Moreover, CONSISGAD takes advantage of the variance in homophily distribution between normal and anomalous nodes to craft a simplified GNN backbone, enhancing its capabil- ity to distinguish effectively between these two classes. Comprehensive experi- ments on several benchmark datasets validate the superior performance of CON- SISGAD in comparison to state-of-the-ar baselines. Our code is available at http:///sttbbbbcoootttt..cooniip
INTRODUCTION
Graph Anomaly Detection (GAD) aims to identify abnormal instances or outliers, e.g., nodes, that exhibit behaviors deviating from the norm (Ma al., 2021). Given the pervasive occurrence of
anomalies and their potential negative impact on various applications, GAD has emerged as a promi- nent research area (Liu et al. 20216] Shi et al. 2022] Tang et al. [022]] Wang al.) (023). Owing to the prevalence of class imbalance characteristics (Liu et al. 2023) in GAD, these studies can pri- marily be categorized into two main approaches: spatial-centric and spectral-centric. Spatial-centric approaches are primarily centered around formulating models by closely analyzing the connecting structure of nodes that require classification, such as dynamically selecting neighboring nodes the target node (Wang et al. 2019a Cui et al.) 2020 Dou et al.) 2020 et al. [020 (201a b). thereby effectively mitigating the impact of imbalances class distributions. Spectral- approaches fo- cus crafting GNN frameworks equipped with proficient spectral filters (Zhu al. [2200] [Tang cet al. 2022 Gao et al. 2023a), to bolster their capacity for improved expressiveness, enabling them to distinguish signals of varying frequencies during neighborhood aggregation.
While existing approaches have demonstrated effectiveness, they still fall short addressing two substantial challenges. Firstly, these methods frequently require extensive supervision during train- ing, which poses a considcrable challenge in scenarios with limited supervision available. Al- though semi-supervised learning (Van Engelen & Hoos) 2020) offers remedy by employing high- confidence unlabeled nodes as pseude-labeled instances, it facilitates label propagation predomi- nantly to nodes showcasing prominent features associated with the labels. This focus inherently
"Corresooniigg authors.

---

Published as a conference paper at ICLR 2024
High Conistenay Divensity
Learnible Amm masking
Anomalous
Anomalous
Random drupping
Normal
Normal
Propection (5))
10
U. Neighbachood Homophilly
Typical data augmentation methods on graphs
Our learnable data. augmentation method
Naighoothood Hamaptuly T-Finance
Amazon
(a) Comparison of the augmentation methods.
(b) The distinction in homophily distribution.
Figure I: The motivation of our proposed model.
results in the overlooking of substantial portion of unlabeled instances that bear less distinctive features, rendering label propagation to these instances particularly challenging. While consis- tency training (Rasmus et al., 2013; Laine & Aila 2017; Tarvainen & Valpola 2017) emerges as promising solution by introducing noise to high-confidence unlabeled caddss-effectivel) trans- forming them into less distinctive instances for further consistency-ban -based regularization-itt appli- cation on graphs typically involves data augmentation through random sampling as the noise (You iet al. 2020; Wang et al. 2020 Zhu et al. 2021] Zhao et al., (021), as shown in Figure [[a] Left). This method introduces an inherent difficulty in calibrating the extent of data augmentation and may result in either ver-auumeenattio or inder-augmentation (Bo et al. 2022).
Secondly, addressing class imbalance has seen numerous studies typically resorting to reweighting or resampling techniques (Wang et al. 2019a; Cui et al. [2020] Dou et al., 2020; Liu et al.) 2020 b)) They typically aim to dynamically select neighbors of the target node with view to
reducing heterophily and, thereby, alleviating the impact of imbalanced class distributions. However, the inherent uncertainty in predicting neighboring labels considerably influences the reweighting or resampling procedure, often complicating the attainment of preferable homophily neighbors.
To address these challenges, we introduce a novel model, CONSISGAD, designed for Graph Anomaly Detection under limited supervision, grounded in the principles of Consistency Training.
In the context of limited supervision, CONSISGAD harnesses the wealth of unlabeled data for con- sistency training, through novel learnable data augmentation mechanism to introduce controlled noise into the dataset, as shown in Figure ((a) Right). In particular, we introduce two key met- rics, namely, label consistency and distribution diversity guide the learning of data augmentation. These metrics assess the relationship between the original data and its augmented version: label con- sistency emphasizes the retention of identical labels, whereas distribution diversity accentuates the disparities in their representation distributions. This dual-metric approach yields a more appropriate augmentation that shares the same label while exhibiting diverse distribution characteristics, thereby facilitating the label propagating to an extensive space where the features are less distinctive.
To address the class imbalance issue, we argue that the homophily distribution serves an effec- tive pattern for distinguishing between normal and anomalous nodes. In Figure [(b) we present statistics on the homophily ratio of each node" on two datasets, Amazon and T-Finance (for more details please see Section 4.1). The x-axis represents the edge homophily score, while the y-axis il- lustrates the proportion of target nodes within the corresponding group (e.g., anomalous or normal). Specifically, normal nodes tend to predominantly associate with other normal neighbors, thereby exhibiting a higher degree of homophily. In contrast, anomalous nodes are often surrounded by a larger proportion of normal neighbors, resulting in lower homophily. This distinction in homophily distribution motivates us to develop a GNN backbone by leveraging the homophily distribution in the context of each target node to effectively discriminate between normal and anomalous nodes.
Additionally, we conduct extensive experiments on four benchmark datasets, alongside one real- world dataset derived from production environment. The ensuing results highlight the superiority of our proposed ADNSISGAD, as it exhibits enhanced performance in comparison to state-of-the-
Forr each target node, we compute the ratio of homophilic edges- those connecting nodes of the same class- to the total count of its neighhoring edges.
2

---

Published as a conference paper at ICLR 2024
art approaches. Notably, GNN model generally outperforms these leading approaches, thereby affirming its efficacy.
PRELIMINARIES
A graph can be represented as G (V, where V is the set of nodes, E is the set of edges, and X E R xdx is the feature matrix of nodes. Let at E Rdx denotes the feature vector of node v. Given a graph encoder g(: 0g) parameterized by fg (e.g., a GNN), we can embed each node into a low-dimensional representation bg IR as h g(u;8g)
Graph anomaly detection (GAD). GAD can be conceptualized as a binary classification task, wherein the node:_ are classified into one of two categories, namely, normal (the majority) and anomalous (the minority) classes. Formally, given the representation of node u, denoted as h predictor P(:3pp can be utilized for making predictions, denoted as Pa RK as follows:
Pe P( 0p) SW + bp),
where O, (W, E RKxd bp E R are learnable parameters, and K in case of anomaly detection. For a labeled node let ye E RR denotes the one-hot label vector, where [k] and only if node e belongs to class k. Typically, given the training set Vir, the loss function formulated by applying cross-entropy loss to the predictions, outlined below.
L= -=- ΣKS yo [k]
Consistency training. In the graph setting, consistency training (Wang et al,, 2020) involves in- troducing noise to high-quality unlabeled nodes generate their augmentations. This allows for the application of consistency-basee regularization between the original and augmented versions, thereby assisting in the training of the main model through the enhancement of label propagation. Specifically, to identify high high-quality nodes, given unlabeled node v and its prediction P, E R can be assessed using threshold т, based on their predicted scores. Formally, given the set of unlabeled nodes Van, the high-quality nodes can be defined as VnG {u For each high-quality node e E Vig. we can compute its one-hot predicted pseudo label vector ye. where J. (arg max P.l = 1, and the other elements are zeros. In this scenario, consistency-basee regularization is enforced between the original and augmented nodes, as described below.
V A 3p.,[k] 2 r).
C. = - K-1 Yo [o]))
(3)
where represents the prediction of the augmented version é as per Equation I By optimizing the model w.r.t. the combined loss, denoted as - Las the model benefits from supplementary guidance provided by the consistency regularization, enhancing label propagation and overall performance.
3 THE PROPOSED MODEL: CONSISGAD
In this section, we present the proposed CONSISGAD for graph anomaly detection, with the overall framework depicted in Figure 2] The CONSISGAD comprises two principal components: consis- tency training and the training of the learnable data augmentation module. On one hand, given the availability of both labeled and unlabeled data, we formulate consistency training by leveraging the learnable data augmentation module to generate superior augmentations. On the other hand, with the unlabeled nodes at our disposal, we optimize the learnable data augmentation module with respect to the proposed consistency and diversity loss, aiming to adaptively produce ideal augmentations.
In the following part, we first introduce our backbone GNN model (Section 3.1 specifically de- signed to effectively address the class imbalance issue inherent in anomaly detection. Following this, delve into the details of consistency training with learnable data augmentation (Section3.2)) a mechanism instrumental in solving anomaly detection in the scenario with limited supervision.
In this paper, we focus solely the node-level graph anomaly detection.
3

---

Published as a conference paper at ICLR 2024
Consistency Training Loss & f
Predictor
Pu
Cross- Entropy (2))
Consistency Loss Lse (Eq,19))
Learnable Duta
Consistency Loss Eg (Eq(31)
Augmentation Arm.
Learnable Data Augmennatiio Loss alar + Laa
Puu
Predictor
Yu
3u.
Diversity Loss Las (Eq))9)
h.
GNN
Filler with Ty. and Tu
GNN
Labeled Node
Unlaboled Node
(a) Consisteney training
(b) Training of the learablee data augmentation
Figure 2: Overall framework of CONSISGAD.
3.1 HOMOPIILY-AWARK NEIGHBORIIOON AGGREGATION
As discussed in the Introduction, the significant difference in contextual homophily distribution be- tween normal and anomalous nodes inspires the formulation the GNN backbone. This backbone capitalizes the homophily distribution within the context of node, thereby enhancing the capa- bility to distinguish between normal and anomalous nodes to deal with the imbalance issue.
Specifically, for node and its neighborhood Ne. we first compute the homophily representation between v and each of its neighbors. In other words, we determine the homophily representation along each edge, to establish the groundwork for calculating the contextual homophily distribution, which can be achieved by aggregating the edge-level homophily representation to finally serve as the node representation. Formally, in the 1th layer, this node representation h can be expressed
h. AGGR { 8(h) 1 :::)))))) : eue No..
(4)
Here 8(,,;03) 0s) is a function parameterized by 0s to calculate the edge-level homophily representa- tion, and we instantiate it MLP(h!-"1[Ag) ")) AGGR(-) is the aggregation function, such sum operator. In the following, we still use h, to denote the output embedding of node v for simplicity.
Analysis. Basically, the edge-level homophily representation can depict the homophily relation- ship between the two terminal nodes of given edge. Given the variability of homophily across different edges, it becomes imperative to represent the contextual homophily representation from the perspective of each individual edge. The aggregation of these edge-level homophily representa- tions subsequently illustrates the overall contextual homophily distribution.
To assess its efficacy, we train the entire CONSISGAD and exclusively visualize the intermedi- ate edge-level homophily representations via T-SNE, calculated by the function 8( : 0s), on two datasets: Amazon and T-Finance. The visualization results are depicted in Figure 3 Specifically, for the heterogencous graph Amazon, there exist three types of relations, each of which visual- ized in separate subfigure. It is important note that four colors are used in each figure to rep- resent the target-neighbor type, namely AN (Anomalous-Normal) NA -Normal-Anomalonn Annomalous-Aooallln and NN Noorall-orrall homophily representation can adeptly mirror the type of edge homophily, thereby providing a solid foundation for aggregation represent the contextual homophily distribution of each node. Addi- tionally, our experimental results, detailed in Section 4.2. demonstrate that our proposed backbone, utilizing homophily-awe aware neighborhood aggregation, can attain performance that comparable to, or even surpasses, that of state-of-the-ee approaches in the realm of graph anomaly detection.
AA The visualizations reveal that the edge-level
3.2 CONSISTENCY TRAINING WITH LEARNABLE DATA AUGMENTATION
To improve the performance graph anomaly detection under limited supervision. we incorporate consistency training (Rasmus al. 2015 Laine & Aila 2017), which enables to harness the
4

---

Published as a conference paper at ICLR 2024
All
(a) Amazon (relation 0) (b) Amazon (relation 1) (c) Amazon (relation
(d) T-Finance
Figure 3: Visualization of edge-level homophily distribution: subfigures (a), (b), and (c) depict the three relations on Amazon, while (d) depicts T-Finance.
inherent information embedded within the graph. This achieved through the use of data augmen- tation for noise injection (Xie et al. 2020). Given the significant impact of data augmentation on the effectiveness of model training, formulating advanced augmentation strategies is paramount importance. For example, in classification tasks, an ideal augmentation should preserve essential information that enables the correct categorization the augmented data, while simultaneously in- troducing diverse elements not explicitly related to the class. This incorporation of diversity serves to expand the representation space, thereby assisting in simulating less distinctive instances for label propagation (Xie al. 2020). In the subsequent section, will first introduce the definitions of the evaluation metrics, and further discuss the concept of learnable data augmentation.
3.2.1 LABEL CONSISTENCY AND DISTRIBUTION DIVERSITY
To synthesize the appropriate augmentations, we draw inspiration from (Bo et al. 2022) to design two metries, namely, label consistency and distribution diversity, to quantitatively evaluate the aug- mentations. Given a noise injection method (e.g., data augmentation) (-; a noised version of the unlabeled node E V.... be defined ê A(E; c, 9A), where small noise is injected. Consequently, with the graph encoder g( 0g). the representation and predicted label vector of the synthetic node ê can be represented h, g 0g) and Üä. respectively. In this case, the label consistency between the original version e and its noised version can be formalized as
C(u, 6) 1( go),
(5)
where I(.) = 1 if the inside condition holds, otherwise II() 0. On the other hand, the distribution diversity between them can be formalized with their representations,
D 6) d( ha),
(6)
where .): a distance function defined on the vector space, egg., Euclidean distance. Ideally, an effective augmentation approach should synthesize augmented instances that maintain high consis- tency with the original instances while involving as much diversity as possible.
While (Bo et al. 2022) also propose metrics for consistency and diversity, our definitions differ from theirs the following aspects: (1) Our metries directly operate on the given data and its augmentations, and do not require validation set for their evaluation, necessary component in (Bo et al. 2022). (2) Our metrics can further guide the learnable data augmentation module to synthesize preferable data augmentations, which will be discussed in Section 3.2.2 In contrast, their approach only aims to select suitable augmentations from pre-defined candidates.
3.2.2 LEARNABLE DATA AUGMENTATION
Existing data augmentation techniques for graphs often rely on hand-crafted or random modifi- cations to the original data, such as node dropping (Feng et al., 2020b), edge dropping (Rong) al. 2020), feature masking (You et al. 2020), etc. discussed in the Introduction, these ap- proaches have difficulty in calibrating the extent of data augmentation and can lead to over- or under-augmentatiion hindering label propagation within the label space on the graph. To generate ideal augmentations, a promising strategy is to make the process learnable, using the instance as well as the evaluation metrics including label consistency and distribution diversity.
To achieve this, employ perturbations the intermediate states as means of introducing noise to the data. This approach is a straightforward method for adding noise to hidden tensors and has been demonstrated to be effective other augmentation strategies graphs (Xia et al. 2022
5

---

Published as a conference paper at ICLR 2024
Initially, we refine the definition of high-quality nodes Vhg (defined in Section 2 in the context of
the anomaly detection setting. Due to the class imbalance issue, normal and anomalous nodes tend to
have distinct confidence levels in their prediction scores. Therefore. we assign separate threshold for each class, specifically, Vhg- = {v v E Vun A pv[0] 2 ma U {o E Vun A Pa[1] [1] 2 Ta), where Tn and Ta represent the thresholds for the normal and anomalous classe Appendix E.6 we present detailed evaluation of the quality of selected high-quality nodes.
Fl respectively. In
Subsequently, given the representation of a high-quality node v E Vig as h he-we duce learnable data augmentation module synthesize the augmented version of its representa- tion, denoted h. through learnable masking, strategically preserving the dimensions exhibiting high consistency and diversity while omitting the others. Formally, h. can be expressed as:
we intro-
h Dim (hy 6 B.)m)
where Atm (...)) ) parameterized by 8 represents the learnable masking module, generating the augmented representation for an input node. To effectively select the appropriate dimensions for preservation and masking, given the input vector h.. we utilize the attention mechanism to calculate the weight for each dimension of h. subsequently sharpening the weights into zeros and ones based on predefined masking rate. Formally, function Aim (:10))) can be instantiated as:
Atm (hn; 0 OA...) ) SHARPENN(TTEEN(L..))
h.-
(8)
Here, (h) denotes the attention function, taking the representation to be augmented as in- put and outputting vector of the same dimension, indicating the importance of each dimension. A simplified version of this attention module can be represented as ATTEN(h) = Wh + b, with W E Rddd and Rd being the weight matrix and bias vector, respectively. SHARPEN E) is function designed to retain the dimensions with the highest values in h as ones and the rest as zeros, by constraining the proportion of zeros with ratio E. For instance, given vector 10.1, 0.4, 0.2, 0.3] and & 0.5, SHARPEN(a; implementation this sharpen function does not truncate gradients, ensuring uninterrupted backprop- agation and facilitating end-to-end model training. The pseudocode for the sharpen function is provided in the Appendix [
O0, 1, 1j. It is noteworthy that in our
To facilitate learnable augmentation, the augmented representations are subsequently used to com-
pute the consistency and diversity loss, adhering to the strategies outlined in Equations ( and (6.. Formally, for high-quality node Vng. initially compute the predictions p. in accor-
dance with Equation ( as well as the pscudo label vector Yv. where ÿe arg max = 1. Con-
versely, for the augmented representation h, we also calculate the prediction w.r.t. Equation ( as p. P(h.;;0, 0p). Subsequently, both the original and the augmented predictions are leveraged to formulate the consistency and diversity loss, namely, La and Lad, as follows:
La. = = - Σxz Yo [k] In (k(),
Lad -a-=-a - EvEnng d(h,, hw).
Finally, we combine the two losses with a weight factor a, ie.,, aLsc Lad. to guide the training of the learnalle data augmentation, shown in Figure Specifically, the training of this module is guided by this fused consistency and diversity loss, rather than the consistency training loss. This because an ideal augmentation should maintain high consistency and diversity with the original version (shown in Figure 2b)),, which is unrelated to the consistency training loss in Figure 2(a). Only the synthesized augmentations can subsequently serve as input for the consistency training.
It is imperative to note that although Lsc (Equation (9) and Le (Equation (3) exhibit similar forms, their objectives are different: Lac aims to optimize the learnable data augmentation module to synthesize the ideal augmentations, whereas Le is utilized for consistency training in conjunction with the main objective L (see Equation (2)). To elucidate this distinction further, we will elaborate on the training paradigm in the subsequent section.
3.3 TRAINING PARADIGM
As depicted in Figure 2 CONSISGAD incorporates two main components: (a) consistency training, and (b) training of the learnable data augmentation module. Consistency training is centered on
We assume the first and second dimensions correspond the normal and anomalous classes, respectively.

---

highlighting the Published as a conference paper at ICLR 2024
refining the GNN model to generate enhanced representations, with parameters of GNN being clusively optimized through this process, In contrast, the training of the learnable data augmentation module is directed towards synthesizing optimal augmentations, instrumental for the consistency training. Therefore, the optimization of this module is solely driven by the consistency and diversity loss. Consequently, these two ceapponnnts-coniisttenn data augmentation module-ar are trained iteratively, with one component being optimized while the other remains fixed. Specifically, the optimization of the learnable data augmentation contributes to the training of the GNN model by providing optimal augmentations. Simultaneously, a proficiently trained GNN encoder, based on consistency training, lays the groundwork for generating superior augmentations. The training procedure and its complexity analysis are detailed in Appendix A
training and the training of the learnable
4 EXPERIMENTS
4.1 EXPERIMENTAL. SETUP
Datasets. We conduct experiments on four benchmark GAD datasets, namely Amazon McAAlley
& Leskovec )013), YeclpChi (Rayana & Akoglu 2015), T-Finance (Tang et al. (022). and T-Social Tang et al. 2022). as summarized in Table Additionally, we perform experiments on an industrial graph from Grab, leading superapp in Southeast Asia. Detailed descriptions are in Appendix B
Baselines. We employ state-of ahrt approaches from two main categories for comparison. (1)
Generic GNN models, including MLP (Rosenblatt) 1958). GCN (Kipf & Welling, 2017), Graph-
SAGE (Hamilton et al.) (017)), GAT (Veličković et al. 20118), GIN (Xu et al. 2019)), and GATv2
(Brody et al.] 2022); and (2) GAD approaches, including CARE-GNN (Dou al. (020), Graph-
Consis (Liu et al. 2020), PC-GNN (Liu et al. (021b). BWGNN (Tang et al. 2022). H2-FDetecte
(Shi et al.] 2022). GHRN (Gao et al. 2023a), GDN (Gao et al., 2023b), and GAGA (Wang et al.
2023). Additionally, we also assess our proposed GNN backbone as presented in Section 3.1 deploy
in the same training paradigm as that of generic GNN models, and refer as CONSISGAD(GNN),
For detailed descriptions of these baselines, please kindly refer to Appendix
Experimental setup. In our major experiments, we focus on settings with limited supervision. Depending on the dataset size, we set the training ratio to 1% for Amazon, YelpChi, T-Finance, and Industrial graph, and 0.01% for T-Social. In all scenarios, the remaining data is split in a 1:2 ratio for validation and testing, while all data is utilized as unlabeled for consistency training. We adopt AUROC, AUPRC, and Macro FI, to assess model performance. The average score and standard deviation across five independent runs reported. More details of the settings are in Appendix D
4.2
PERFORMANCE EVALCATION AND ANALYSIS
4.2.1 GRAPH ANOMALY DETECTION
With limited supervision. We present the performance comparison on four benchmark datasets with a 1% training ratio in Table I (Amazon and YelpChi) and Table 2 (T-Finance and T-Social), and the comparision on industrial data in Appendix E. Our proposed CONSISGAD demonstrates superior performance in most cases, underscoring its efficayy in graph anomaly detection. The only deviation is observed in the Amazon dataset, where BWGNN(homo) registers the highest Macro Fl, and CONSISG AD closely follows as the runner-up. This discrepancy may stem from BWGNN's re- liance on Macro Fl to select its optimal models, potentially neglecting the other two metries where CONSISGAD excels. Notably, our proposed GNN backbone, CONSISG AANSSADD ADGNNN), surpasses all baselines on YelpChi, T-Finance, and T-Social datasets, as indicated in blue, and maintains com- petitive performance on the Amazon dataset. This underscores the ability of our backbone GNN to capture the homophily distribution within the context of each node for anomaly detection. Further- more, the full model CONSISGAD consistently outperforms CONSISGAD(GNi) effectiveness of consistency training coupled with learnable data augmentation.
In addition, we observe that models explicitly designed for GAD generally outperform classic GNN models across the datasets. Specifically, mnectral-based models like BWGNN and GHRN tend to exhibit superior performance. In the Amazon dataset, node feature-oriented methods such MLP and GDN yield promising results. This might be attributed to node features playing a more pivotal role than connections in representing nodes on this specific dataset.
7

---

Published as a conference paper at ICLR 2024
Amazon AUPRC
YelpChi
Methods
AUROC
Macro F1
AUROC
AUPRC
Macro
MLP
=0.3
1..37=1.83
87.53
72. 1820.3
31.09=05t
61.61=0t
GCN
87.34.0.99
48.06:2273
70.94
54.65
17.07
35.59
GraphSAGE
90.12++0.4
73.17=4465
84.25+2.26
73.70 73.702
34.57=075
63.33=a51
GAT
80.74 30
45.46#11.09
63.45+12282
70. 14:119
28. 28.90+199
61.22=132
GIN
84.35+0075
29.96=2200
1..20=1.37
56. 40.82
18.34
$3.58=041
GATv2
85.39
65.74
26.20
:2087
31.87
62.23=0056
CARE-GNE GNNN
89.6810.96
50.56:1366
75.74
31.09
61.62=087
GraphConsis
64.23
21.38 10.37
55.35.18.9
78.91 110.88
38.40..261
64.96_256
PC-GNN
91.18
17.92.1149
85.25 12209
75.17 10.44
36 36.601091
64.23
BWGNN(homo)
88.56:10.57
19.26
90.48 1.08
72.15
3..93
63.24-003
(hheeerrr
84.64+1.31
64.00
80.41 +-4.29
77.62+2..7
+9.87
66,54-073
H2-FDetector
83.81+2.57
49.37 4.446
72.46+t4.01
12.38+1113
32.37+3325
63.97
GHRN(homo)
88.35++208
74.50=4.57
86.35+2260
72.03++0.00
30.76+1244
61.32=037
GHRN(hetero)
84.40+2.7
60.84=9.50
78.81=4445
75.33+1144
34.53+2x3
63.62=141
GDN
92.16:10.12
81.87 10.17
89.75
75.92.10.1
38.04
64.81 2025
GAGA
82.61
56,59 #6.60
76.85
71.61+2.33
31.96+3337
61,81
CONSISGAD(GNN)
92.01
78.49
85.53.1.51 90.03.10.3
80.95
43.25
67.62_031
CONSISGAD
93.9110.58
83.33
83.36100.3
47.33
69.72.0.3
Table I: Comparison (%) on Amazon and YelpChi, with the best bolded and runner-up underlined.
T- T-Finance AUPRC
T-Social AUPRC
Methods
AUROC
Macro F1
AUROC
Macro FI
MLP
92.17 +0.44
52.79
82.33
66.95
6.00
54.09+061
GCN
29.2
53.94=3
77.16+1.00
83.30
23.79-243
16.162092
GraphSAGE
19.42+1.36
49.08=634
17.62+187
71.45
8.73+091
56.47=004
GAT
87.40
45, 10.60.11
75.49 13.63
73.46.13.32
13.47
61.98
GIN
81.29 1.06
21.66 3.98
65.38
+8.79
16.24-555
61.62+1.95
GATv2
73.25+10000
18.70
63.1649..2
79.89
16.74-2.10
62.99+1.44
CARE-GNN
91.45.t0.40
72.27=109
83.68
-0M-
OOM
OOM
GraphConsis
92.61 #0.47
70.70=185
85.37
-0M
-OM-
-OM
PC-GNN
91.74.10:8
74.77 1098
86.97
64.68 10.4
4.30
49.66..012
BWGNN
93.08
77.79
1.5
84.40
49.96
76.37
H2-FDetector
-OOM
10MM
-OOM
-00M-
-00M
-0OM
GHRN
91.93
65.94=438
80.05
84.20+3.0t
37,04=1102
71.25+4332
GDN
8..75
54.27=431
76.62+3.0
67. 1.49
7.51
55.76+082
GAGA
92.36
64.34=601
81.10.2.0
78.92+1.36
23.72-481
65.58+1300
CONSISGAD(GNN)
94.72
83.92
93.34
$3,40
76.45
CONSISGAD
95.33
86.63 0044
90.97
94.31 +-0.00
58.38 2.10
78.08
Table 2: Comparison (%) on T-Finance and T-Social, with the best bolded and runner-up underlined.
Here, "- O0M means the Out Of GPU Memory issue when running the model.
Under varying supervision. We extend our comparison to include varying supervision levels, specifically 1%, 3%, 5%, 10%, and 40%, focusing on two datasets and the most competitive base- lines: BWGNN, GHRN, GDN, and GAGA. For Amazon and YelpChi, we employ the homo and heter versions of BWGNN and GHRN, respectively, owing their superior performance previous experiments. The AUPRC metric results are depicted in Figure 4 We observe that CONSISGAD surpasses its competitors training ratios up to 10%, showcasing its efficacy graph anomaly detection under limited supervision. This is attributed to the robust GNN backbone and the con- sistency training with learnable data augmentation. backbone reveals that the performance gap narrows with increase in training data. This aligns with expectations, as the availability of more labeled data tends to diminish the impact of consis- tency training and learnable data augmentation. For results related to the other two metrics, kindly refer to Appendix E.2 which also shows similar trends.
comparison between CONSIsGAD and our
4.2.2 MODEL. ANALYSIS
Ablation study: influence label consistency and distribution diversity. To examine the con- tributions of label consistency and distribution diversity to the training of CONSISGAD,
8

---

Published as a conference paper at ICLR 2024
CarAGAD
CaparDAD Cracalenc
(AAA
CaparSKD Druneo
AUPRC (36)
X5
60-
AUPRC (9))
23
Combiik (RCSSiiamm)
10
10
Training Ratio (%6
Training Ratio (96
(a) Amazon.
(a) YolpChi.
Amazon
YelyCli
T-Finance
T-Social
Figure 4: Experiments under varying supervision.
Figure 5: Ablation study.
ducted ablation study, omitting each element while keeping the rest of the model intact. The results, focusing on the AUPRC metric, are depicted in Figure with similar patterns observed for the other metries available in Appendix E.3 A performance decline is noted upon the removal of either component, underscoring their synergistic impact on augmentation quality and, consequently, the consistency training process. Predominantly, label consistency emerges as more crucial, adher- ing to the fundamental principle of preserving label consistency in data augmentation.
Additional analysis. Due to space constraints, additional analyses are relegated to the Appendix. Included are comparisons with traditional stochastic graph augmentation methods (Appendix E.4). an exploration of our method's adaptability across various GNN architectures (Appendix) E.5 an ex- amination of our model's 's sensitivity to of exact labels on consistency training (Appendix E..). Furthermore, we analyze the performance of CONSISGAD(GNN) in generic multi-class node classification tasks in Appendix E.8
(Appendix E.7). and study on the impact
5 RELATED WORK
Graph Anomaly Detection. Research on GAD can be broadly categorized into spatial-centric and spectral-centric methods. Spatial-centric techniques primarily address the class imbalance issue by segregating the neighbors into homophilous and heterophilous sub-groups and employing distinct mosssage-passing strategies for each (Dou et al.,
2020 Liu et al., 2020 202Ib; Dong et al. [022]] Huang et al. 2022 Shi et al. 2022 Wang et al.
2023 Zhuo et al. 2024), or other angles (Zhang
al. 1 et al. 2022 Qin
2022 Gao al. 2023b). ). On the other hand, spectral-
centric methods arise from the observation that the class imbalance leads to
signals in the graph spectral domain, often utilizing band-pass spectral filters identify these anomalous signals (Tang al. 2022 Gao et al. [2023a). However, these methods often overlook scenarios with limited supervision, assuming abundant supervision available. Furthermore, a majority of existing works opt to mitigate the heterophily issue rather than harness neighborhood homophily to enhance predictions.
Consistency training. Consistency training (Bachman et al. 2014) enforces the stability of model
outputs with regard to perturbed inputs. Various extensions have been proposed to exploit unlabeled
data in fields like vision (Miyato et al.) 2018 Berthelot al. 2019
2020 Xie et al.) 2020 Sohn Berthelot et al. [2022). language Liang et al. 2018 Clark et al. (018)), or graph (Degg
let al. 2020
| are the first one to utilize consistency training for graph anomaly detection with limited supervision.
2019 Feng et al. 2019 Wang al. 2020 Feng et al. 2020a Verma al. 200 However,
Data augmentation on graphs. We delegate Appendix F the discussion of our method within the literature of data augmentation on graphs, with further comparison between existing automatic data augmentation techniques with our own.
CONCLUSIONS
This paper tackles graph anomaly detection under limited supervision by introducing CONSISGAD. Specifically, our model leverages unlabeled data for consistency training and proposes a learnable data augmentation module for improved noise injection. Furthermore, homophily distribution between normal and anomalous classes to build a tailored GNN backbone. Experiments demonstrate the superior performance of CONSISGAD D over state-of-the-ar methods.
exploit the disparity in

---

Published as a conference paper at ICLR 2024
ACKNOWLEDGMENTS
This research is supported by the National Research Foundation, Singapore under its Al Singapore Programme (AISG Award No: AISG2-TC-2021-000))
REFERENCES
Philip Bachman, Ouais Alsharif, and Doina Precup. Learning with pseudo-ensembles. Advances in neural information processing systems, 27, 2014.
Yogesh Balaji, Tom Goldstein, and Judy Hoffman. Instance adaptive adversarial training: Improved accuracy tradcoff's in neural nets. arXiv preprint arXiv:1910.0805.1 2019.
David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning. Advances in neural informa- tion processing systems, 32, 2019.
David Berthelot, Nicholas Carlini, Ekin D. Cubuk, Alex Kurakin, Kihyuk Sohn, Han Zhang, and Colin Raffel. Remixmatch: Semi-supervised learning with distribution matching and augmenta- tion anchoring. In International Conference on Learning Representations, 2020.
David Berthelot, Rebecca Roelofs, Kihyuk Sohn, Nicholas Carlini, and Alexey Kurakin. Adamatch: A unified approach to semi-supervised learning and domain adaptation. In International Confer- ence on Learning Representations, 2022.
Deyu Bo, BinBin Hu, Xiao Wang, Zhiqiang Zhang, Chuan Shi, and Jun Zhou. Regularizing graph neural networks via consistency-diversii graph augmentations. In Proceedings of the AAAI Con- ference on Artificial Intelligence, volume 36, pp. 3913-3921, 2022.
Shaked Brody, Uri Alon, and Eran Yahav. How attentive are graph attention networks? In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022, 2022.
Kevin Clark, Minh-Thame Luong, Christopher D. Manning, and Quoe V. Le. Semi-supervised se- quence modeling with cross-view training. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing. Brussels, Belgium, October 31 November 4, 2018, pp. 1914-1925, 2.18.
Guillem Collell, Drazen Prelec, and Kaustubh R Patil. A simple plug-in bagging ensemble based on threshold-ne moving for classifying binary and multiclass imbalanced data. Neurocomputing, 275: 330-340, 2018
Limeng Cui, Haeseung Seo, Maryam Tabar, Fenglong Ma. Suhang Wang, and Dongwon Lee. De- terrent: Knowledge guided graph attention network for detecting healthcare misinformation. In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pp. 492-502 502, 2020.
Jesse Davis and Mark Goadrich. The relationship between precision-recall and roc curves. In Proceedings of the 23rd international conference on Machine learning, pp. 233-240, 2006.
Zhijie Deng, Yinpeng Dong, and Jun Zhu. Batch virtual adversarial training for graph convolutional networks. arXiv preprini arXiv: 1902.9999. 2019.
Linfeng Dong, Yang Liu, Xiang Ao, Jianfeng Chi, Jinghua Feng. Hao Yang. and Qing He. Bi- level selection via meta gradient for gased fraud detection. In International Conference on Database Systems for Advanced Applications, pp. 387-394. Springer, 2022.
Yingtong Dou, Zhiwei Liu, Li Sun, Yutong Deng, Hao Peng, and Philip S Yu. Enhancing graph neural network-based fraud detectors against camouflaged fraudsters. In Proceedings of the 29th ACM international conference on information & knowledge management, pp. 315-324, 2020.
Fuli Feng, Xiangnan He, Jie Tang, and Tat-Seng Chua. Graph adversarial training: Dynamically regularizing based on graph structure. IEEE Transactions on Knowledge and Data Engineering, 33(6):2493-2504 2019.
10

---

Published as a conference paper at ICLR 2024
Wenzheng Feng, Jie Zhang, Yuxiao Dong, Yu Han, Huanbo Luan, Qian Xu, Qiang Yang, Evgeny Kharlamov, and Jie Tang. Graph random neural networks for semi-supervised learning on graphs. Advances in neural information processing systems, 33:22092- 22103, 2020a.
Wenzheng Feng, Jie Zhang, Yuxiao Dong, Yu Han, Huanbo Luan, Qian Xu, Qiang Yang, Evgeny Kharlamov, and Jie Tang. Graph random neural networks for semi-supervised learning on graphs. Advances in neural information processing systems, 33:22092-22103, 2020b.
Yuan Gao, Xiang Wang, Xiangnan He, Zhenguang Liu, Huamin Feng, and Yongdong Zhang. Ad- dressing heterophily in graph anomaly detection: A perspective of graph spectrum. In Proceed- ings of the ACM Web Conference 2023, pp. 1528 1538, 2023a.
Yuan Gao, Xiang Wang. Xiangnan He, Zhenguang Liu, Huamin Feng, and Yongdong Zhang. Al- leviating structural distribution shift in graph anomaly detection. In Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pp. 357-365, 2023b.
Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs Advances in neural information processing systems, 30, 2017.
Mengda Huang, Yang Liu, Xiang Ao, Kuan Li, Jianfeng Chi, Jinghua Feng, Hao Yang, and Qing He. Auc-oriented graph neural network for fraud detection. In Proceedings of the ACM Web Conference 2022, pp. 1311 1-1113 2022.
Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In 3rd Inter- national Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Truck Proceedings, 2015.
Thomas N. Kipf and Max Welling, Semi-supervised classification with graph convolutional net- works. In 5th International Conference on Learming Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings, 2017.
Günter Klambauer, Thomas Unterthiner, Andreas Mayr, and Sepp Hochreiter. Self-normalizing neural networks. Advances in neural information processing systems, 30, 2017.
Kezhi Kong, Guohao Li, Mucong Ding, Zuxuan Wu, Chen Zhu, Bernard Ghanem, Gavin Taylor, and Tom Goldstein. Robust optimization as data augmentation for large-scale graphs. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 60-69, 2022.
Samuli Laine and Timo Aila. Temporal ensembling for semi-supervised learning. In International Conference on Learning Representations, 2017.
Zhixun Li, Dingshuo Chen, Qiang Liu, and Shu Wu. The devil is in the conflict: Disentangled information graph neural networks for fraud detection. In 2022 IEEE International Conference on Data Mining (ICDM), pp. 1059-1064. IEEE, 2022.
Davis Liang, Zhiheng Huang, and Zachary Lipton. Learning noise-invariant representations for robust speech recognition. In 2018 IEEE Spoken Language Technology Workshop (SLT), pp. 56-63. IEEE, 2018
Can Liu, Li Sun, Xiang Ao, Jinghua Feng, Qing He, and Hao Yang. Intention-aware heteroge- neous graph attention networks for fraud transactions detection. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pp. 3280-3288 2021a
Songtao Liu, Rex Ying, Hanze Dong, Lanqing Li, Tingyang Xu, Yu Rong, Peilin Zhao, Junzhou Huang, and Dinghao Wu. Local augmentation for graph neural networks. In International Con- ference Machine Learning, pp. 14054-14072, 2022.
Yang Liu, Xiang Ao, Zidi Qin, Jianfeng Chi, Jinghua Feng, Hao Yang, and Qing He. Pick and choose: a gan-based imbalanced learning approach for fraud detection. In Proceedings of the web conference 2021, pp. 3168-3177 2021b.
Zemin Liu, Yuan Li, Nan Chen, Qian Wang, Bryan Hooi, and Bingsheng He. A survey of imbalanced learning on graphs: Problems, techniques, and future directions. arXiv preprint arXiv:2308. 13821, 2023.
11

---

Published as a conference paper at ICLR 2024
Zhiwei Liu, Yingtong Dou, Philip S Yu, Yutong Deng, and Hao Peng. Alleviating the inconsis- tency problem of applying graph neural network to fraud detection. In Proceedings of the 43rd international ACM SIGIR conference research and development in information retrieval, pp- 1569-1572, 2020.
Xiaoxiao Ma, Jia Wu, Shan Xue, Jian Yang, Chuan Zhou, Quan Z Sheng, Hui Xiong. and Leman Akoglu. comprehensive survey on graph anomaly detection with deep learning. IEEE Trans- actions on Knowledge and Data Engineering, 2021.
Sunil Kumar Maurya, Xin Liu, and Tsuyoshi Murata. Simplifying approach to node classification in graph neural networks, Journal of Computational Science, 62: 10165,,, 2022.
Julian John McAuley and Jure Leskovec. From amateurs to connoisseurs: modeling the evolution of user expertise through online reviews. In Proceedings of the 22nd international conference on World Wide Web, pp. 897-908, 2013.
Takeru Miyato, Shin-ichi Maeda, Masanori Koyama, and Shin Ishii. Virtual adversarial training: regularization method for supervised and semi-super learning. IEEE transactions on pattern analysis and machine intelligence, 11(8):1979-1993, 2018.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high- performance deep learning library. Advances in neural information processing systems, 32, 2019.
Fabian Pedregosa, Gaäl Varoquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vincent Dubourg, et al. Scikit-lear: Machine learning in python. the Journal of machine Learning research, 12:2825-2830, 2011.
Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, and Bo Yang. Geom-gen: Geometric graph convolutional networks. In International Conference on Learning Representations, 2020. URL http:///peeeeeeiiww..e////oonlns
Zidi Qin, Yang Liu, Qing He, and Xiang Ao. Explainable graph-based fraud detection via neural meta-graph search. In Proceedings of the 31 ACM International Conference on Information & Knowledge Management, pp. 4414-4418, 2022.
Antti Rasmus, Mathias Berglund, Mikko Honkala, Harri Valpola, and Tapani Raiko. Semi- supervised learning with ladder networks. Advances in neural information processing systems, 28, 2015.
Shebuti Rayana and Leman Akoglu. Collective opinion spam detection: Bridging review networks and metadata. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 985-994, 2015.
Yu Rong. Wenbing Huang. Tingyang Xu, and Junzhou Huang. Dropedge: Towards deep graph convolutional networks on node classification. 8th International Conference on Learning Rep- resentations, ICLR 2020, Addis Ababa, Ethiopia, April 26-30, 2020, 2020.
Frank Rosenblatt. The perceptron: a probabilistic model for information storage and organization in the brain. Psychological review, 65(6):386, 1958.
Fengzhao Shi, Yanan Cao, Yanmin Shang. Yuchen Zhou, Chuan Zhou, and Jia Wu. H2-fdetector: A gan-based fraud detector with homophilic and heterophilic connections. In Proceedings of the ACM Web Conference 2022, pp. 1486-1494, 2022.
Kihyuk Sohn, David Berthelot, Nicholas Carlini, Zizhao Zhang, Han Zhang, Colin A Raffel, Ekin Dogus Cubuk, Alexey Kurakin, and Chun-Liang Li. Fixmatch: Simplifying semi- semi-supervised learning with consistency and confidence. Advances in neural information processing systems, 33:596-608, 2020.
Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research, (5()):192-11953 2014.
12

---

Published as a conference paper at ICLR 2024
Jianheng Tang, Jiajin Li, Ziqi Gao, and Jia Li. Rethinking graph neural networks for anomaly detection. In International Conference on Machine Learning, Pp. 11076-21089 PMLR, 2022.
Antti Tarvainen and Harri Valpola. Mean teachers are better role models: Weight-averaged con- sistency targets improve semi-supervised deep learning results. Advances in neural information processing systems, 30, 2017.
Dimitris Tsipras, Shibani Santurkar, Logan Engstrom, Alexander Turner, and Aleksander Madry- Robustness may be at odds with accuracy. arXiv preprini S.di::8805.12155 2018.
Jesper E Van Engelen and Holger H Hoos. A survey on semi-supervised learning. Machine learning, 109(2):373-440, 2020.
Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pictro Liò, and Yoshua Bengio. Graph Attention Networks. International Conference on Learning Representations, 2018.
Vikas Verma, Alex Lamb, Christopher Beckham, Amir Najafi, Ioannis Mitliagkas, David Lopez- Paz. and Yoshua Bengio. Manifold mixup: Better representations by interpolating hidden states. In International conference on machine learning, pp. 6438-64477 2019.
Vikas Verma, Meng Qu, Kenji Kawaguchi, Alex Lamb, Yoshua Bengio, Juho Kannala, and Jian Tang. Graphmix: Improved training of gnns for semi-supervised learning. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pp. 10024-10032, 2021.
Daixin Wang, Jianbin Lin, Peng Cui, Quanhui Jia, Zhen Wang, Yanming Fang. Quan Yu, Jun Zhou, Shuang Yang, and Yuan Qi. semi-supervised graph attentive network for financial fraud de- tection. In 2019 IEEE International Conference on Data Mining (ICDM), pp. 598-607, IEEE, 2019a.
Minjie Wang. Da Zheng, Zihao Ye, Quan Gan, Mufei Li, Xiang Song, Jinjing Zhou, Chao Ma, Lingfan Yu, Yu Gai, al. Deep graph library: A graph-centrie, highly-performe package for graph neural networks. arXiv preprint arXiv:/909.013. 2019b.
Yiwei Wang. Wei Wang, Yuxuan Liang, Yujun Cai, Juncheng Liu, and Bryan Hooi. Nodeaug: Semi- supervised node classification with data augmentation. In Proceedings of the 26th ACM SIGKDD International Conference Knowledge Discovery & Data Mining, pp. 207-217, 2020.
Yiwei Wang, Wei Wang, Yuxuan Liang, Yujun Cai, and Bryan Hooi. Mixup for node and graph classification. In Proceedings of the Web Conference 2021, pp. 3663-3674, 2021.
Yuchen Wang. Jinghui Zhang, Zhengjie Huang, Weibin Li, Shikun Feng, Ziheng Ma. Yu Sun, Di- anhai Yu, Fang Dong. Jiahui Jin, et al. Label information enhanced fraud detection against low homophily in graphs. In Proceedings of the ACM Web Conference 2023, pp. 406-416, 2023.
Jun Xia, Lirong Wu, Jintao Chen, Bozhen Hu, and Stan Z Li. Simgrace: A simple framework for graph contrastive learning without data augmentation. In Proceedings of the ACM Web Confer- ence 2022, pp. 1070-1079, 2022.
Qizhe Xie, Zihang Dai, Eduard Hovy, Thang Luong, and Quoc Le. Unsupervised data augmentation for consistency training. Advances in neural information processing systems, 33:6256-6266 2020.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural net- works? In 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6-9, 2019, 2019.
Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. Graph contrastive learning with augmentations. Advances in neural information processing systems, 33: 5812-5823, 2020.
Yuning You, Tianlong Chen, Yang Shen, and Zhangyang Wang. Graph contrastive learning auto- mated. In International Conference on Machine Learning, pp. 12121-12132. PMLR, 2021.
13

---

Published as a conference paper at ICLR 2024
Ge Zhang, Jia Wu, Jian Yang, Amin Beheshti, Shan Xue, Chuan Zhou, and Quan Z Sheng. Fraudre: Fraud detection resi-tesistant to graph inconsisteney and imbalance. In 2021 IEEE International Conference on Data Mining (ICDM), pp. 867-876. IEEE, 2021.
Hongyi Zhang, Moustapha Cissé, Yann N. Dauphin, and David Lopez-Paz. mixup: Beyond empiri- cal risk minimization. In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 May 3. 2018, Conference Track Proceedings, 2018
Yingxue Zhang. Soumyasundar Pal, Mark Coates, and Deniz Ustebay. Bayesian graph convolutional neural networks for semi-supervised classification. In Proceedings of the AAAI conference artificial intelligence, volume 33, pp- 5829-5836, 2019.
Tong Zhao, Yozen Liu, Leonardo Neves, Oliver Woodford, Meng Jiang, and Neil Shah. Data aug- mentation for graph neural networks. In Proceedings of the aaai conference artificial intelli- gence, volume 35, pp. 1 1015-11023, 2021.
Jiong Zhu, Yujun Yan, Lingxiao Zhao, Mark Heimann, Leman Akoglu, and Danai Koutra. Beyond homophily in graph neural networks: Current limitations and effective designs. Advances in neural information processing systems, 33:7793-7804, 2020.
Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. Graph contrastive learning with adaptive augmentation. Proceedings of the Web Conference 2021, pp. 2069-2080, 2021.
Wei Zhuo, Zemin Liu, Bryan Hooi, Bingsheng He, Guang Tan, Rizal Fathony, and Jia Chen. Par- titioning message passing for graph fraud detection. In The Twelfth International Conference on Learning Representations, 2024. URL http:://pwuaeeiee.eetttooo/dlddd
14

---

Published as a conference paper at ICLR 2024
APPENDIX
A ADDITIONAL DETAILS OF TRAINING PARADIGM
We provide the pseudocode for training CONSISGAD in Algorithm I In Lines 2-3, we sample batch of training nodes and a batch of unlabeled nodes for processing. In Lines 4-10, we construct set of high-quality nodes from the unlabeled batch, and attach pesudo-labels to high-quality un- labeled nodes. In Lines I 11-15, we train the learnable data augmentation based on the combination of label consistency and distribution diversity losses, during which the parameters of the graph en- coder and predictor are frozen. In Lines 16-21, we train the graph encoder and the predictor with the combination of cross-entropy loss on labeled data and consistency training loss on high-quality unlabeled data, during which the parameters of the learnable augmentation are fixed.
Algorithm The Training Paradigm of CONSISGAD
Input: A graph G {V. E, }), set of labeled nodes Ver, set of unlabeled nodes Van, graph encoder g(: fg), predictor P(- 8p), learnable augmentation module (: (+:..)) labeled batch size B, unlabeled batch size μB, anomalous threshold Ta, normal threshold Tn, weight of the label consistency loss a.
Output: 0g and 0p.
1: while not converged do
2: Sample a batch of labeled nodes N,, S Vir, with size B;
3: Sample a batch of unlabeled nodes Xun S Vun. with size nB;
4: Initialize the set of high-quality nodes Xng +- 0;
5:
for E Xan do
6: he < -g(v; 0g:0g)
Calculate the embeddings.
7: Pe 5- P(h,; 0p):
D Equation conduct the prediction.
8:
if [0] Tn or P. 2 then
9:
y. aar max pol + 1;
>> Assign pesudo- label.
10:
Kng + Xng Ue;
Add to high-quality set.
11:
for E Xng do
12:
h Alm Os.m))
Equation
augmentation on high-quality nodes. EEquation 7 prediction.
13:
P. P(h,; 6p)
14:
Csc +- - E El
[u(k] In p.l.), Lad + EveXin d(hr. hw); Equation
15:
Optimize aLac + Lad while freezing 0, and Op:
16:
for Xer do he c g(v; 0g); Pe P(hu: 8p):
17:
Calculate the embeddings. Equation 7.. prediction.
19:
C+ - EvEx, Ek yulkk In po(k) > Equation cross-entropy loss on labeled nodes.
20:
C. + ----EEE Eizo [Klk] In p.(k);
Equation consistency loss.
21:
Optimize L. while freezing 0simi
22:
return fg and 0p.
We provide the pseudocode for the sharpening function in Algorithm In Line 1, we initialize an empty output vector with the same shape as the input vector for storing intermediate results. In Lines 3-4, we mask previously computed elements in the output vector. In Lines 5-6, we integrate the mask with the input vector, followed by SoftMax operation to sharpen the result. Line we update the output vector and enter the next iteration. Finally, we return the output vector.
Complexity analysis. As illustrated in Algorithm [ our model is composed of two primary com- ponents: consistency training and the training of the learnable data augmentation module. These components operate iteratively in each iteration of the process. This approach potentially incurs a higher computational cost compared to the standard training procedures of graph neural networks. In this part, we provide a complexity analysis and analyze the possibility of using it on large graphs.
At the outset, focus analyzing the complexity of backbone GNN model, outlined in Equation (4). This model is a critical component in Algorithm I for calculating node em- beddings. Considering target node v, in the first GNN layer, the function 06)))08) is im-
15

---

Published as a conference paper at ICLR 2024
Algorithm 2 Sharpen Function
Input Input vector h, drop ratio ç, dimension of the input vector d, sharpening temperature small value to avoid logarithm of zero c.
Output Output vector h.
1: Initialize h 5- 0
D Construct an empty vector with the same shape as the input.
2: for all E (I,...: [Ed]
do
3: m (1- hh)
4: m log(m + +e)
Mask Top-(i-1) elements.
5:
y - (-h+ am) m/)t
6:
y < (yftMax(y)
> Integrate the mask with the input and sharpen the result. Update the output vector
7:
h h + m
8:
return h
plemented as MLP(N!-'(nn]-)) A typical example of this MLP is o (h! + by). The computational complexity in this first layer is O(2ddx + Nd + 2d), where dx represents the dimension of the input feature vector, d the intermediate dimension N the average node degree. Each subsequent layer contributes an additional complexity of (2d + Nd + 2d). Given total GNN layers, the overall complexity of the GNN backbone sums up O(2ddx + Nd 2d + (L- 1) + Nd + 2d)) O(2ddx 2Ld + 2Ld + LNd 2d²).
the embeddings, and
In every iteration of Algorithm D we sample batch of labeled and unlabeled nodes for subsequent computations. These batches are of sizes B (for labeled nodes) and μB (for unlabeled nodes), respectively. We can split the whole process into three steps as follows.
We begin by selecting high-quality nodes from the sampled batch of unlabeled nodes. In Line 6, the GNN backbone introduces complexity of O(2ddx + 2Ld2 2Ld + LNd 2d2), ). as previously analyzed. The prediction step in Line 7 has complexity of O(Kd+ 2K), where K is the number of classes. Lines 8-10 involve checking the high-quality nodes with a complexity of K. Overall, for batch size of B, Lines 5-10 collectively result in complexity of O(u + 2Ld + 2Ld LNd 2d + Kd + 3K)).
Each high-quality node is augmented and predicted, forming the basis for the consistency and diversity loss calculations. For Line 12, the complexity of the Sharpen function in Algorithm 2 involves O(8 [dldd d across its steps. Consequently, Line 12 in Algorithm I Tincurs a complexity
of O(8[Ed d d + 3d). Line 13, similar to Line 7, involves complexity of O(Kd 2K). Line 14 includes forming both the consistency and diversity losses, with complexities of O(uBK" and (22BBd), respectively. Summing up, Lines 11-14 entail complexity of (B d2 + 3d + Kd + 2K) + μBK* + 2uBd).
The consistency training involves complexity calculations similar to the earlier sections. Lines 17 and 18, as previously analyzed, involve a complexity of O(2ddx 2Ld + 2Ld + LNd 2d + Kd + 2K). Lines 19 and 20, pertaining to the loss calculations, have complexities of O(B and O(uBK2), respectively. Thus, the total complexity for Lines 16-20 over iterations O O(B(2dxx + 2Ld + 2Ld LNd 2 + Kd + 2K) + BK2 + pBK2).
In each iteration of Algorithm 1 we aggregate the complexities from the previous sections to derive the overall complexity. This can expressed as O(2B(H + 1)ddx + B(2 + 2T. l 2)d + (2nBL+ fBLN -ELBLN-uL -uBK+ 8pB [Ed] +MBB+KKBBi 2BL BLN BK B +2μBK²
2BK + BB3).
Particularly in our anomaly detection scenario, where typically K 2 due to the binary classifi- cation nature, and L generally ranges from 1 to 3 as the number of GNN layers, the complexity of model is predominantly influenced by the feature dimension dx. the hidden dimension d, and the average node degree N. This indicates that with appropriately set sypperparaamttrs, our model shows promising potential for application large-scale graphs.
16

---

Published as a conference paper at ICLR 2024
B DESCRIPTIONS OF DATASETS
The datasets are summarized Table The Amazon dataset (McAuley & Leskovec 2013) aims to detect fraudsters paid give fake reviews for products under the Musical Instruments category Amazon.com. It includes three types of edges: U-P-U (users reviewing at least one same product), U-S-U (users having at least one same mutual review TF-IDF similarities). The YelpChi dataset (Rayana & Akoglu 2015) aims to identify anomalous hotel and restaurant reviews on Yelp.com. contains three types of edges: R-U-R (reviews posted by the same user), R-S-R (reviews with the same star rating on the same product), R-T-R (reviews posted the same month on the same product). The T-Finance dataset (Tang al.) 2022) aims to find anomalous accounts in transaction network, including fraud, money laundering, and online gambling. The T-Social dataset (Tang et al. 2022) aims to catch abnormal users social network. Finally, the Industrial graph, sourced from Grab Holdings Inc., depicts transaction graph in a real-world setting, capturing online transactions within a leading super app. To maintain anonymity, omit the explicit details of the graph. However, it roughly comprises over million nodes and tens millions edges.
rating within week), U-V-U (users with top-5%
Please note that limited supervision has been assessed in several state-of- sate--ofther of-the-art baselines, as indi- cated in (Tang et al. 2022). To ensure a fair comparison, we have employed the same data split as they did.
C DESCRIPTIONS OF THE BASELINES
In this section, we will introduce baselines used in more details, their papper-prramter settings, and their implementation specifics.
C.I GENERIC GNN MODELS
MLP (multi-layer perceptron (Rosenblatt) 1958)) ) A multi-layer perceptron network with one
hidden layer and ReLU activation.
GCN (Graph Convolutional Network (Kipf & Welling 2017): A graph neural network that
performs graph spectral convolution via a localized first-order approximation of spectral filters.
GraphSAGE (Graph Sample and AggregatE (Hamilton et al. 2017)): A graph neural network that samples and aggregates neighboring features to generate node embeddings. also proposes three ways of aggregation: mean, LSTM, and pooling. In the experiments, the mean aggregator is used.
GAT (Graph Attention Networks /Veličković et al. 2018 ): A graph neural network that applies the attention mechanism to the neighborhood aggregation process. The number of attention heads is set to 2 in the experiments.
GATy2 (Graph Attention Networks v2 (Brody et al., 2022)); ; GAT improves GAT with a modified attention mechanism, which allows dynamic attention. The number of attention heads is set to 2 in our experiments.
GIN (Graph Isomorphism Network (Xu et al., 2019 A graph neural network that generalizes the Weisfeiler-Lehmann (WL) graph isomorphism test. In our experiments, the sum operation is used aggregate neighboring features, and MLP is deployed update node embeddings. The deployed MLP consists of one hidden layer and ReLU activation.
The MLP is implemented via PyTorch (Paszke al. 2019). For graph neural network models, use the official implementation provided by DGL (Wang et al. 2019b).
C.2 GAD MODELS
In this subsection, we will introduce the graph anomaly detection models employed in our experi- ments.
17

---

Published as a conference paper at ICLR 2024
# Nodes
Edges
Features
Anomaly
Train: Valid:Test
Amazon
11,944
4,398,392
25
6.87%
19:33%:66%
YelpChi
45,954
3,846,979
32
14.53%
19:33%%:66%
T-Finance
39,357
21,222.543
10
4.58%
1%:33%%:66%
T-Social
5,781,065
73,105,508
10
3.01%
0111::33.33%::6666666
Industrial graph
1M
~00
17
< 0.6%
19::33%:66%
Table 3: Statistical summary of the datasets used in our experiment.
CARE-GNN (CAmoufage-REsistan Graph Neural Network (Dou et al., 2020 This ap- proach employs neural classifier to estimate similarity between node and its neighbors, and filters out dissimilar neighbors for a central node. The optimal filtering threshold is found through reinforcement learning. It also proposes relation-aware neighbor aggregator deal with different relation types in the graph.
GraphConsis (Liu et al. 2020 This approach identifies three inconsistency issues in graph anomaly detection tasks, namely, context, feature, and relation inconsistencies. To deal with the context inconsistency, this work assigns each node learnable context emhedding capture its local structure. To handle the feature inconsistency, this work filters neighbors based on estimated consistency scores from a neural classifier. To counter the relation inconsistency, this work trains an embedding for each relation and uses a self-attention mechanism to aggregate neighbors.
PC-GNN (Pick and Choose Graph Neural Network (Liu et al., 2021b) This approach adopts a label-balanced sampler to pick nodes and edges for training, where the sampling probability is inversely proportional to the label frequency. addition, it proposes a neighborhood sampler that over-samples the neighborhood of fraud nodes and under-samples the neighborhood of normal ones.
BWGNN (Beta Wavelet Graph Neural Network (Tang al. 2022) This approach finds that anomaly can cause energy shift from the low-frequency part to the high frequency part in the graph spectral domain. It leverages the Beta kernel to create band-pass filters with spatial and spectral locality for anomaly detection. For multi-relation graphs, BWGNN provides two options, namely homo and hetero. The BWGNN(homo) converts the mutli-relation graph into single graph for con- volution, while the BWGNN (hetero) applies convolution to each relation separately and aggregates output from each relation via maximum pooling.
H2-FDetector (Graph Neural Network-based Fraud Detector with Homophilic and Het- erophilic Interactions (Shi et al. 2022) 8 This approach detects homophilic and heterophilic edges via an auxiliary neural classifier, which trained with an additional loss function. It adopts differ- ent aggregation strategy for detected heterophilic edges where the opposites of node embeddings are used. Additionally, it averages embeddings in each class and the averaged embedding as the class prototype. Node representations are required to be close to their corresponding class prototype.
GHRN (Graph Heterophily Resistant Network (Gao al. 2023a This approach theoretically proves that identifying heterophilic edges in the spatial domain is equivalent to extracting high- frequency signals in the spectral domain. It proposes remove heterophilic edges based on graph spectral theory and to use the new graph for model training. As GHRN adopts BWGNN as its backbone, GHRN(homo) and GHRN(hetero) follow the same definition as BWGNN(homo) and BWGNN(hetero), respectively.
GDN (Graph Decomposition Network (Gao et al. 2023b TO This approach partitions node rep- resentations into class features and surrounding fcatures. For class features, it applies class straints to ensure that nodes within the same class have similar class features. For surrounding fea-
SGDN
18

---

Published as a conference paper at ICLR 2024
tures, it applies connectivity constraints to ensure that neighboring nodes have similar surrounding features.
GAGA (Group AGgregation enhanced TrAnsformer Waang et al. 2023 This approach plicitly uses partially observed labels to partition neighbors into three groups: normal, fraud, and unknown nodes. Each group of nodes is treated differently during processing. It augments node features with trainable hop, relation, and group embeddings, and uses a transformer encoder to transform node features.
D DETAILED EXPERIMENTAL SETTINGS
D.1 DETAILS OF EVALUATION METRICS
We employ 3 metrics to systematically evaluate model performance. Following common settings in previous works (Dou al. 2020 Tang al.] 2022), we select the Area Under the Receiver Operating Characteristic Curve (AUROC) as one of our metric. However, as indicated in (Davis & Goadrich 2006), the AUC score sometimes gives an overly optimistic view of a model if the dataset has a highly skewed label distribution. To get a more thorough view of model performance, we pick another two metrics for evaluation: Area Under the Prevision Recall Curve (AUPRC) and F1-Macro, the unweighted mean of per-class Fl-scores. To compute F1-Macro, apply the threshold-moving strategy (Collell et al. 2018) to all baselines, which adjusts the classification threshold to achieve the best score in validation and directly uses the adjusted threshold in test. All metrics are in the range from 0 to 1, and a higher score indicates a better model performance.
D.2 HYPER-PARAMETE SETTINGS
Hyper-parameter settings of baselines. For the GAD baselines, we utilize the public code repos- itories provided by the authors, adhering to the default hyper-parameters specified in the original papers or the repositories. This ensures integrity our comparative analysis, as these parame- ters have been meticulously fine-tuned on the benchmark datasets by the authors to achieve optimal performance.
In particular, for CARE-GNN, the RL action step size is set as 0.02 and the similarity loss weight is set as For GraphConsis, the number of layers is set as 2 while the sample numbers for the first and second layers are set to 10 and 5, respectively. For BWGNN, the order of the kernel function is set to 2 for Amazon, YelpChi, and T-Finance, and to for T-Social. Two versions of the BWGNN considered, namely the homo and hetero versions. For H2-FDetecto, the two hyper-parameters and 72 are
'n and 7/2 are both set to 1.2 for YelpChi, T-Finance, and T-Social, while in Amazon, set to 0.4 and 1.4, respectively. For GHRN, the deleting ratio is set 0.015 for Amazon, T-Finance, and T-Social, and to 0.1 for YelpChi. For GDN, the top- K feature is set to 10 for all datasets. For GAGA, the number of hops and the number of heads the transformer model are respectively, for all datasets.
and 4,
Hlpper-parameter settings of our CONSISGAD. For generic GNN baselines and our model, we set the dimension of hidden features as 64, number of layers 1. the activation function SeLU (Klambauer et al. 2017), and the number of epochs to be 100. Mini-batch training is adopted with a training batch size set to 32 for the Amazon dataset and to 128 for the others. Model parameters optimized with the Adam optimizer (Kingma & Ba 2015) where the learning rate is set to be 0.001 and weight decay be 0.00001. When evaluating generic GNN models multi-relation graphs, such as Amazon and YelpChi, we convert the graphs to corresponding single-relation graphs by merging multiple relation graphs together.
There are multiple important hyper-parameters in CONSISGAD, including the ratio of the unlabeled batch size to training batch size H [ anomalous threshold Tus normal threshold Tni weight of the label consistency loss a, distribution distance function D(-.). and the drop ratio & in the sharpening function. Here we report the specific hyper-parameter values in each dataset Table 4
http:://githubb... http:///ihuu..coommeee www.//ioono-oooeiieiioee www.rorrroooonoaaaa.o wyc/GAGA
IIn general, the unlabeled batch size is usually several times larger than the training batch size. Thus, this ratio represents this multiple.
19

---

Published as a conference paper at ICLR 2024
Methods
Amazon
YelpChi
T-Finance
T-Social
5
5
Ta
82
88
Tn
97
91
95
95
1.0
0.5
5.0
0.5
D (
euc.
0.3
0.1
0.2
0.1
Table 4: Plyper-parameee settings for CONSISGAD, Here, for space efficiency, we use enc. to stand for cuclidean distance and cos. for cosine distance.
Industrial Graph AUPRC
Methods
AUROC
Macro F1
MLP
99.35...11
39.35
10.83
GCN
82.70
8.38-064
62.58
GraphSAGE
99.64
62.44
83.18
GAT
85.94
12.83
65.31 1099
GIN
94.74
1.95
73.78
GATv2
88.85
14.50
65.94
CARE-GNY
99.56
4
73.27
BWGNN(homo)
98.46:10.0
62.37
80.80=1m0
GHRN
99.45
35.60
69.37
GDN
9..7
63.78++0.2
79.55+0.10
GAGA
9..75
65.19
82.37+0099
CONSISGAD(GNNN
99.74 7.000
67. 67.26
82.73+0.33
CONSISGAD
99.77
69.06.10.68
13.10
Table 5: Comparison (%) on Industrial Graph, with the best bolded and runner-up underlined.
D.3 DATASETS
The data splitting is based on the stratified sampling in Scikit-learn (Pedregosa et al. 2011 which keeps a consistent anomaly ratio in all sets.
D.4 EXPERIMENTAL ENVIRONMENT
All the experiments are conducted on a server running Ubuntu 22.04.2 with 3. 3.1 Intel Xeon Gold 6346 CPU, 1024GB RAM, and 8 NVIDIA Tesla A100 GPUs with 80GB of memory each. CONSISGAD is implemented based on Python 3.7.15, Py PoTcchh 1.13.1, and DGL 1.1.0.
E ADDITIONAL EXPERIMENTS
E. GRAPH ANOMALY DETECTION ON INDUSTRIAL GRAPH
presents presents the experimental results obtained from the Industrial Graph, which is derived from production environment. It is evident that CONSISGAD consistently achieves optimal performance across all three metrics, aligning with the observations made in our main paper. It is noteworthy that, given the pronounced imbalance characteristics inherent real-world production settings, the AUROC is exceptionally high for all evaluated methods.
E.2 PERFORMANCE UNDER VARYING SUPERVISION
Figure 6 and Figure illustrate the performance of the model under varying levels of supervision, as measured by the AUROC and Macro Fl metrics, respectively. The observations align with the discussion presented in the main paper.
20

---

Published as a conference paper at ICLR 2024
97.5
ConiSADD
ConasAAIINN))
GDN
95.0
BWGNSSaerro
AUROC (%)
92.5
85
90.0
GHRNilommo)
75
CoIsSGADGGNN)
GIN
82.5
(WNNN()omo)
40
10
40
Training Ratio (%)
Training Ratio (%) (a) YelpChi.
(a) Amazon.
Figure Experiments under varied supervision in terms of the AUROC metric.
92.5
ConcaGAD
Gi(RN(hvtemm
ConcsAAD(CNN)
80-
BWGNSSherro)
GAGA
Macro F1 (%)
87.5
75
85.0
82.5
80.0
CaisGGD CONEStAAR(GNNN)
GHRNN(hmme)
77.5
RWNNN((vmoo)
GAGA
10
40
10
40
Training Ratio (%)
Training Ratio (%) (a) YelpChi.
(a) Amazon.
Figure 7: Experiments under varied supervision in terms of the Macro F1 metric.
E.3 INFLUENCE OF LABEL CONSISTENCY AND DISTRIBUTION DIVERSITY
Figure 8(a) and Figure 8(b) visualize the contributions of the label consistency and distribution diversity to CONSISGAD, in terms of AUROC and Macro Fl scores, respectively. We can achieve similar conclusion discussed in Section 4,2
E.4 COMPARISON WITH OTHER GRAPH AUGMENTATION TECHNIQQES
In this section, we benchmark our learnable data augmentation against several stochastic augmen- tation methods. Specifically, we substitute our augmentation module with widely-recognized tech- niques in the consistency training framework, including DropNode (Feng al. 2020a). DropEdge (Rong et al., 2020), and Dropout (Srivastava al., 2014). We apply Dropout to both input features, denoted as DropInput, and intermediate features, referred to DropHidden. It is noteworthy that DropHidden serves as a non- nen-learnable analogue to our augmentation module. For a fair comparison, determine the optimal drop rate for each method within the interval of (0, 0.5]. with step size of 0.1. The outcomes, depicted in thrrough the three metrics, underscore the preeminence of our proposed learnable data augmentation over the traditional stochastic alternatives. A salient ob- servation is that among conventional augmentation methods, employing DropHidden and DropEdge in consistency training usually yield more substantial and stable performance improvements across all datasets. This empirical insight substantiates our decision to integrate learnable data augmenta- tion intermediate states and suggests the potential exploration of applying such augmentation to graph topology (Xia et al. 2022) We also list the optimal drop rate in Table 6
E.5 FLEXIBILITY WITH OTHER GNN MODELS
We investigate how traditional GNN models perform when equipped with consistency training and learnalle data augmentation. We pick two representative GNN models, namely GCN and Graph-
21

---

Published as a conference paper at ICLR 2024
CanDAD
Orsediap
95
Sasaettting Orairane
OaaaicAD vo Canirnt
CheraGADiio Mtundy
OssniCAD Diiinily
85
AUROC
73
Marro F1
54.
45-
45-
Arta000
YépChi
V-Pizance
7-Snnl
Amnaz0
YelpChi
F-Fmncee
T-Sccal
(a) AUROC
(b) Macro FI.
Figure 8: Influence of Label Consistency and Distribution Diversity. Subfigure (a) depicts the result on the AUROC metrie. Subfigure (b) depicts the result on the Macro Fl metric.
ConDrDAD (Dealado
AUPRE (99)
45
Arsionn
YdpChi
T-Fansoe
T-uciill
(a) AUPRC.
Ceeddup
IrensttD thophhpp
Condricb (Drotiee
CandrcAD (Draiiado
AUROC (56)
75
55
45
YelpChi
1:Social
(b) AUROC
thophhpp
95
Macro (96)
k5
55
Amooon
YelpChu
TSoccal
(c) Macro
Figure 9: Comparison between the learnable augmentation and traditional stochastic augmentation. Subfigure (a) depicts the result on the AUPRC metric. Subfigure (b) depicts the result on the AUROC metric. Subfigure (c) depicts the result the Maero Fl metric.
SAGE, and replace our backbone model with them. As indicated in Tables 7 GNN model trained with consistency training and learnable data augmentation consistently outperforms its counterpart across all metrics, which showcases the flexibility of CONSISGAD to facilitate the training of vari- base GNN architectures.
22

---

Published as a conference paper at ICLR 2024
Methods
Amazon
YelpChi
T-Finance
T-Social
CoNsISGAD((rrophnpu))
0.1
0.1
0.1
0.4
CoNSISGAID(DroNNooio
0.2
0.1
0.1
0.5
CoNSIsGA (DroopGeD)
0.2
0.1
ConsIsGADDDropFiideen
0.3
0.1
0.2
0.1
Table 6: The optimal drop rate for each augmentation technique in each dataset.
Methods
Amazon
YelpChi AUPRC
T T-Finance AUPRC
AUROC
AUROC
AUROC
GCN
87. 34
48 28.06
70.94.24
17 20.0
35.59
89.29.a19
53,94_1m
77.16
w CONSISGAD
87.72=042
48.42=1.6
73.88 +148
54.9+a054
17.40=0.5
43.06=7.40
89.28=012
57.41=205
78.19
GraphSAGE
90. 12:44
73.17:44
84.25
73.70
34.57=0.8
63. H3.3
89.4 19.42+116
49.08
77.62
w CONSISGAD
91.94
79.61=1.0
88.78=361
73.82+04r
34.88=058
63.41#62
91.23=a500
56.85-12
80.90+100
Table 7: The performance (%) of traditional GNN models when equipped with CONSISGAD.
E.6 ANALYSIS OF THE QUALITY OF HIGH-QUALITY NODES
In this subsection, we examine the performance of high-quality nodes. We visualize Macro scores of high-qualityy nodes at each epoch during training and compare these with scores from the test set. Figure 10 depicts the dynamic of Macro F1 scores for both high-quality and test nodes. Our findings reveal that the high-quality nodes consistently exhibit higher Macro FI scores compared to test nodes. Specifically, the average performance on high-quality nodes surpasses that on test nodes by margins of 1.01% % 0.83%, 0.71%, and 0.64% the Amazon, YelpChi, T-Finance, and T-Social datasets, respectively. Generally, both high-quality nodes and test nodes show gradual increase performance, with the former driving the improvement of the latter. An exception lies in the T- Social dataset, on which the performance fluctuates a bit. The underlying reason might be that the batch size and training data size are relatively small compared the size of the whole dataset, which causes fluctuation of the performance. This outcome highlights the superior quality of high-quality nodes and validates effectiveness of our selection criteria for consistency training.
E.7 ANALYSIS OF HYPER-PARAMETEE SENSITIVITY
Weight of the label consistency loss Figure illustrates the effect of different label consis- tency weights a on model performance. We experiment with a range of a values: {0.1, 0.2, 0.5, 1.0, 2.0, 5.0, 10.03, and measure the corresponding model performance. Our result indicates that an a value of around 1.0 yields optimal performance for the Amazon and YelpChi datasets, whereas value of around 5.0 is preferable for the T-Finance dataset. Overall, model performance remains stable with moderate a value. If a is set to a excessively high value, the performance will be greatly impaired. This is likely due to the diminished diversity in generated augmentations, which is crucial for effective consistency training.
Drop ratio Figure 12 depicts the impact of various drop ratios on model performance. In this analysis, We test drop ratios & in the range of {0.0, 0.1, 0.2, 0.3, 0.4, 0.5}. The result reveals that maintaining within 0.1 to 0.3 is foolproof decision for all datasets. If is set too small, CONSISGAD degrades to the backbone model and cannot leverage abundant information encoded in unlabeled data for training. Conversely, higher risks losing important information, making it hard for the model to discern valuable patterns.
Normal threshold and anomalous threshold T.. Figure 13 and Figure 14 illustrate how the model behaves under different normal thresholds tn and anomalous thresholds Ta respectively. We experiment with normal thresholds set at (89, 91, 93, 95, 97, 99) and anomalous thresholds at (79, 92, 85, 88, 91}. Overall, the result suggests that our model, CONSISGAD, exhibits robustness against the range of tested thresholds. This resilience likely stems from the adaptability of our learnable augmentation module, which can dynamically adjust to varying threshold values during training.
23

---

Published as a conference paper at ICLR 2024
93
high-qualityy nodes
nodes
70
92
Macro F1 (%)
Maero F1 (%)
91-
65
90-
60
88
55
87
high-qualitt modes
test nodes
60
80
0
80
Epoch
Epoch
(a) Amazon.
(b) YelpChi.
high quality nodes
cest nodes
78
Maero Fl (%)
90-
Macro F1 (%)
76
74
88
72
86
70:
84
68
high-qua digh-qualitt rodes
test nodes
60
80
100
20
80
100
Epoch
Epoch
(c) T-Finance.
(d) T-Social.
Figure 10: Dynamic of Macro Fl scores on high-quality nodes and test nodes. The X-axis denotes epochs during training and Y-axis the corresponding Macro score. The orange lines represents the high-quality nodes, while the blue lines represent the test nodes. Subfigre(a)-(G) depict the result on Amazon, YelpChi, T-Finance, and T-Social, respectively.
95.0
90-
92.5
AUROC (%)
AUPRC (%)
Macro F1 (%)
85
90.0
YolpChi
YolpChi
VayCai
87.5
T-Firemx
T-Fimmoe
60
50
82.5
0.2
0.5
1.0
2.0
5.0
10.0
0.1
0.2
0.5
1.0
2.0
5.0
10.0
0.1
0.2
0.5
1.0
2.0
10.0
(a) AUROC.
(b) AUPRC.
(c) Macro FI.
Figure 11: The performance of CONSISGAD with varied weights of the label consistency loss a in terms of AUROC (Subfigure a), AUPRC (Subfigure b), and Maero Fl (Subfigure c). Blue, orange, and green lines depict results on Amazon, YelpChi, and T-Finance, respectively.
E.8 PERFORMANCE THE BACKBONE GNN MODEL MORE GRAPHS.
In this subsection, examine the performance of our backbone GNN model generic multi-class node classification tasks with diverse homophily ratios. We follow the experimental procedure of recent work, the Feature Selection Graph Neural Network (FSGNN) (Maurya al. 2022). and use
24

---

Published as a conference paper at ICLR 2024
95.0
92.5
80
AUROC (%)
AUPRC (%)
Maero F1 (%)
85
90.0
70-
Amazon YolyCli Finanee
Amnzon YohcCl
Amazos YohyCi
87.5
60
F-Staaeee
F-nanae
85.0
75
50-
80.0
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
5
5
5
(a) AUROC.
(b) AUPRC.
(c) Macro FI.
Figure 12: The performance of CONSISGAD with varied drop ratios & in terms of AUROC (Sub-
figure a), AUPRC (Subfigure b), and Macro FI (Subfigure c). Blue, orange, and green lines depict results on Amazon, YelpChi, and T-Finance, respectively.
95.0-
90
80
92.5
AUROC (%)
AUPRC (%)
Macro F1 (%)
85
Amazonn
Amazon YolyChi
Amazon
YolyChi T-Finance
YelpCii
87.5-
T-Finara::
T-Firance
60
85.0
82.5-
91
97
99
91
99
91
93
99
Tn
Tn
Tn
(a) AUROC.
(b) AUPRC.
(c) Macro FI.
Figure 13: The performance of CONSISGAD with varied normal thresholds in terms of AUROC (Subfigure a), AUPRC (Subfigure b), and Macro F1 (Subfigure c). Blue, orange, and green lines depict results on Amazon, YelpChi, and T-Finance, respectively.
their public repository 13 for experimentation. The experiment consists of three homophily graphs and six heterophily graphs, with homophily ratio ranging from 0.11 0.81. For each dataset, we compute the average accuracy across ten publicly available data splits for evaluation, which are widely adopted by researchers in the community (Pei et al. 2020] Zhu et al., 2020 Maurya al. 2022). ). For our GNN backbone model, we set the number of layers to be two and keep the remaining architecture untouched. For each dataset, we carry out lightweight fine-tuning on the learning rate and weight decay. Specifically, we pick the best learning rate from {0.1. 0.01, 0.001 and weight decay from [0.01, 0.001, 0.0001} based on the validation performance. Table summarizes dataset statistics and corresponding results, where the performance of other baselines are taken from (Maurya et al. 2022).
Note that our proposed GNN backbone, CONSISGAD(GNNN, is based the difference of contex- tual homophily distribution between normal and anomalous nodes. Such a phenomenon com- monly in the graph anomaly detection task (i.e., the imbalanced binary classification task) where normal nodes have high homophily distribution while anomalous nodes have low homophily distribution. This prominent distribution discrepancy lays down the foundation of GNN back- bone. When it comes to multi-class node classification tasks, the homophily-aware neighborhood aggregation (Equation 4 in the GNN backbone will model the label distribution within node's neighborhood. If this neighborhood label distribution exhibits distinguishable patterns for different classes, we would expect our backbone model function well. From Table we observe that our GNN backbone model performs comparably to existing baselines in the three homophily graphs.
25

---

Published as a conference paper at ICLR 2024
95.0-
90
92.5-
AUROC (%)
AUPRC (%)
Macro F1 (%)
85
90.0
Amazon
70-
Amazon YelyChi T-Fineras:
Amazon
YelyChi
80
YepChi
87.5-
T-Finence
T-Fisanes
60
75
85.0
82.5
79
82
85
88
91
79
82
85
88
91
79
82
855
88
91
Ta
Ta
Ta
(a) AUROC
(b) AUPRC.
(c) Macro F1.
The performance of CONSISGAD with varied anomalous thresholds in terms of AUROC (Subfigure a), AUPRC (Subfigure b), and Macro F1 (Subfigure c). Blue, orange, and green lines depict results Amazon, YelpChi, and T-Finance, respectively.
Figure 14:
Cura
Citeseer
Pubmed
Chameleon
Wisconei
Texts
Comell
Sqpirrel
Acter
Mean Acc.
ratio
0.81
0.74
0.30
0.11
a Nodes
2,708
3,327
19.717
2.277
251
183
185
5,201
7,600
a Edges
5,278
4.732
44,338
36,101
499
309
205
198,353
26.659
a Featusss
1,438
3,703
500
2,325
1,703
1,703
1,703
2,059
932
& Classes
7
8
3
5
5
GUN
87. -.2
76.0 14
87.38-oue
59,82:2.
59 50.
59 49.4645.5
57.03
36, 34
30 265000
61.62
GAT
22:68-100
75 462177
84 K8
$4,692
55 m
58. 38g4
58 27
10.62271
26 28
58.55
OrggSAGE
76.0 06.04.1
88.45
58.73.158
81.18
$2.43
75
41.51
Chiby4JK
85.49-115
29u07
63.7943.2
82.55
78.
MixTlup
87.61
85.31
12.22
GEOM-GON
85.27
77.09
90105
12
OUNU
17.13.13
$1.57
17.84
1437
HIGCN-1
86.02-132
27.07
57.11a:
26:67
84. M0
36.42::4
WRGAT
88.20
26:8
88.52
m7
36 .m
83.82,x30
33.37
72.93
GPRGNN
88.49 .005
08
88.99 .ue
66.474241
85.85-177
50.49 4.30
81 19.87
49.13 11.33
38.04
73:37
ESONN
98.23 1.77
77.40 100
89.73 a.4
18.95:030
38.43 1.22
87.57 14:8
87.84.43
74.10 11:05
35.75.005
78.67
CONSISGADIGNNI
86.32-132 1.72
73.83:131
89.39 0344
44.82:1M
36.47
83.24
83.51:699
33.08 1378
37.38.125
63.39
Table Mean classification accuracy on generic multi-class node elassification tasks with different homophily ratios. Results of baseline models are taken from (Maurya et al. (2022). For FSGNN, we list the performance of the best variant for each dataset. Best results are bolded and runner-up underlined. Here, "N/A" denotes non-reported results.
Our GNN backbone is built upon the Sassage-Passingg Neural Network (MPNN) framework, which allows handling homophily information naturally. For heterophily graphs, our backbone model achieves good performance in the Wisconsin, Texas, and Cornell datasets, but faces challenges in the Chameleon, Squirrel, and Actor datasets. Our further investigations in Figure [3 reveal that, in Wisconsin, Texas, and Cornell, nodes of different classes have distinct label distribution among their neighborhood, which allows our backbone model to distinguish different classes effectively. How- ever, such distinct patterns our backbone model on these datasets. Notably, despite a low accuracy on the Actor dataset, our model achieves a new state-of-the-art result, indicating its potential in handling heterophily graphs in multi-class node classification tasks. Future work may explore integrating our GNN backbone with other techniques enhance performance on heterophily graphs.
absent in Chameleon, Squirrel, and Actor, explaining the struggle of
E.9 INFLUENCE OF EXACT LABELS FOR CONSISTENCY TRAINING
In our current settings, both labeled and unlabeled data are used for consistency training, but la- beled samples are treated as unlabeled, using their predicted labels instead of exact labels. In this subsection, we investigate the effectiveness using exact labels for labeled nodes during consis- tency training. Our results, presented in Table and Table 10 suggest that using exact labels in consistency training does not markedly enhance performance across most datasets. This lack of im- provement may stem from the fact that labeled data has already been utilized in the cross-entropy loss, and their reuse in the consistency training does not contribute significantly to performance en- hancement. Notably, decrease in performance observed in the T-Social dataset. We hypothesize
26

---

Published as a conference paper at ICLR 2024
2
4
5
2
4
3
5
2
2
Class
Caass
Class
4-
4-
4-
32
5
5
42
-02
Class
Class
Class
(a) Wisconsin.
(b) Texas.
(c) Cornell.
640
2
2
Class
415
Class
4-
1020
4.2
4
1111
5
4.50
Class
Class
Class
(d) Chameleon.
(e) Squirrel.
(f) Actor.
Figure 15: Neighborhood label distribution for different classes of nodes. Each row represents node class, while each column represents neighbor class. A darker color denotes higher probability. The difference between two rows depicts the difference of neighhorhood label distribution between corresponding classes. Rows in Subfigure (a)-(c) distinguishable. Therefore, Subfigure (a)-(c) represent the set of graphs where nodes of different classes have distinct label distribution among their neighborhood, which are suitable CONSISGAD(GNN), On the other hand, rows in Subfigure (d)-(f) are less distinguishable, which poses challenges to our backbone model.
Amazon AUPRC
YelpChi AUPRC
Methods
AUROC
Macro F1
AUROC
Macro FI
CONSISGAD
93,91 93.82+uas
83.33+034
90.03-aas
83.36+a5s 82.91
47.33
69.72+030 69.44=029
CONSISGAD (Exact Label)
83.16=046
89.88=a30
47.23=098
Table 9: Model performance when using exact labels of labeled nodes in consistency training on Amazon and YelpChi datasets.
T-Finance AUPRC
T-Social AUPRC
Methods
AUROC
Macro Fl
AUROC
Macro Fl
CONSISGAD
95.33+t030
86.63=044 86.942013
90.97=aa3
58.38=210 94.31 78.08 77.42=007
CONSISGAD (Exact Label)
95.09
91.32_018
93.87=030
56.54=186
Table 10: Model performance when using exact labels of labeled nodes in consistency training on T-FFinacce and T-Social datasets.
this could be attributed to the model overfitting to label noise, which could mitigated by the usage of predicted labels.
27

---

Published as a conference paper at ICLR 2024
F DISCUSSION OF DATA AUGMENTATION ON GRAPHS
F.1 DATA AUGMENTATION ON GRAPHS
Graph data augmentation techniques can be classified into four categories. Stochastic augmentation
randomly samples noise to node features and graph structures (Srivastava et al.
2014 Feng et al.
2020a [o et al., 2022). Adversarial perturbation (Deng et al. Feng et al. 2019 Kong al,
2022] noises node features by calculating virtual adversarial perturbations. Generative-mode based
augmentation employs generative models to generate artificial features for augmentation (Zhang
ct al.
2019 Zhao et al., 2021 Liu et al. 2022) Interpolation-base augmentation utilizes the
MixUp-like like Zhang et al. 2018 Verma et al. 2019) methods to synthetize instances on graphs
Verma et al. 2021 Wang et al. 2021). Nonetheless, these approaches fail to calibrate the extent of
data augmentation and suffer from over- or under- anuder-augmenationn In the realm of graph contrastive learning, several automatic data augmentation approaches have been proposed to address these lim- itations (You et al., [021]] Zhu et al.) 2021), and we provide an in-depth comparison between our learnable augmentation and these methods Appendix F.2
F.2 DETAILED COMPARISON WITH EXISTING AUTOMATIC DATA AUGMENTATION TECHNIQUES
In the realm of graph contrastive learning, various automatic data augmentation methods, such as JOAO (You et al. 2021 and GCA (Zhu et al. 202I), have been introduced. JOAO learns sampling distribution for augmentation pairs using a min-max optimization process, while GCA generates augmented graphs by adaptively dropping edges and node features based on node centrality scores. Our learnable augmentation module presents notable differences from these approaches, particularly in terms of augmentation quality evaluation and learning objectives.
Augmentation quality evaluation. JOAO adopts an adversarial training strategy. prioritizing aug- mentations that yield the greatest contrastive loss. This approach inherently aims enhance the distribution diversity of augmentations. However, it may inadvertently introduce excessive noise due to overlooked label consistency, leading to suboptimal performance, as discussed in prior stud- ies (Balaji et al.) 2019; Tsipras et al. 22088.. GCA assumes that good augmentation should drop unimportant edges and features while keeping important ones. The importance is measured through node centrality scores. This method, while intuitive, does not necessarily guarantee high consistency and diversity in augmentations. In contrast, our work does not rely on pre-defined node importance metrics. Instead, we posit that effective augmentations should enhance node's diversity without altering its label, maintaining high label consistency. To this end, we formulate differentiable dis- tribution diversity and label consistency metrics to evaluate augmentation quality and to guide the training of our augmentation module.
Learning objectives. The objective of JOAO to select the optimal augmentation pair from a predetermined pool, relying heavily on domain knowledge for pool construction and configuration. The adaptive augmentation module GCA remains fixed and non-learnable throughout the training process. This is due to the static nature of node centrality scores, resulting in constant dropping rates for edges and node features. Furthermore, operates independently encoder employed. By contrast, our work introduces novel learnable augmentation module through learnable masking. This module designed to synthesize custom augmentations for individual nodes, updating continuously throughout training adapt to the dataset and evolving GNN encoder.
the specific GNN
28


Reviews:
[{"review_id": "quyBPeaSTj", "reviewer": "Reviewer_ZNLh", "summary": "In this paper, the authors tackle the problem of anomaly detection in graphs by introducing a novel approach---consistency training coupled with a learnable data augmentation mechanism. Their method involves leveraging a simple GNN backbone that emphasizes edge-level homophily representation for anomaly detection. By exploiting disparities in homophily distribution, the proposed model achieves enhanced anomaly detection capabilities. Additionally, the authors introduce two evaluation metrics designed to optimize their innovative learnable data augmentation technique, guiding its effectiveness in data synthesis. In their experimental evaluation, the authors assess the performance of their model across four benchmark datasets commonly used for graph-based anomaly detection, along with a private dataset. The proposed model generally outperforms existing state-of-the-art baselines across three key evaluation metrics.", "questions": "1. How about the correctness of the \"high-quality nodes\"?\n\n2. The authors should perform a sensitivity analysis for the crucial hyperparameters in the proposed model.\n\n3. Can the proposed GNN backbone effectively handle generic multi-class node classification tasks?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. I find the proposed learnable data augmentation mechanism intriguing. Intuitively, this approach appears effective, as it can be finely tuned through the optimization of two core metrics: label consistency and data distribution. Through iterative optimization of these components---the GNN module and the learnable data augmentation module---it seems both elements can be well-trained, enhancing the overall performance of the model.\n\n2. The node clusters displayed in Figure 3 provide a compelling visual representation of the effectiveness of the proposed GNN backbone. The well-separated node clusters, especially concerning different edge relations, serve as a strong validation of the necessity of leveraging distinctions in homophily distribution for anomaly detection. This visualization underscores the robustness of the proposed method.\n\n3. The paper is skillfully composed, ensuring clarity and coherence in conveying the research concepts. Additionally, the experiments conducted are generally comprehensive, offering substantial evidence to support the effectiveness of the proposed model.", "weaknesses": "1. Regarding consistency training, the proposed model employs thresholds to identify \"high-quality nodes\" from the unlabeled data for training. This step, akin to semi-supervised learning, assigns synthetic labels to unlabeled data for consistency training. The performance of these \"high-quality nodes\" is pivotal for downstream iterative training, emphasizing the significance of their accuracy. Hence, the authors should analyze the actual quality of these \"high-quality nodes\" and the accuracy of their predicted labels. This aspect holds significant importance in evaluating the reliability and effectiveness of the model.\n\n2. The paper introduces essential hyperparameters, including $\\alpha$ and $\\xi$. While the authors provide their specific settings in the experiments, the impact of these parameters on the performance of the model remains unexplored. The authors should perform a sensitivity analysis for the crucial hyperparameters in the proposed model.\n\n3. The proposed GNN backbone shows promise for anomaly detection by capturing distinctions in the homophily distribution of nodes in graphs. However, it raises intriguing questions about its performance on graphs with varying levels of heterophily. Specifically, how well does the proposed GNN backbone perform on graphs with low or high heterophily when applied to generic multi-class node classification tasks?", "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": "", "extra_scores": {}}, {"review_id": "4lYXOAmO5O", "reviewer": "Reviewer_RZbU", "summary": "This paper delves into the challenge of graph anomaly detection with limited supervision. To address this, the authors introduce ConsisGAD, a novel model rooted in consistency training. ConsisGAD leverages variance in homophily distribution between normal and anomalous nodes to craft an effective GNN backbone. The authors also propose a learnable data augmentation mechanism for consistency training using unlabeled data. The paper presents comprehensive experiments on benchmark datasets to validate the effectiveness of the proposed model.", "questions": "Please see the Weaknesses", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well-structured and presented in a clear manner. It effectively communicates the motivation behind the proposed model, making it accessible to readers. \n\n2. The proposed model, comprising homophily-aware neighborhood aggregation and consistency training with learnable data augmentation, is innovative. The homophily-aware aggregation method is straightforward yet effective, especially for edge-level homophily representation, enhancing the anomaly detection process. The proposed label consistency and distribution diversity concepts are intriguing, guiding the optimization of learnable data augmentation.\n\n3. The paper demonstrates a thorough evaluation through extensive experiments, which strengthens the empirical foundation and validates the performance across different datasets.", "weaknesses": "Weaknesses:\n\n1. The paper should acknowledge related works that are pertinent to the proposed learnable data augmentation, such as [a] and [b]. It is crucial to cite and discuss the distinctions between these works and the proposed approach, providing readers with a clear understanding of the novel contributions made by this study.\n\n2. The paper predominantly explores the concept of applying learnable data augmentation for graph anomaly detection. While this is valuable, investigating its applicability in broader graph learning tasks, such as node classification with contrastive learning, could significantly expand its scope. For example, how about its benefits to generic graph contrastive learning tasks, compared to existing contrastive techniques?\n\n3. While consistency training might usually be deployed on unlabeled data, I wonder if it would be beneficial to utilize labeled data for consistency training as well. Specifically, labeled data has exact labels, which might provide effective information for consistency training the model in dealing with the taks of graph anomaly detection.\n\n\n[a] Graph Contrastive Learning Automated. Yuning You, Tianlong Chen, Yang Shen, Zhangyang Wang. ICML 2021\n[b] Graph Contrastive Learning with Adaptive Augmentation. Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, Liang Wang. WWW 2021.", "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": "", "extra_scores": {}}, {"review_id": "7qs6BpkZpo", "reviewer": "Reviewer_tbTo", "summary": "This paper has addressed the challenge of graph anomaly detection under limited supervision by introducing a novel model, which effectively leverages the abundance of unlabeled data for consistency training by incorporating a novel learnable data augmentation mechanism. Furthermore, CONSISGAD exploits the disparity in homophily distribution between normal and anomalous nodes, enabling the formulation of a refined GNN backbone that enhances its discriminatory power between the two classes.", "questions": "see above", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The logic of the whole paper is relatively clear and there are no obvious grammatical errors.\n\n2. There are quite sufficient experiments to verify the proposed method.", "weaknesses": "1) why Eq4 can achieve the edge-level homophily representation? where does it differ from GCN aggregation? \n\n2) as you said, GAD has low homophily distribution, whether  the homophily-aware neighbourhood aggregation you propose will be effective for abnormal nodes, I deeply doubt it.\n\n3) I don't find  the definition of Vhq in Section 2,  whiat is the meaning of Vun?\n\n4) please compare  your learnable augmentation with other augmentation methods  \n\n5) please give complexity analysis", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (spotlight)