Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
Authors: Junyu Luo
Yuhao Tang
yiwei Fu
Xiao Luo
Zhizhuo KOU
Zhiping Xiao
Wei Ju
Wentao Zhang
Ming Zhang
Venue: ICML 2025 poster (2025)
Keywords: Unsupervised Graph Domain Adaptation
Domain Adaptation
Data-efficient Graph Learning
Primary area: general_machine_learning->transfer_multitask_and_metalearning
TL;DR: SLOGAN boosts Unsupervised Graph Domain Adaptation by using causal discovery, generative intervention, and adaptive calibration  to master domain shifts, delivering more robust and accurate graph AI.

Abstract: Unsupervised Graph Domain Adaptation (UGDA) leverages labeled source domain graphs to achieve effective performance in unlabeled target domains despite distribution shifts. However, existing methods often yield suboptimal results due to the entanglement of causal-spurious features and the failure of global alignment strategies. We propose SLOGAN (Sparse Causal Discovery with Generative Intervention), a novel approach that achieves stable graph representation transfer through sparse causal modeling and dynamic intervention mechanisms. Specifically, SLOGAN  first constructs a sparse causal graph structure, leveraging mutual information bottleneck constraints to disentangle sparse, stable causal features while compressing domain-dependent spurious correlations through variational inference. To address residual spurious correlations, we innovatively design a generative intervention mechanism that breaks local spurious couplings through cross-domain feature recombination while maintaining causal feature semantic consistency via covariance constraints. Furthermore, to mitigate error accumulation in target domain pseudo-labels, we introduce a category-adaptive dynamic calibration strategy, ensuring stable discriminative learning. Extensive experiments on multiple real-world datasets demonstrate that SLOGAN significantly outperforms existing baselines.

Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
Junyu Luo 12 Yuhao Tang² Yiwei Fu Xiao Luo Zhizhuo Kou Zhiping Xiao
Wei Ju 12 Wentao Zhang² Ming Zhang"
Abstract
1. Introduction
Graph Neural Networks (GNNs) have demonstrated their effectiveness in graph-structured data analysis, including molecular structures (Turutov & Radinsky, 2024; Kim et al., 2023), social networks (Kumar et al., 2020; Li et al., 2021), traffic networks (Chowdhury et al., 2024) and RAG (Jiang et al., 2024; Luo et al., 2025). Graph classification is an important task in graph learning, which targets at predicting the labels of the entire graphs (Ying al., 2018; Ranjan et al., 2020; Zhang et al., 2018). GNN-based graph classifi- cation approaches typically use message-passing network in conjunction with a readout operator to aggregate the node features into graph-level representations, followed by classifier for downstream tasks such as molecular property prediction in drug and material seience (Xu et al., 2021).
Unsupervised Graph Domain Adaptation (UGDA) leverages labeled source domain graphs to achieve effective performance in unlabeled target do- mains despite distribution shifts. However, ex- isting methods often yield suboptimal results due to the entanglement of causal- -uusal-spurious features and the failure of global alignment strategies. We propose SLOGAN (Sparse Causal Discovery with Generative Intervention), a novel approach that achieves stable graph representation transfer through sparse causal modeling and dynamic in- tervention mechanisms. Specifically, SLOGAN first constructs a sparse causal graph structure, leveraging mutual information bottleneck con- straints to disentangle sparse, stable causal fea- tures while compressing domain--ependent spuri- ous correlations through variational inference. To address residual spurious correlations, we innova- tively design a generative intervention mechanism that breaks local spurious couplings through cross- domain feature recombination while maintaining causal feature semantic consistency via covari- ance constraints. Furthermore, mitigate error accumulation in target domain pseudo-labels, we introduce category-adaptiee dynamic calibra- tion strategy, ensuring stable discriminative Iearn- ing. Extensive experiments on multiple real-world datasets demonstrate that SLOGAN significantly outperforms existing baselines.
Despite the effectiveness of existing approaches, their as- sumption of consistent distribution between training and inference datasets rarely holds, especially in real-world sce- narios. This mismatch leads to out-of-distribution (OOD) challenges (Wu et al., 2020; Lin et al., 2023; You et al., 2022). addition, the scareity of labeled data in the target domain brings extra challenges, making supervised meth- ods infeasible (Hao al., 2020; Suresh al., 2021). One typical method to tackle this problem is Unsupervised Do- main Adaptation (UDA), which leverages labeled data from a source domain to enable task performance in an unlabeled target domain (Deng et al., 2021; Long et al., 2018).
UDA has been extensively studied in the context of Eu- clidean data (e.g., images) through self-learnng (Wei et al., 2021a; Xiao & Zhang, 2021), adversarial domain trans- fer (Ganin et al., 2016; Saito et al., 2018), or domain discrepancy minimization techniques (Lee et al., 2019a), However, it is non-trivial to develop a UDA approach for non- Eun-Euclidean graph data. There are significant chal- lenges due to the complex topology and rich semantics of graphs (Velickovic al., 2019; Huang & Zitnik, 2020). which mainly attributed to: (I) Feature entanglement and persistent spurious correlations. Graph data inherently encodes both causal relationships and statistical correlations.
Sttte Key Lahoratory for Multimedia Information Processing. School Computer Science, PKU-Anker LLM Lab 'Peking Uni- versity 'University of California, Los Angeles "Hong Kong Univer- sity of Science and Technology Paaul G. Allen School of Computer Science and Engineering, University of Washington. Correspon- dence to: Xiao Luo <xiaoluo@ ww..ula..cdu.......... Zhiping Xiao <patx- i uw.edu>, Ming Zhang <mzhang es @s@@pku.cco eku.cdu.cn>
Proceedings of the nnnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
Traditional methods that rely solely on semantic labels for model training often fail to distinguish between these two

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
dynamic stability optimization to address error propagation risks in target domain pseudo-labels. We propose category- adaptive confidence thresholds for dynamic and balanced sample selection. Through cross- joint optimization, SLOGAN achieves progressive alignment of causal features, enhancing the framework's 's robustness. Extensive experi- ments on 6 benchmark datasets demonstrate SLOGAN's consistently superior performance over existing methods.
HO
HO
HO
OH
OH
OH
Domaln Adaptation
Causal Factors
Feature
Entongle
Spurious Factors
Female
Male
Rat
Mice
The contribution of this paper is summarized as follows. (1) We focus on sparse stability and dynamic robustness in UGDA, proposing framework based on stable learning and causal intervention that effectively extracts domain-invann invariant representations. (2) We introduce SLOGAN, which intro- duces stable causal feature extraction with generative inter- ventions and adaptive pseudo-label calibration achieve high-peut performance. (3) We provide theoretical guarantees for the optimization error bound in the target domain. (4) We conduct extensive experiments to demonstrate SLOGAN's superior performance and varfied our motivation.
Figure 1. Illustration of causal and spurious factors using the PTC dataset. Causal fuctors (above) represent inherent molecular struc- tures that directly determine carcinogenicity properties. Spurious factors (below) exhibit statistical correlations but lack causal rela- tionships, potentially hindering cross-domain generalization.
types of relationships, leading to the entanglement of causal and spurious factors. For instance, in the Predictive Toxi- cology Challenge (PTC (Helma et al., 2001)) illustrated in Figure 1, while specific molecular structures serve as causal factors for carcinogenicity determination, experimental vari- ables such as gender and species merely exhibit statistical correlations with the labels. Without explicit disentangle- ment, these spurious factors can interfere with cross-domain generalization through residual correlations, causing the model to rely on unstable mechanisms in the target do- main. (2) Alignment collapse and global strategy failure. Existing methods typically rely on adversarial learning to align domain distributions (Dai et al., 2022; Shen et al., 2020). However, their global alignment strategy can lead to information collapse, discarding crucial carriers like rare substructures, while failing to suppress spurious factors ef- fectively. These challenges are particularly severe in graph data due to their complex structure and digh-dimensional sparsity, necessitating explicit intervention mechanisms.
2. Preliminaries
Unsupervised Graph Domain Adaptation. For each graph sample G = (V,E), V denotes the set of nodes and & S V V represents the edge set. The node feature matrix is X IRIiidd where each row Ty Rd is the feature representation for node E V. d denotes the dimension of node features. A labeled source dataset is D.o {(9 ) comprising Noo graph examples 9: with corresponding labels yf". An unlabeled target dataset is Dia = {95- No.. which contains Nt graph ex- amples Ghe without label. These two domains have the same label space (1, (1.... C}: however, their data distributions have a huge gap. Our goal is to transfer knowledge from the labeled source graphs to the unlabeled target graphs.
To address the above challenges in graph domain adapta- tion, we propose Sparse Causal Discovery with Generative Intervention (SLOGAN) for Unsupervised Graph Domain Adaptation. SLOGAN leverages sparse causal discovery and dynamic intervention learning to extract stable causal mechanisms while suppressing spurious correlations. Our framework consists of three key components: First, S1.O- GAN focuses causal-spurious feature disentangiement, based on the structural causal model and Information Bot- tleneck (IB) principle, we decompose graph representations into causal and spurious features. This decomposition com- presses label-irrelevant spurious information while preserv- ing sparse, stable causal patterns. Second, SLOGAN intro- duces generative intervention mechanism, avoid global alignment collapse. We design a generative model to recon- struct original graph representations with cross-domain spurious feature exchange strategy. By perturbing local cou- pling of spurious features, this approach forces the model to rely solely on causal features for reconstruction, effectively suppressing spurious residuals. Third, SLOGAN introduces
Graph Neural Networks. Given a graph G = (V,E) with node features X, GNN learns node representations via message passing. For each node v at layer l:
1 UPDATE (n 10-"),AGC (UN8-1) | u (e)))))
(1)
where AGG aggregates neighbor features and UPDATE up- dates node features. The final graph representation is:
CLA (READOUT (I | (oEV)))
CLA
(2)
where READOUT pools node features and CLA generates predictions. The model is trained with cross-entropy loss:
Li
lo
DD00
Motivation Challenges. Existing UGDA methods face
2

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
Unbiased Discriminative Learning
Maximize
Causal Factors
Mutual Info.
Coup
Category-adaptive Callbration
GNN
Target Domain
dis
Generative Intervention
Information Bottleneck
Minimize
Generative Model
Linw
Mutual Info
Source Domain
Covariance
Spurious Factors
Constraints
Figure Overview SLOGAN. The framework consists three key components: (1) A structural causal model disentangle causal and spurious factors from graph representations. (2) An unbiased discriminative learning module with category-adappe calibration. (3)
generative intervention mechanism with covariance constraints to suppress the influence of spurious factors across domains.
two fundamental limitations. First, deep entanglement of causal and spurious features leads models to rely on domain- specific correlations, compromising cross-domain general- ization. Second, global alignment strategies often cause alignment collapse by disrupting critical causal substruc- tures while preserving spurious couplings. These challenges necessitate explicit causal-spurious disentanglement and lo- cal stability preservation, which motivates sparse causal graph construction and generative intervention mechanism.
L
C
PL
Stability Guorantees
Sparse Independence 2e D/Y
G
Suppressed Dependencies
Local Covariance Control Cou(Z,, 2²) =P
Predictive Stability. 1(Y:2") I(X;X)-
D
S
D
Figure 3. Causal graph for UGDA. Dashed arrows indicate sup- pressed dependencies through sparse stability constraints.
3. Methodology
3.1. Framework Overview
labels, C' denotes causal features, S spurious features, and PI. represents pseudo-labels. The dashed arrows highlight suppressed dependencies through stability constraints. This causal structure enables three key mechanisms:
In this paper, we introduce SLOGAN, as shown in Fig. 2, which achieves reliable knowledge transfer through three complementary stability-enhancing components: (1) Sparse causal discovery through feature disentanglement, (2) Pro- gressive stable alignment via discriminative learning with confidence calibration, and (3) Generative intervention with covariance constraints for spurious feature suppression.
Sparse Feature Generation: C + G + enforces min- imal sufficient causal pathways while allowing residual spurious correlations
Label Stability: - + C PL creates cross-domain stability through pseudo-label constrained learning
3.2. Sparse Causal Discovery via Feature Disentanglement
Domain Sparsity: Do S <- D isolates domain-
specific variations to spurious features
We address domain shift in UGDA through sparse stability learning, where key challenge lies identifying stable causal features (Z") that remain predictive across domains while suppressing unstable spurious features (Z*). Our approach implements sparse variable independence (SVI) through three staiiliy-enforriin mechanisms:
Stability-Awrr Disentanglement Learning. Using GNN- derived features z, we implement sparse variable indepen- dence (SVI) through:
max I(Y: Z 3I 2 + min I(Z::)
(4)
Stable Causal Graph Construction. As illustrated in Fig. 3, the structural causal model establishes sparse dependencies between variables to ensure stability (Yu et al., 2023). The graph depicts key causal relationships where L. represents
Stable Prediction
Residual Control
Spurious Suppression
This objective comprises three key components: (1) max- imizing mutual information between causal features and labels ensures stable prediction across domains, (2) control-
3

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
ling residual information between spurious features and orig- inal representations prevents feature collapse, and (3) mini- mizing mutual information between spurious features and labels reduces the impact of Nomain-specifi variations.
between causal and spurious features while allowing neces- sary correlations. Third, predictive stability is guaranteed as (Y;; 29) 2 xX); through feature compression, where e controls information loss during causal feature ex- traction, ensuring that causal features preserve essential predictive information from the input.
Causal Feature Extraction. To improve the extraction of causal features, the objective is to maximize the mutual information between the causal feature z" and the semantic label y (Wang et al., 2024a). We employs InfoNCE (He et al., 2020), which samples positive pairs from the joint distribution p (z", .)) and negative pairs from the marginal distributions p (z") p (y). We disentangle the causal feature z with:
The composite stability objective Cdis = CMr + Lir is minimized to disentangle causal features from spurious ones, ensuring domain-invarian representations while preserving semantic information.
3.3. Unbiased Discriminative Learning
To overcome target domain data scarcity while preventing overconfidence in pseudo-labels (Karim et al., 2022), we develop subility-preserving discriminative learning mech- anism. Our approach combines causal feature reliability with adaptive sample selection to maintain class-balanced supervision:
min Cirs Exper x log (eff (5)
where E F=(2",) implements bilinear mapping Fz 2z Wy with learnable parameter matrix W. This bilinear form captures pairwise interactions between causal features and labels while maintaining computational efficiency.
We first leverage causal features to determine the distribu- tion of graph classification,
Spurious Feature Suppression. To effectively disentan- gle spurious features, we minimize the mutual information between spurious features z" and semantic labels y while maintaining residual information through a constrained op- timization:
p ta
(zz tt)
where & projects causal features n to label space. We quantify prediction certainty through maximum class proba- bility:
min Ci.s [(z' - 2),
(6)
max p ta [c]
(10)
where S/" is the confidence score. Subsequently, to achieve unbiased pseudo-label estimation, we introduce adaptive confidence thresholds. The class-adaptive coefficients are:
where 3 balances the competing objectives. We adopt the Variational Information Bottleneck (VIB) framework due
to its effectiveness in learning compressed representations while maintaining relevant information. Using VIB, we derive variational bounds to control spurious correlations:
Me = max(s;" [ar"] max p [d]] = c
(11)
Therefore, the class-unbiased threshold for class is:
T(z", y) S Ep(x y)) [log [[)] (pp())(())) (log q(y (x"),, (7)
Te M..
(12)
where q approximates the true conditional distribution. For the mutual information between spurious and graph-level features, we employ a bilinear estimator di to derive:
where is the initial confidence score threshold, which is set to 0.95 following (Sohn et al., 2020). Then, obtain the refined confident set C as:
I(z", z) S Ep(r* x)) [v]
C = (G cc arg maxp! to s/a > Te}. e
(13)
The reconstruction constraint [(z z) S Ta prevents com- plete feature collapse while breaking comain-speciffi cou- plings, enabling effective spurious feature suppression dur- ing adaptation.
Cross-domain stability is enforced through optimization:
1
Lia
log P [ot"]]
(14)
C
G.TEC
Stability Guarantees. Our formulation ensures three fun- damental stability properties. First, sparse indepen- dence (2e 1. DIY) is achieved through domain-invariant contrastive learning, ensuring that causal features remain independent of domain shifts conditioned on labels. Second, local covariance control maintainsCov(Z* ((z))) < 8-1 via Lagrange optimization, preventing excessive entanglement
where j denotes the pseudo-label of G.oa We also optimize source data using Eqn. 3 with causal features mitigate overconfidence. The supervised loss is Leup L.o Lia- This dual-domain strategy ensures: (I) causal feature preser- vation via L.o- (2) error-resistant adaptation via L... and (3) class- balsnce learning via adaptive thresholding, com- plementing the feature disentanglement from Section 3.2.
4

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
3.4. Generative Intervention with Covariance Constraints
samples. Afterwards, the target domain is considered for optimization. The summarized overall algorithm can be found in the Appendix A.
Our method uses a targeted approach to ensure models don't 't rely on misleading patterns that vary across domains. Con- sider social network analysis: when classifying discussion topics, our method can distinguish between fundamental net- work structures (like community clusters and information flow patterns) and platform-specifte features (like temporary trending hashtags or regional engagement patterns).
3.5. Theoretical Guarantees
Our theoretical analysis establishes probabilistic bound on the target domain error through three stability conditions.
Theorem 3.1. Under stable causal graph construction, assume the following conditions hold: (1) Causal Suffi- ciency: I(;; Z") > Io where Z is the causal variable and Ie is an information contraint. (2) Spurious Suppres- sion: I(Y; Z²) S EL, where Z is the spurious variable. (3) Generative Intervention: E| Z G 2 S 62. where G is the generation model. Then, for any predictor h E H. with probability at least 1 ō, the target domain error er is bounded as follows:
We achieve this through a generative intervention mecha- nism that deliberately exchanges domain-speciff features between samples while preserving essential structural pat- terns. This forces the model to focus only on truly predic- tive patterns that work consistently across different environ- ments, establishing two key stability properties: (I) indepen- dence from spurious domain- specciicc correlations through controlled feature swapping, and (2) preservation of essen- tial causal patterns through reconstruction consistency.
e S Eg(h)+ + + C(ng,))), (19)
Specifically, we use a generative model G (---) to recon- struct graph representations based on causal and spurious features. The reconstruction model a two-layer MLP. The reconstruction function is optimized by I,2 distance as:
where L is the lipschitz constant of the loss function, C is a constant, and ns is the sample size in the source domain. Here, (T(h) represents the error in the target domain, while (g) denotes the empirical error in the source domain.
(15) Here, z is the graph representation, x and z" are the causal and spurious features. During the adaptation process, to break local correlations, we swap the spurious parts of sam- ples from different domains within a mini-batch B, generat- ing new composite samples:
Lge E Iz G (z", z²) 2
The proof sketch follows three key steps: (1) bounding feature reconstruction error via the generator's fidelity, (2) quantifying spurious correlation suppression in domain dis- crepancy through mutual information constraints, and (3) incorporating statistical generalization error to establish a bound through empirical risk. Detailed proof is provided in Appendix B.
= G Gzf 21
(16)
where * represents the composite representation combin- ing causal features zł from sample with spurious features z from sample k in different domains. Then, we enforce intervention invariance through dual constraints:
Complexity Analysis. The computing complexity is mainly introduced by GNN. For given graph g = (V, ) d is the feature dimension, |V] denotes the number of nodes, and represents the number of GNN layers. The complexity of our GNN is (LL(V|d²). i.e., linear to [V].
Linu Cre + E 85 ||, 1:1
(17)
where Cre is the reconstruction loss. Using invariant leam- ing under intervention, we achieve robust cross-domain representations by eliminating spurious factors. The recon- struction loss Ere maintains reconstruction capability while the intervention term ensures robustness. This achieves: (I) elimination of domain-specifee spurious couplings via feature recombination, and (2) preservation of causal fea- tures through consistent predictions.
4. Experiments
4.1. Experimental Settings
4.1.1. DATASETS
We investigate unsupervised graph domain adaptation lever- aging benchmark datasets, adopting both cross-dataset and dataset split scenarios for a thorough evaluation. For cross-dataset scenarios we achieve domain adaptation on PTC (Helma et al., 2001). PTC are inherently unbiased across sub-datasets. For dataset-split scenarios, previous works (Ding et al., 2018; Yin et al., 2022; Lu et al., 2023) to split the dataset by graph density. The dataset splitting experiments are performed on the TWITTER-Res Graph-Partin (Pan et al., 2015), NCII (Wale & Karypis, 2006) and Letter-Med (Riesen & Bunke, 2008), using their
Overall Optimization. In nutshell, the overall adaptation training objective is:
follow
L L= Lsup + Latis + niinn
(18)
where and 17 serve as hyperparameters to balance the contributions of the submodules, which is anlyzed in Sec- tion 4.6. Here, we first warm up our framework on source
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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
Table 1.
The classification results (in %) PTC (source->tageed
Methods
MR-MM
MM-MR
MR MR-FFM
FM FM-
MR -R-
FR -MR MM-FM FM-ME MM-FFR FR-MM FM-
FR-FFM Avg.
GIN
61.8
64.3
57.7
56.5
45.7
53.5
37.7
42.6
44.5
59.4
66.2
54.3
53.7
GCN
63.2
62.9
66.2
55.1
45.7
67.6
62.3
54.4
64.8
58.0
60.3
52.0
59.4
GAT
60.0
46.0
70.7
57.1
46.3
65.9
54.5
53.8
53.2
69.0
65.9
51.7
57.8
SAGE
58.8
55.1
67.6
56.5
47.4
66.2
48.1
48.2
45.1
58.0
63.2
52.6
55.6
Mean Teacher
61.8
61.4
73.2
60.9
52.9
50.7
65.2
44.1
35.1
66.7
55.9
42.9
55.9
InfoGraph
63.2
60.0
66.2
59.4
48.6
67.6
55.1
56.4
64.8
63.8
69.1
54.3
60.7
DANN
67.5
64.3
55.7
73.2
71.0
62.8
ToAlign
70.5
45.7
67.6
66.7
54.3
67.6
58.0
50.0
67.6
71.0
76.5
55.7
62.6
DUA
62.0
63.1
73.6
52.2
54.3
63.4
53.7
55.9
60.6
69.4
63.2
54.3
60.5
DARE-GRAM
61.8
54.3
73.3
53.6
55.7
66.2
56.4
54.1
39.4
69.6
66.2
55.7
60.5
CoCo
65.1
63.8
73.0
60.3
55.2
72.8
62.1
55.9
63.2
70.5
70.1
54.2
63.8
MTDF
65.9
64.8
76.9
61.2
56.0
73.9
62.6
56.8
69.0
71.1
71.6
56.0
65.5
Ours
71.1
65.7
74.6
55.4
71.8
66.7
70.4
78.3
76.6
67.8
Table 2. The classification results (in %) on NCT1 (source ttargtt). NO, N1, N2, and N3 are sub-datasets.
Methods
NO-NI
NO-N2
NO-N3
NI-N0
NI-N2
NI--3
N2-NO0
N2-NI
N2-N3
N3-+N0
N3-N1
N3-N2 Avg.
GIN
66.0
60.6
50.3
68.0
68.4
69.9
61.0
65.6
73.1
48.3
59.4
62.9
62.8
GCN
55.8
59.1
$4.0
73.3
65.0
70.7
73.5
60.7
70.2
67.8
54.5
55.1
63.3
GAT
63.4
60.0
41.7
70.1
73.2
56.3
60.5
62.7
54.9
55.8
50.1
74.5
59.7
71.7
70,6
57.2
64.8
63.4
Meun Teucher
54.9
45.2
51.6
73.8
72.8
47.1
InfoGraph
66.5
61.0
$7.6
62.7
64.6
67.1
69.9
60.7
50,2
DANN
67.5
ToAlign
65.5
61.7
47.1
73.3
68.0
59.2
63.1
64.9
DUA
60.7
58.5
56.1
50.5
66.5
DARE-GRAM
69.4
59.2
55.8
69.9
68.9
70.4
68.9
60.1
57.6
65.0
64.7
CoCo
70.9
68.7
70.0
68.5
71.2
59.6
$6,4
67.7
MTDEFF
67.5
70.9
71.8
76.7
65.0
73.1
77.2
62.5
74.3
75.9
61.0
$7.8
69.5
Ours
71.4
64.1
63.1
71.8
72.8
72.5
76.3
61.7
70.9
70.6
diverse nature evaluate our domain adaptation capability. The details and statistics of the datasets are provided in the Appendix C.I.
Ours
DANN
66-
4.1.2. BASELINES
54
We employ a wide range of state-of-the-art baselines: (1) Graph neural networks, including GCN (Welling Kipf, 2016), GIN (Xu et al., 2018), GAT (Veličković et al., 2018), and GraphSAGE (Hamilton et al., 2017). (2) Semi- supervised graph methods, including InfoGraph (Sun et al., 2020) and Mean- Tean-Teacher (Tarvainen & Valpola, 2017). (3) Domain adaptation methods, including ToAlign (Wei et al., 2021b), DANN (Ganin al., 2016), DUA (Mirza et al., 2022) and DARE-GRAM (Nejjar al., 2023). (4) Graph adaptation methods, including CoCo (Yin al., 2023) and MTDF (Tang et al., 2024), the latest state-of-the-ar the method for UGDA. More details are available in the Appendix C.2.
Infograph
Mea Teacher
250
500
750
1000
1250
1500
1750
2000
Adaptation Time Imolosochi
Figure 4. Scalability analysis on NCII. Circle radius indicates pa- rameter count. SLOGAN achieves best performance with minimal latency and parameters.
formed over 30 epochs. The loss weight, 7 and are set to 0.003 and 0.1, according to the sensitivity experiments. More details are available in the Appendix C.I.
4.1.3. IMPLEMENTATION INPLEMENTATION DETAILS
The baseline methods follow the same settings as the orig- inal papers. We use layer GCN encoder with hidden dimension of 128. We use Adam optimizer for 100 epochs source domain training with learning rate of 0.001 and batch size of 128. For the target domain, adaptation is per-
4.2. Performance Comparison
In this section, we compare SLOGAN with baselines, as shown in Table 1, and 2. The observations are as follows: (1) Our experiments demonstrate a notable advantage of do- main adaptation methods in most cases. This highlights the
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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
Table classification results (in %) on TWITTER- -ecEERRReal--ee Real-Graphh Parthal (source -ttrget)) TO, T1, T2, T3 are sub dat-satsssts.
Methods
TO yT1
TO
.T2
TO
YT3
T1
>TO
T1
>T2
T1
YT3
T2
>TO
T2
XTI
T2 >T3
T3
yTO
T3
,TI
T3
>T2
Avg.
GIN
59.7
62.8
60.4
64.2
62.2
61.3
61.7
63.2
61.0
62.3
61.8
62.4
61.9
GCN
62.0
62.9
59.7
64.1
63.4
59.8
64.2
62.8
60.5
62.7
61.4
62.7
62.2
GAT
60.6
63.2
60.0
63.1
61.6
59.8
63.5
61.6
59.5
63.4
62.1
63.7
61.9
SAGE
61.0
64.6
62.1
61.9
61.9
60.8
62.9
62.6
60.9
61.7
60.9
63.4
62.1
MeanTeacher
52.2
49.2
46.1
49.0
50.7
46.1
49.5
51.7
52.6
48.1
48.0
51.1
49.5
InfoGraph
63.9
65.1
61.6
65.6
65.0
59.2
64.3
63.3
60.8
63.3
62.4
63.3
63.2
DANN
58.4
60.0
58.0
59.0
59.4
57.4
57.7
58.1
58,4
58.2
$7.9
60.4
$8.6
ToAlign
58.6
59.5
55.5
57.7
58.1
56.3
57.8
$7.7
57.6
60.2
57.7
DUA
62.1
65.8
56.0
62.0
65.3
63.6
60.8
64.2
63.4
64.7
63.1
DARE-GRAM
61.7
65.7
65.7
64.4
62.1
64.0
64.9
64.2
64.3
63.6
66.1
62.1
64.0
64.6
61.6
64.5
62.1
62.8
62.5
63.5
63.5
MTDF
64.5
66.4
65.1
64.7
65.2
62.2
64.9
63.5
63.2
63.2
63.4
64,4
64.2
Ours
65.1
66.5
62.3
66.2
65.4
62.4
66.6
64.4
62.2
65.8
64.4
65.1
64.7
Table classification results (in %) on Letter- Med (source ttaget)) LO.
L22, and are sub-datasets.
Methods
10-+11
10-+1.2
1.0+1.3
L1-+L0
L1-112
L1-+1.
12-+10
1.2+1.1
1.2-1.3
1.3+1.0
1.3-111
1.3+1.2
Avg.
GIN
$4.0
54.0
47.8
31.0
48.7
46.0
38.1
58.4
19.5
26.5
51.3
41.6
GCN
57.2
59.3
59.6
43.4
51.9
51.9
40.4
54.3
51.9
45.1
34.5
60.8
50.9
GAT
79.6
71.7
67.3
61.9
75.2
76.1
55.8
78.8
75.2
54.0
69.9
70.8
69.7
SAGE
81.4
71.7
66.4
66.4
78.8
70.8
51.3
77.0
72.6
50.4
65.5
77.9
69.2
Teacher
70.8
73.5
58.4
62.8
76.1
57.5
38.1
75.2
51.3
54,0
54,0
56.6
60.7
InfoGraph
80.5
66.4
62.8
51.3
74.3
69.0
42.5
63.7
62.0
54.3
59.3
69.0
62.9
DANN
70.8
73.3
53.1
53.1
73,5
50.4
38.9
77.9
60.2
50.4
61.1
63.7
60.5
ThAlign
74.3
72.5
62.8
64.6
76.1
50.4
62.8
73.5
59.3
50.6
54.9
54,0
63.0
DUA
79.6
71.7
67.3
61.9
75.2
76.1
55.8
78.6
75.2
54.8
69.9
70.8
69.7
DARE-GRAM
81.4
71.7
66.4
66.4
78.8
70.8
$1.3
77.0
72.6
50.4
65.5
77.9
69.2
CoCo
76.5
70.3
68.8
68.3
80.2
72,8
55.3
77.6
75.3
59.5
68.1
79.2
71.0
MTDF
78.8
72.1
68.0
68.1
79.0
71.3
56.9
75.2
78.1
60.0
69.9
78.7
71.3
Ours
83.2
73.6
69.9
68.1
79.6
77.0
57.5
78.8
80.1
60.2
74.3
79.6
73.5
challenge of the UGDA task. (2) Semi-supervised methods, such as InfoGraph, generally outperform better. However, their relative underperformance in certain scenarios can be attributed a lack of specific mechanisms handle domain shifts. (3) UDA methods (e.g.. ... DANN) exhibit superior per- formance in unsupervised domain adaptation tasks (e.g., BM + B). However, their effectiveness is sometimes dimin- ished in graph data, especially when dealing with complex datasets. (4) SLOGAN shows significant improvements in dataset splitting and cross-dataset scenarios, standing out, especially in cases where other methods falter. The improvement in accuracy reaches up 2.3% across these datasets.
Source Target
Source
Target
(a) Spurious feature
(b) Causal feature
Figure 5. Visualization of causal and spurious features distin- guished by domains. Best viewed in color.
versely, causal features maintain a consistent distribution across both domains, underscoring their domain-agnostic nature. (2) Causal features are more aligned semantic labels. As shown in Figure 6, the causal features signifi- cantly partitioned according to positive and negative labels, illustrating their critical role in label prediction.
4.3. Scalability Analysis
As shown in Figure 4, SLOGAN shows superior efficiency and performance. It shows SLOGAN's potential for practi- cal applications where computational resources are limited.
4.5. Ablation Study
4.4. Visualization
Table 5 presents ablation study results the NCII dataset, detailing the model's performance without specific components. We find that each component: Disentangle- ment of causal and spurious features (Lais), unbiased dis- criminative learning using causal features (Ceup), invariant learning under intervention (Lin).. The absence any one
We use t-SNE to visualize causal and spurious features,
shown in Figure 5 and 6. We make the following observa- tions: (1) Causal features are domain-agnostic. As shown in Figure 5, spurious features exhibit a significant bifurcation, aligning with either the source or the target domain. Con-

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
Table 5. The Ablation Study classification results (in %) on NCT1 (source-ttarger NO, N1, N2, and N3 are sub-datasets.
Methods
NO-NN NI-NO NO-+N2 N2-NO NO-N3 N3-NN N1-N2 N2-NI NI NI- N3-N1 N2--33 N3-+N2 Avg.
Baseline
55,8
59.1
54.0
73.3
65.0
70.7
73.5
60.7
70.2
67.8
54.5
55.1
63.3
SLOGAN wo Coup
71.0
59.7
53.9
72.3
72.3
69.4
73.8
69.4
71.4
67.8
58.7
69.9
67.5
SLOGAN w/ Line
70.4
61.2
63.1
71.4
72.3
70.9
75.3
71.8
72.3
74.9
59.8
70.4
69.5
SLOGAN w/ Ldss
71.1
63.7
61.3
73.5
73,8
71.4
75.3
72.3
71.4
71.6
59.3
70.0
69.6
Ours
71.4
64.1
63.1
71.8
72.3
72.8
76.7
72.5
73.3
76.3
61.7
70.9
70.6
ics (Borgwardt et al., 2005), and cheminformatic (Hansen et al., 2015; Kojima et al., 2020; Gilmer et al., 2017). Mod- em GNNs employ pressage-passing mechanisms with hier- archical pooling operations (Lee et al., 2019b; Wang et al., 2024b) for graph classification.
Negative Positive
Negative Pasitive
Unsupervised domain adaptation (UDA) has become piv- otal approach for knowledge transfer from labeled source data to unlabeled target domains (Shi et al., 2022; He et al., 2022; Zhang et al., 2023; Pilancı & Vural, 2022), with ex- tensive applications. e.g., in computer vision (Long et al., 2018: Zou et al., 2018). The primary strategies in UDA in- clude domain alignment (Yan et al., 2017; Lee et al., 2019a) and self-learning (Wei et al., 2021a; Xiao & Zhang, 2021). Self-learning methods, enhanced by semi-supervised learn- ing techniques, aim to improve target domain performance through methods like pseudo-labeling (Sohn et al., 2020).
(a) Spurious feature
(b) Causal feature
Figure 6. Visualization of causal and spurious features distin-
guished by labels. Best viewed in color.
NCD
78
NCI1
Acpuracy (%6
75
Twitter
PTC
Accuracy (9))
75
Twitter
PTC
772
69
68
66
Graph Domain Adaptation (GDA) (Ju et al., 2024) remains under-explored compared to its Euclidean counterparts. While node-level adaptation has seen initial progress (Wu et al., 2020; Zhang et al., 202 1), graph-level adaptation faces unique challenges due to structural complexity and seman- tic richness (Zeng et al., 2024; Yin et al., 2023; Luo et al., 2024a). Existing approaches can be categorized into two main streams: (1) Global alignment methods (Dai et al., 2022; Shen al., 2020) that directly minimize domain dis- crepancy through adversarial learning, but risk discarding crucial substructures while preserving spurious correlations; (2) Self-training approaches (Wei et al., 2021a; Luo et al., 2024b) that leverage pseudo-labels for target domain super- vision, but suffer from error propagation and confirmation bias. These methods often struggle with feature entangle- ment between causal and spurious factors, leading to unsta- ble adaptation performance. SLOGAN tackles these limita- tions through a novel perspective of sparse causal discovery and generative intervention.
8.003
0.01
y Loss Weight
7 Loss Weight
Figure 7. Sensitivity analysis loss weight y and 17-
component leads decrease in accuracy, with the removal of Lais showing the most considerable impact, followed by Cop and fine- This shows the critical role each plays in the model's s overall effectiveness.
4.6. Sensitivity Analysis
We test loss weight 7 and 7, as shown in Figure 7. We varied y E {0.003, 0.01, 0.03, 0.33 and E (0.01, 0.03, 0.1, 0.3, 1]. indicate a marginal impact on the accuracy across different datasets. The results show that SLOGAN is robust to the hyper-parameters. The stability across a broad range of weights suggests that while the Loup and Linv components essential, their performances are robust to weight variations. We set 7 0.003 and 1 0.1 as the default value according to the experiments.
Causal Discovery & Disentanglement provides theoreti- cal foundation for stable representation learning (Arjovsky et al., 2019; Zhao et al., 2023; Wang et al., 2024a) and stable learning (Yu et al., 2023). Recent works in graph learning (Chen et al., 2022: Yang et al., 2023; Cheng et al., 2024) combine causal inference with graph neural architec- tures, while disentanglement methods (Zhou et al., 2023) aim to separate invaaiint factors. Our work ad-
5. Related Works
Graph classification (Ma et al., 2023; Jiang et al., 2023; Zhang et al., 2022) has emerged as fundamental task for structured data analysis with applications spanning social networks (Liu et al., 2021; Li et al., 2021), bioinformat-
8

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
vances this line by introducing sparse causal graphs and generative interventions specifically designed for graph- structured domain shifts. While IDEA (Wang et al., 2024a) applies causal disentanglement to image retrieval, SLOGAN uniquely addresses unsupervised graph domain adaptation through sparse causal modeling and a generative interven- tion based on cross-domain feature recombination.
arXiv: 2019.
Borgwardt, K. M., Ong. C. S., Schönauer, S., Vishwanathan, S., Smola, A. J., and Kriegel, H.-P. Protein function prediction via graph kernels. Bioinformatics, 2005.
Chen, Y., Zhang, Y., Yang. H., Ma. K. Xic. B.. Liu, T., Han, B., and Cheng. J. Invariance principle meets out- of-distribution generalization on graphs. arXiv preprint wwXiv:2202.0544/ 2022.
6. Conclusion
This paper addresses causal-spurious feature entanglement and global alignment collapse in unsupervised graph do- main adaptation. Our sparse causal modeling framework achieves stable knowledge transfer through innovations in causal graph construction, generative intervention mecha- nisms, and pseudo-label calibration. Extensive experiments demonstrate superior performance, with theoretical analysis proving our method's 's target error bound inversely corre- lates with causal feature retention. Future directions include theoretically quantifying intervention impacts, extending the framework to graph generation and temporal prediction, and exploring source-free graph domain adaptation, which has garnered increasing attention for its independence from source domain data.
Cheng, D., Li, J., Liu, L.,, Liu, J., and Le, D. Data- driven causal effect estimation based on graphical causal modelling: A survey. ACM Computing Surveys, 56(5); 1-37, 2024.
Chowdhury, J., Shivaraman, V., Sundaram, S., and Sujit, P. Graph-based prediction and planning policy network (gp3net) for scalable self-driving in dynamic environ- ments using deep reinforcement learning. In Proc. of Association for the Advancement of Artificial Intelligence (AAAI), volume 38. pp. 1600611614,, 2024.
Dai, Q.. Wu, X.-M,, Xiao, J., Shen, X., and Wang, D. Graph transfer learning via adversarial domain adaptation with graph convolution. 2022.
Impact Statement
Deng, W., Cui, Y., Liu, Z.., Kuang, G., Hu, D., Pietikäinen, M., and Liu, L. Informative class-conditioned feature alignment for unsupervised domain adaptation. In Proc. of ACM International Conference on Multimedia (MM), 2021.
This work advances unsupervised graph domain adaptation by addressing causal-spurious feature entanglement and alignment collapse through a novel sparse causal discovery framework. Our approach enables reliable knowledge trans- fer via causal graph construction, generative interventions, and pseudo-label calibration. We provide theoretical guaran- tees through target error bounds and demonstrate practical applications in molecular property prediction, social net- work analysis, and urban traffic modeling. By disentangling causal mechanisms from spurious correlations, our method enhances the reliability of graph learning systems in critical domains such as healthcare and autonomous systems.
Ding, M., Tang. J., and Zhang, J. Semi-supervised learning on graphs with generative adversarial nets. 2018.
Ganin, Y., Ustinova, E., Ajakan, H., Germain, P., Larochelle, H., Laviolette, F., Marchand, M., and Lempitsky, V. Domain-adversarial training of neural networks. Journal of Machine Learning Research, 2016.
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., and Dahl, G. E. Neural message passing for quantum chem- istry. In Proc. of International Conference Machine Learning (ICML), 2017.
Acknowledgment
This paper is partially supported by grants from the Na- tional Key Research and Development Program of China with Grant No. 2023YFC3341203 and the National Nat- ural Science Foundation of China (NSFC Grant Number 62276002). The authors are grateful to the anonymous re- viewers for their efforts and insightful suggestions to im- prove this article.
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Yan, H., Ding, Y., Li, P., Wang. Q., Xu, Y., and Zuo, W. Mind the class weight bias: Weighted maximum mean discrepancy for unsupervised domain adaptation. In Proc. of Computer Vision and Pattern Recognition (CVPR), 2017.
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Yin, N., Shen, L., Li, B., Wang, M., Luo, X., Chen, C., Luo, Z., and Hua, X.SS Deal: An unsupervised domain adaptive framework for graph-level classification. In Proc. of ACM International Conference on Multimedia (MM), 2022.
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adaptation via In Proc. of International Conference on Learning Repre- sentations (ICLR), 2022.
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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
A. Algorithm
The overall algorithm of SLOGAN summarized in Algorithm We use the structural causal model to disentangle causal factors and spurious factors, with the information bottleneck principle. For causal factors, we employ an unbiased pseudo-labeling for discriminative learning on the target domain. For spurious factors, utilize generative model for invariant learning to mitigate their influence.
Algorithm 1 Optimization Algorithm of SLOGAN
Input: Source dataset D target dataset D
Output: GNN-based classifier (-))
1: Pre-train (-) using D
2: for epoch = 1, 2, -.. do
3: for each batch do
4: Sample mini-batch 8 and B from Deo and D'o;
5:
Generate confident target graphs C
6: Generate reconstruction samples;
7: Calculate the loss objective using:
8: Update parameters of (-)) by back-propagation;
9: end for
10: end for
B. Proof of Target Domain Error Bound
Theorem B.1. (Generalization Bound) Under stable causal graph construction, assume the following conditions hold: (I) Causal Sufficiency: I(Y; Zo) > Le, where Z is the causal variable and Le is an information contraint. (2) Spurious Suppression: I(Y: -²) G1. where Z is the spurious variable. (3) Generative Intervention: E|IZ G(Z 2 12123 c2.
where G is the generation model. Then, for any predictor h E H. with probability at least 1 ō, the larget domain error (h) is bounded as follows:
eT(h) S (h) Cv + LLVE2 + C(ns,
(20)
where L is the lipschitz constant of the loss function, is a constant, and ng the sample size in the source domain. Here, (T) represents the error in the target domain, while (h) denotes the emprical error in the source domain.
Proof: For any H. the source and target domain errors are defined based on Z. along with its causal and spurious components Z and 2", which can be stated as follows,
(h) B ()), <g(h) E, ((()))",))) Y)),
(21)
cr (h) = B(zYyT [[(h()), Y),.
(h) = Ezzy)~ [(h(G(Z* Y)),
(22)
Since the loss function and the predictor h are assumed to be lipschitz continuous, the gap between (s(h) and (g(h) is bounded as,
lcs(h) (s))) E2, [I(M -(M((())))))(((( 22)), Y)I & 1 G S I
(23)
where the second inequality follows from the lipschitz continuity property, and the third follows from Jensen's 's inequality. Similarly, we have (er(h) (T)) S Lifez- Next, since I(Y; Z*) c1, the total variation distance between P(Y|Z*) and Z)) satisfies:
Zz (P' S E [DL (P(IZ))))))) - 5
(24)
Here, the inequality follows from Pinsker's 's inequality, implying that the dependency of Y on Z is suppressed to ((vG) Under the causal sufficiency condition [(; zn) > Ie. the variable Z informative for predicting Y. Assuming the causal mechanism stable across the source and target domains, the prediction based on 2o remains consistent. Hence, the primary
13

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
Table 6. Statistics of the datasets.
Datasets
Graphs Avg. Nodes Avg. Edges
PTC_FM
349
14.11
14.48
PTC_FI FR
351
14.56
15.00
PTC
PTC_MM
336
13.97
14.32
PTC_MR
344
14.29
14.69
NCII
4110
29.87
32.30
144033
4.03
4.98
Letter-Med
2250
4.67
3.21
discrepancy between source and target domain errors arises due to Z", leading to, (k) - (,) S CVe Combining this with inequality (equation 23), we obtain,
(T(h) S (1) LVEE (())) CVEi + LV S Ses(h) + CCVE + + 2L//22.
(25)
Following the proof in (Rosenfeld & Garg, 2023), can derive the statistical generalization bound, that is, with probability at least 1 - 6, the source domain error satisfies:
log(1/8)
cs(h) S (h(h) +
(26)
2ng
Thus, we conclude that the target domain error (r(h) is bounded as er(h) (ss(h) CVE, + IiVe C(ns:
C. Extra Experimental Details
C.1. Extra Dataset Details
Our study diverse of real-world datasets, encompassing areas from cheminformatics social networks, assess unsupervised graph domain adaptation method. We employ both dataset division and cross-dataset strategies for validation. Below is information on these datasets, and statistics of the datasets are shown in table 6:
Cross-dataset scenarios, which include PTC (Helma et al., 2001). The datasets are inherently unbiased across sub- datasets. We utilize their original splits as defined, ensuring a stringent test of our model's adaptahility across different domains. This setup aims to validate our approach's 's effectiveness handling variations inherent separate datasets, each representing unique challenges regarding chemical structures biological attributes.
Dataset-split scenarios, which contain NCII (Wale & Karypis. 2006), TWITTER-Reale -eaa--Ga (Pan et al., 2015) and Letter-Met Med (Riesen & Bunke, 2008) datasets. We follow previous works (Ding et al., 2018; Yin et al., 2022; Lu et al., 2023) to split the dataset by graph density, using their diverse nature to evaluate our domain adaptation capability, The datasets are divided into four subsets (e.g.. TO, T1, T2, and T3 for TWITTER-ReS SeaER-Rel--raphh (trapaParttial), organized by increasing levels of graph density. The split according density introduces domain shifts, providing framework for evaluating the effectiveness of our domain adaptation method.
Below is information on these datasets, and statistics of the datasets shown in table 6:
Predicative Toxicology Challenge (PTC) (Helma et al., 2001): Comprising chemicals for toxicology prediction, the PTC dataset contains compounds classified for carcinogenic potential in rodents. We categorize it into four groups: PTC_ _M (female mice), PTC FR (female rats), PTC MM (male mice), and PTC (male rats), each reflecting different domains based on the rodent's gender and species.
14

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Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation
NCTI (Wale& & Karypis, 2006): Central cheminformatics, the NCII dataset represents chemical compounds used in anti-cancer activity screening, especially for lung cancer. Graphs in NCI1 symbolize compounds, where nodes atoms, edges are chemical bonds, and node attributes indicate atom types through one-hot encoding. Based on edge density variation, we divide NCII into four subsets, NO, N1, N2, and N3.
TWITTER-Real Reaa--GraapPaariial (Pan et al., 2015): This dataset derives from Twitter for sentiment analysis, consisting of oweee-representative graphs. Here, nodes represent terms and emoticons, and edges signify their co-occurrence, We partition this dataset into TO, T1, T2, and T3, categorizing by edge density.
Letter-Med (Riesen Bunke, 2008): collection of images comprising handwritten letters and medical documents. In these images, nodes represent the endpoints of strokes, while edges correspond to the lines connecting them. The letters exhibit significant distortion, which introduces complexity to recognition. This dataset is primarily utilized for optical character recognition and handwriting recognition tasks within the medical domain.
C.2. Extra Baseline Details
In our study, we compare SLOGAN with an extensive selection of state-of-the-ar baselines, spanning a wide array of strategies within the domain:
GIN (Xu et al., 2018): GIN refines the Weisfeiler-Lehman graph isomorphism test to improve capture ability for complex graph topologies.
GCN (Welling Kipf, 2016): GCN leverages simplified spectral graph convolution technique to merge node features.
GAT (Veličković et al., 2018): GAT applies attention mechanisms fostering dynamic and locality-sensitive graph learning.
GraphSAGE (Hamilton et al., 2017): GraphSAGE innovatively samples and aggregates neighborhood features, effectively adapting unseen nodes post-training.
Mean-Teacher (Tarvainen & Valpola, 2017):
Employing student-teacher paradigm, this technique refines semi- supervised learning through prediction consistency, leveraging an ensemble of student models as the teacher.
InfoGraph (Sun al., 2020): Aiming to maximize mutual information across graph levels, InfoGraph generates potent graph representations under remi-supervised scheme.
DANN (Ganin al., 2016): DANN cultivates features that relevant the source task yet domain-agnostic, incorporating gradient reversal layer to align domain distributions.
ToAlign (Wei et al., 2021b): ToAlign applies task-oriented priors for structured feature decomposition and alignment, bridging source and target domain disparities with finesse.
DUA (Mirza et al., 2022): DUA leverages batch norm statistics to online oost-time target data adaptation.
DARE-GRAM (Nejjar et al., 2023): DARE-GRAM proposes to achieve cross-domain alignment with the inverse Gram matrix instead the original feature.
CoCo (Yin et al., 2023): CoCo contrast representation from different branch to improve the topology mining in the target domain, which is the latest state-of-the afethhr-rt method in unspervised graph domain adaptation.
15


Reviews:
[{"review_id": "cZd85n5ZeP", "reviewer": "Reviewer_FTCi", "summary": "This paper proposes SLOGAN, a framework for Unsupervised Graph Domain Adaptation that addresses two key challenges: the entanglement of causal and spurious features, and the failure of global alignment strategies in graph data. SLOGAN constructs a sparse causal graph using mutual information bottleneck principles to disentangle stable causal features from spurious ones. It introduces a generative intervention mechanism to suppress residual spurious correlations via cross-domain feature recombination and employs a category-adaptive calibration strategy to improve pseudo-label reliability in the target domain.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for your valuable feedback and thoughtful comments. We address each point below:\n\n---\n\n> Q1. While the paper thoroughly discusses prior work on UDA, GNNs, and causal representation learning, it overlooks several recent works that integrate causal inference with domain adaptation in structured data.\n\nThank you for your constructive suggestion. We will enhance our literature review to include recent works integrating causal inference with domain adaptation in structured data. [1] presents important contributions to invariant causal representation learning with exponential family distributions. In our revised manuscript, we will provide a discussion and add proper references of how our approach relates to and advances beyond these existing methods. The revised paragraph is as follows:\n```\nWhile [1] makes significant contributions to invariant causal representation learning for general out-of-distribution generalization, our work extends these principles specifically for graph-structured data by introducing sparse causal discovery mechanisms that capture the unique interplay between node features and graph topology, enhancing transfer capabilities across heterogeneous graph domains.\n```\n\n[1] Invariant causal representation learning for out-of-distribution generalization. ICLR 2021.\n\n\n> Q2. Although the paper reports significant improvements, it does not consistently report standard deviations.\n\nThanks for your constructive suggestion. We will add the standard deviation metrics for results. We have already conducted these measurements across 5 independent runs with different random seeds. The results for PTC, Letter-Med and NCI1 datasets are shown below.\n\n| Method | PTC | Letter-Med | NCI1 |\n|--------|-----|------------|------|\n| CoCo | 63.8±0.8 | 71.0±1.0 | 67.7±0.8 |\n| MTDF | 65.5±0.6 | 71.3±1.2 | 69.5±1.3 |\n| Ours | 67.8±0.6 | 73.5±1.0 | 70.6±0.9 |\n\n\n\n> Q3. The paper's writing occasionally suffers from dense technical jargon, which may hinder readability for a broader machine learning audience.\n\nWe appreciate your feedback. We will improve the manuscript's accessibility by focusing on two key areas:\n\n1. Clarifying complex technical concepts with intuitive explanations\n2. Adding illustrative examples for abstract mechanisms\n\nFor instance, in Section 3.4, we will revise the description of our generative intervention approach from:\n\"We design a generative model to reconstruct original graph representations with a cross-domain spurious feature exchange strategy. By perturbing local coupling of spurious features, this approach forces the model to rely solely on causal features for reconstruction, effectively suppressing spurious residuals.\"\n\nTo the more accessible:\n```\nOur method uses a targeted approach to ensure the model doesn't rely on misleading patterns. Consider the TWITTER dataset in our experiments: when classifying discussion topics in social networks, our method can distinguish between fundamental network structures (like community clusters and information flow patterns) and platform-specific features (like temporary trending hashtags or regional engagement patterns). It achieves this by deliberately exchanging these platform-specific features between different network samples while preserving the essential community structures, forcing the model to focus only on truly predictive patterns that work consistently across different social media environments.\n```\n\nThese revisions will maintain the paper's technical rigor while making it more accessible to readers from various machine learning backgrounds.\n\n---\n\nThank you again for your constructive comments, which will help us improve the quality of our paper.", "claims_and_evidence": "The paper provides both theoretical guarantees and empirical validation across six benchmark datasets. The improvements over strong baselines are consistent and often exceed 3%, with ablation studies demonstrating the necessity of each proposed component. However, one minor issue is that standard deviations are not consistently reported when improvements are marginal, which could better support claims of significance in those cases.", "methods_and_evaluation_criteria": "The use of sparse causal discovery and generative intervention directly targets the core challenges in UGDA making the methodology appropriate and novel for this setting. The evaluation is thorough and reflects real-world graph distribution shifts. Comparisons with a broad range of baseline methods, including graph neural networks, semi-supervised models, and domain adaptation techniques, further validate the relevance and robustness of the proposed framework.", "theoretical_claims": "The paper provides a theoretical result in Theorem 3.1, which presents a probabilistic bound on the target domain error under three stability conditions: sufficient mutual information between causal features and labels, suppression of mutual information between spurious features and labels, and low reconstruction error via a generative model. However, the proof is not included in the main body and is deferred to Appendix C.", "experimental_designs_or_analyses": "The authors conduct extensive evaluations across six benchmark datasets, using both cross-dataset and dataset-split settings to simulate realistic domain shifts.", "relation_to_broader_scientific_literature": "While previous UDA methods have focused on Euclidean data using global domain alignment techniques, SLOGAN addresses the unique challenges of graph-structured data, which involve complex topologies and high-dimensional sparsity.", "essential_references_not_discussed": "While the paper thoroughly discusses prior work on UDA, GNNs, and causal representation learning, it overlooks several recent works that integrate causal inference with domain adaptation in structured data.\n\n[1] Lu, Chaochao, et al. \"Invariant causal representation learning for out-of-distribution generalization.\" International Conference on Learning Representations. 2021.", "other_strengths_and_weaknesses": "1. Although the paper reports significant improvements, it does not consistently report standard deviations.\n\n2. The paper’s writing occasionally suffers from dense technical jargon, which may hinder readability for a broader machine learning audience.", "other_comments_or_suggestions": "NA", "questions_for_authors": "See weaknesses", "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": "VXsxWBTu52", "reviewer": "Reviewer_hucj", "summary": "This paper studies the unsupervised graph domain adaptation problem, which aims to transfer the knowledge learned on labelled data to the data in the target domain with significantly different distribution.\n\nThe motivation of the paper is that the existing works cannot obtain satisfying performance due to the entanglement of causal -spurious features and the failure of global alignment. \n\nThe proposed method, SLOGAN, aims to resolve the challenge by adopting the sparse causal modelling technique. This technique is mainly developed with the mutual information bottleneck constraints based on the constructed sparse causal graph. Beside, a generative intervention is also proposed to address the residual spurious correlations. Finally, the error accumulation in target domain pseudo-labels are addressed with a category adaptive dynamic calibration method.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful review and constructive feedback. We appreciate the opportunity to clarify these points and improve our paper.\n\n---\n\n> Q1. The code of the method has been released, but the model.py and main.py seems only contain graph neural networks, while the location of the code for the proposed method is unclear.\n\nWe thank the reviewer for pointing out the lack of clarity in our code organization. The proposed method SLOGAN is indeed implemented in the provided code, but we acknowledge that the current structure and variable naming could be improved for better readability.\n\nThe core components of our method can be found in the main.py file:\n\n- Causal Feature Extraction: Implemented in lines 28-34 with causal_loss function, which corresponds to our sparse causal modeling approach using contrastive objectives.\n\n- Spurious Feature Suppression: Implemented in lines 36-42 with non_causal_loss function, which implements our variational information bottleneck for separating domain-specific correlations.\n\n- Generative Intervention Mechanism: Implemented in lines 44-54 with the GraphGenerator class, which enables cross-domain feature recombination.\n\n- Information Bottleneck Disentanglement: Lines 204-224 in the training loop implement our causal-spurious feature disentanglement using mutual information constraints.\n\n- Generative Intervention Processing: Lines 224, where augemented views are generated by recombining causal and shuffled spurious features, with covariance constraints implemented as an MSE loss.\n\nTo improve clarity, we will:\n\n1. Reorganize our code to better align with the paper's methodology sections\n2. Rename variables to directly match terminology in the paper \n3. Add comprehensive comments explaining the implementation of each component\n4. Create separate modules for each key component (causal discovery, intervention mechanism, and confidence calibration)\n\nWe will update our repository with these improvements to facilitate understanding and reproducibility.\n\n> Q2. I would recommend the authors to also highlight the second best methods in the tables. Besides, the year of the baselines would also be helpful for checking whether the baselines are up-to-date.\n\nWe appreciate this valuable suggestion. In the revised version, we will:\n\n1. Highlight the second-best methods in all result tables (using underlined values or alternative formatting)\n2. Add publication years for all baseline methods to provide context on the recency of comparisons\n\nRegarding up-to-date baselines, we have already compared with recent state-of-the-art methods published in 2024, such as MTDF. In the revised version, we will also enrich the comparison with recent methods [1,2]. This will enhance table readability and allow readers to better assess our method's improvements relative to the most recent state-of-the-art approaches.\n\nMethod|MR→MM|MM→MR|MR→FM|FM→MR|PTC Avg\n---|---|---|---|---|---\nDEAL|64.5|63.4|73.2|59.9|63.3\nTO-UGDA|66.2|64.2|73.8|61.5|65.0\nOurs|71.1|65.7|74.6|66.8|67.8\n\n[1] TO-UGDA: target-oriented unsupervised graph domain adaptation. Scientific Reports, 2024.\n\n[2] Deal: An unsupervised domain adaptive framework for graph-level classification. ACM MM 2022.\n\n    \n> Q3. The graph domain generalization problem seems to be closely related to continual graph learning, which also aims to train a model over graphs with different distributions. I would recommend the authors to discuss the difference between these two research directions.\n\nThank you for highlighting this important connection. We agree that discussing the relationship between graph domain generalization and continual graph learning would strengthen our paper. We will add a dedicated paragraph with proper references in the related work section addressing this relationship:\n\n\"While graph domain generalization and continual graph learning both address distribution shifts in graph data, they differ in several key aspects. Continual graph learning focuses on sequential learning across multiple tasks without catastrophic forgetting, enabling models to adapt to new distributions while retaining performance on previously encountered ones. In contrast, graph domain generalization aims to learn domain-invariant representations that transfer directly to unseen target domains without adaptation. Our approach, SLOGAN, specifically addresses the latter by identifying stable causal mechanisms that generalize across domains rather than incrementally adapting to new distributions.\"\n\nWe believe this discussion will provide valuable context and clarify the positioning of our work within the broader landscape of graph learning research.\n\n---\n\nThank you again for your constructive comments, which will help improve our paper.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes", "experimental_designs_or_analyses": "Yes", "relation_to_broader_scientific_literature": "Domain adaptation of graph learning model will be useful for various application scenarios involving graph data.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Strengths:\n\n1. The adopted datasets are comprehensive, ranging from cheminformatics to social networks, therefore the applicability of the proposed method is evaluated over different scenarios.\n\n2. The proposed strategy to remove spurious correlation and discover the causal relationship for boosting the domain generalization performance, is promising and reasonable. The proposed method also outperforms the baselines in most tasks.\n \nWeakness:\n\n1. The code of the method has been released, but the model.py and main.py seems only contain graph neural networks, while the location of the code for the proposed method is unclear.", "other_comments_or_suggestions": "1. I would recommend the authors to also highlight the second best methods in the tables. Besides, the year of the baselines would also be helpful for checking whether the baselines are up-to-date.\n\n2. The graph domain generalization problem seems to be closely related to continual graph learning, which also aims to train a model over graphs with different distributions. I would recommend the authors to discuss the difference between these two research directions.", "questions_for_authors": "N/A", "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": "hlB1SbRySF", "reviewer": "Reviewer_HSdG", "summary": "The paper presents SLOGAN, a novel approach for transferring knowledge from a labeled source domain to an unlabeled target domain on graph data. The key innovation of SLOGAN lies in its three-component framework: sparse causal discovery, generative intervention mechanisms that break local spurious couplings; and category-adaptive dynamic calibration for stable pseudo-label learning. The authors provide theoretical guarantees for the optimization error bound and demonstrate SLOGAN's effectiveness on benchmark datasets, showing consistent improvements over existing UGDA methods.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the thorough assessment of our work and the constructive feedback. Below, we address each of the concerns raised.\n\n---\n\n> 1. Symbols in Eq. 16 not well-defined\n\nWe apologize for the lack of clarity in Eq. 16. This equation describes our generative intervention mechanism where we swap spurious features between samples from different domains. Specifically, $z^c_i$ represents the causal features from sample $i$, $z^s_k$ represents the spurious features from sample $k$ (from a different domain), $G$ is our generative model, and $z^+_{i,k}$ is the newly generated composite representation. We will improve the definition of these symbols in the revised manuscript.\n\n> 2. Insufficient discussion on Unbiased Discriminative Learning\n\nWe agree that this section deserves more explanation. In our approach, unbiased discriminative learning addresses two critical challenges:\n\n1. Class imbalance: Our category-adaptive confidence thresholds (Eq. 11-12) dynamically adjust selection criteria based on class-specific confidence distributions, preventing majority class dominance.\n\n2. Error propagation: By implementing cross-domain stability through both source supervision and target pseudo-labeling, we create a balanced optimization objective that mitigates the risk of error accumulation.\n\nWe will expand this discussion in the revised manuscript, further clarifying how these mechanisms ensure unbiased learning across domains.\n\n> 3. Articulation of contributions and module cohesion\n\nWe appreciate this feedback and will revise the manuscript to more clearly articulate our contributions. Specifically, we will emphasize how our three components form a unified framework:\n\n1. Sparse causal discovery identifies stable causal patterns while isolating spurious correlations\n2. Generative intervention breaks residual spurious couplings through cross-domain feature recombination\n3. Category-adaptive calibration ensures stable pseudo-label learning\n\nThese components work together synergistically: causal discovery provides the foundation, generative intervention strengthens it by eliminating remaining spurious correlations, and adaptive calibration ensures robust knowledge transfer.\n\n> 4. Experimental setup details\n\nWe agree that more detailed information would enhance reproducibility. In the revised manuscript, we will add a dedicated section specifying hardware (e.g., NVIDIA A100 GPU with 40GB memory) and training parameters (e.g., batch size, optimizer, learning rate, and training epochs).\n\n> 5. Discussion of theoretical aspects\n\nOur theoretical framework provides a principled foundation for SLOGAN through a probabilistic error bound directly connected to our three-component architecture. The bound shows that target domain error depends on three stability conditions: causal sufficiency (ensuring predictive information is preserved), spurious suppression (minimizing label-spurious correlations), and generative intervention fidelity (maintaining semantic consistency during feature recombination). The bound's dependence on $\\sqrt{\\epsilon}_1$ and $\\sqrt{\\epsilon}_2$ demonstrates why our unified approach outperforms single-strategy methods—optimal domain adaptation requires both preserving causal mechanisms and breaking spurious correlations simultaneously. This theoretical insight explains our empirical results where each component contributes to reducing a specific term in the overall error bound.\n\n> 6. Color visibility in Figure 4\n\nWe thank the reviewer for this practical suggestion. We will adjust the color scheme to improve visibility, specifically making the \"Ours\" indicator more distinct from other methods using a higher contrast color.\n\n> 7. Minor issues\n\nWe will address all minor issues in the revised manuscript, including correcting punctuation in Eq. 6, ensuring consistent labeling (SLOGAN vs. Ours) in Table 5, reformatting Algorithm 1 to appear on a single page, and adding a detailed description of the MTDF baseline in the appendix.\n\n---\n\nWe appreciate the reviewer's careful reading and thoughtful suggestions, which will significantly improve the quality of our final manuscript.", "claims_and_evidence": "Yes, all the claims made in the submission supported by clear and convincing evidence.", "methods_and_evaluation_criteria": "Yes, the methods and evaluation criteria make sense for the problem at hand.", "theoretical_claims": "The paper presents theoretical claims regarding optimization error bounds. The theoretical claims are generally well-formulated and grounded in established principles. The proofs are provided and seem sound, though a more detailed analysis of the theoretical section would be beneficial to fully verify all mathematical derivations.", "experimental_designs_or_analyses": "The authors evaluate SLOGAN on benchmark datasets covering diverse domains, with multiple source-target adaptation scenarios for each dataset. The ablation studies effectively isolate the contribution of each component, while the visualization experiments provide intuitive understanding of the feature disentanglement.", "relation_to_broader_scientific_literature": "The broader scientific literature on Graph classification, Unsupervised domain adaptation, Graph Domain Adaptation and Causal Discovery is well-established.", "essential_references_not_discussed": "The related papers are surveyed comprehensively.", "other_strengths_and_weaknesses": "Strengths:\n\n1. The framework integrates causal principles with graph adaptation in a novel way, providing a theoretically grounded approach to domain adaptation.\n2. The proposed SLOGAN offers a solution to the problem of feature entanglement between causal and spurious factors in graph domain adaptation.\n3. The category-adaptive calibration strategy addresses a common challenge in pseudo-labeling approaches.\n4. Comprehensive experimental evaluation with consistent performance improvements.\n\nWeaknesses:\n\n1. The symbols in Eq. 16 are not well-defined.\n2. The disscussion on Unbiased Discriminative Learning is insufficient.\n3. The authors could more clearly articulate their contributions and explain why the various modules form a unified whole.\n4. The experimental setup details are inadequate. For reproducibility purposes, the authors should provide specific information about their computational resources.\n5. While the authors provide theoretical guarantees and proofs, which is commendable, more discussion around these theoretical aspects is needed.\n6. In Figure 4, the color used to indicate \"Ours\" should be adjusted to make it more visible and distinguishable from other methods.", "other_comments_or_suggestions": "1. Eq. 6 contains punctuation issues that should be corrected for final revision.\n2. In Table 5, the method is inconsistently labeled as both \"SLOGAN\" and \"Ours\".\n3. Algorithm 1 should be adjusted to appear on a single page with the section for readability.\n4. The appendix lacks a detailed description of the MTDF baseline.", "questions_for_authors": "See above in Weaknesses.\nI may change my score based on the authors' responses regarding weaknesses.", "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": "k5BIHgHb0X", "reviewer": "Reviewer_CW2H", "summary": "This paper studies unsupervised graph domain adaptation from a causal perspective. The authors claim that existing methods fail to achieve optimal performance due to the entanglement of causal-spurious features. To address this issue, the authors proposed SLOGAN for graph classification domain adaptation by sparse causal modeling and dynamic intervention mechanisms. Specifically, mutual information bottleneck is utilized to construct a sparse causal graph structure, then a generative intervention mechanism is designed to break local spurious couplings. Experimental results on 5 public graph classification datasets demonstrate that the proposed model can outperform recent baselines with different gains.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the thorough review. Below, we address each of your concerns in detail.\n\n---\n\n> Q1. Should test more domain split perspectives\n\nThank you for this valuable suggestion. Our cross-dataset experiments (Tables 1, 3, 4, 6) incorporate natural shift, feature shift, and label shift between datasets (e.g., PTC). To directly address feature shift concerns, we conducted additional experiments on Letter-Med using clustering-based feature distributions to create domain shifts. Results demonstrate SLOGAN's robustness across varied shift scenarios. We will review the paper to include the setup and comprehensive discussion of this experiments.\n\nMethod|LF0→LF1|LF0→LF2|LF1→LF3|LF3→LF0|Avg\n---|---|---|---|---|---\nCoCo|79.9|75.6|69.8|61.3|71.7\nMTDF|80.4|75.3|70.2|61.9|72.0\nOurs|82.7|76.8|72.1|64.2|74.0\n\n> Q2. Should verify in synthetic experiments\n\nWe appreciate your suggestion. To complement evaluations, we implemented synthetic experiments following [3]. We constructed Erdös-Rényi graphs containing both causal factors (structural motifs consistent across domains) and spurious factors (domain-specific correlations). Our experimental design established two domains (D0 and D1). Analysis confirms that SLOGAN successfully conducts knowledge transfer based on causal factors. We will incorporate comprehensive details of this experiment in our revised manuscript.\n\nMethod|D0→D1|D1→D0|Avg\n---|---|---|---\nCoCo|74.2|73.7|74.0\nMTDF|74.3|74.0|74.2\nOurs w/o $L_{dis}$|76.8|76.0|76.4\nOurs|79.1|78.4|78.8\n\n\n> Q3. Should explain stability and robustness\n\nThanks for your comment. Our claims are supported by adaptation results (visualizations in Figure 5 and 6), ablation studies (Table 5), and theoretical guarantees (Section 3.5 on bounded target error).\n\nAdditionally, to directly address your question about robustness, we conducted additional experiments on Letter-Med by adding Gaussian noise (σ) to node features. Results show the robustness across noise levels. We will update the manuscript with these results.\n\nMethod|σ=0.1|σ=0.2|Avg\n---|---|---|---\nCoCo|67.5|64.4|66.0\nMTDF|67.8|64.2|66.0\nOurs|70.4|67.8|69.1\n\n> Q4. Question on performance improvement\n\nThanks for your comment. SLOGAN shows consistent improvements across all six datasets, with gains reaching 2.3% and 2.2% on challenging benchmarks. In graph learning, particularly in UDA settings where labeled target data is unavailable, such consistent improvements are considered significant. For context, recent work TO-UGDA [2], although achieving relatively limited improvements on some datasets (e.g., 0.5% over CoCo), is still recognized for its methodological contributions. Notably, our synthetic experiments (Q2) show even more substantial gains, with SLOGAN outperforming baselines by 4.6%. Our work's value lies in both the performance gains and the novel perspective for graph domain adaptation theory.\n\n\n> Q5. Should explain L_dis's effectiveness\n\nThanks for your comment. The effectiveness varies due to dataset characteristics, with greater benefits observed in datasets having cleaner feature distributions and more challenges under higher noise or complex feature correlations. This phenomenon aligns with our theoretical analysis, as disentanglement is inherently more effective when causal signals are more clearly. Our newly added synthetic experiments (Q2) also support this. Across synthetic and real-world datasets (in paper), $L_{dis}$ contributes meaningfully to overall performance (average 1.7%). We will enrich this discussion in the revised manuscript.\n\n> Q6. Should test various architectures\n\nThank you for this suggestion. We chose GCN as primary backbone for fair comparison with baselines. We have now conducted additional experiments as shown below. This confirms the architecture-agnostic nature of SLOGAN. We will revise accordingly.\n\nMethod|TWITTER|NCI1|Letter-Med|PTC\n---|---|---|---|---\nOurs(GCN)|64.7|70.6|73.5|67.8\nOurs(GAT)|64.5|70.4|75.6|66.4\nOurs(GIN)|64.4|70.4|70.3|65.9\n\n\n> Q7. Should enrich the comparison\n\nThank you for the constructive suggestion. We will add [1,2] into comparison and enrich the background section. The results on PTC are shown below, which shows SLOGAN's superiority.\n\nMethod|MR→MM|MM→MR|MR→FM|FM→MR|PTC Avg\n---|---|---|---|---|---\nDEAL|64.5|63.4|73.2|59.9|63.3\nCoCo|65.1|63.8|73.0|60.3|63.8\nTO-UGDA|66.2|64.2|73.8|61.5|65.0\nOurs|71.1|65.7|74.6|66.8|67.8\n\n> Q8. Undefined Term\n\nThe $L_{re}$ in Equation (17) refers to the reconstruction loss. This definition will be explicitly included in the revised manuscript.\n\n---\n\nWe sincerely appreciate your constructive feedback, which has helped us improve the clarity and comprehensiveness of our work.\n\n\n[1] Deal: An unsupervised domain adaptive framework for graph-level classification. ACM MM 2022.\n\n[2] TO-UGDA: target-oriented unsupervised graph domain adaptation. Scientific Reports 2024.\n\n[3] Nikolentzos, G., & Vazirgiannis, M. (2020). Random Walk Graph Neural Networks. NeurIPS 2020.", "claims_and_evidence": "The authors claim that they focus on sparse stability and dynamic robustness in unsupervised graph domain adaptation. However, there are no experimental results to support this claim. For instance, how stable and robust is the proposed model?", "methods_and_evaluation_criteria": "The authors fail to include synthetic graphs that are generated by causal factors and spurious factors. This could be a direct way to show the proposed model indeed could transfer among the causal factors.", "theoretical_claims": "I did not fully check the correctness of the proof in the appendix.", "experimental_designs_or_analyses": "The authors only use density to split the graphs to construct the domain discrepancies. However, lots of other perspectives are overlooked, i.e., feature shift, label shift. It is unclear whether the proposed model still can achieve satisfied performance under these settings.", "relation_to_broader_scientific_literature": "The key contribution combines causal discovery and graph domain adaptation. As we can see from the experimental results, the performance improvement is only marginal.", "essential_references_not_discussed": "The authors did not discuss and compare with the following paper:\n\n[1] Yin, Nan, et al. \"Deal: An unsupervised domain adaptive framework for graph-level classification.\" Proceedings of the 30th ACM International Conference on Multimedia. 2022.\n\n[2] Zeng Z, Xie J, Yang Z, et al. TO-UGDA: target-oriented unsupervised graph domain adaptation[J]. Scientific Reports, 2024, 14(1): 9165.", "other_strengths_and_weaknesses": "Pros:\n\n1.\tThis paper investigates unsupervised graph domain adaptation from a causal discovery perspective, which is less explored in the community.\n\n2.\tTheoretical analyses are given to prove the effectiveness of the proposed model.\n\n3.\tExperiments on different datasets and ablation studies are given verify the effectiveness of the proposed model.\n\nCons:\n\n1.\tThe authors fail to include synthetic graphs that are generated by causal factors and spurious factors. This could be a direct way to show the proposed model indeed could transfer among the causal factors. \n\n2.\tThe authors claim that they focus on sparse stability and dynamic robustness in unsupervised graph domain adaptation. However, there are no experimental results to support this claim. For instance, how stable and robust is the proposed model? \n\n3.\tAs we can see from the experimental results, the performance improvement is only marginal. For instance, the improvement is less than $2\\%$ in most datasets.\n\n4.\tAccording to ablation studies in table 5, sometimes $L_{dis}$ is useless and the authors did not explain why it fails in these situations.\n\n5.\tThe authors only verify the GCN architecture. It is not clear whether the proposed model also works in other architectures like GAT and GIN.\n\n6. The authors did not discuss and compare with the following papers:\n\n[1] Yin, Nan, et al. \"Deal: An unsupervised domain adaptive framework for graph-level classification.\" Proceedings of the 30th ACM International Conference on Multimedia. 2022.\n\n[2] Zeng Z, Xie J, Yang Z, et al. TO-UGDA: target-oriented unsupervised graph domain adaptation[J]. Scientific Reports, 2024, 14(1): 9165.", "other_comments_or_suggestions": "In Equation (17), it is not clear what is $L_{re}$, which is not defined in the paper.", "questions_for_authors": "Please refer to the weakness part above.", "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:

Meta-review: This paper examines the problem of unsupervised graph domain adaptation from a causal perspective. The authors claim that existing methods fail to achieve optimal performance due to the entanglement of causal-spurious features, and to address this issue, they proposed SLOGAN for graph classification domain adaptation by sparse causal modeling and dynamic intervention mechanisms. In particular, mutual information bottleneck is utilized to construct a sparse causal graph structure, and then a generative intervention mechanism is designed to break local spurious couplings. Experimental results on 5 public graph classification datasets demonstrate that the proposed model can outperform recent baselines with different gains. The proposed method is well motivated and nicely designed, supplemented with comprehensive experimental evaluation.
Decision: Accept (poster)