Meta-Learning for Graphs with Heterogeneous Node Attribute Spaces for Few-Shot Edge Predictions
Authors: Zhong Chuang
Yusuke Tanaka
Tomoharu Iwata
Venue: Accepted by TMLR ()

Abstract: Prediction of edges between nodes in graph data is useful for many applications, such as social network analysis and knowledge graph completion. Existing graph neural network-based approaches have achieved notable advancements, but encounter significant difficulty in building an effective model when there is an insufficient number of known edges in graphs. Although some meta-learning approaches were introduced to solve this problem, having an assumption that the nodes of training graphs and test graphs are in homogeneous attribute spaces, which limits the flexibility of applications. In this paper, we proposed a meta-learning method for edge prediction that can learn from graphs with nodes in heterogeneous attribute spaces. The proposed model consists of attribute-wise message-passing networks that transform information between connected nodes for each attribute, resulting in attribute-specific node embeddings. The node embeddings are obtained by calculating the mean of the attribute-specific node embeddings.The encoding operation can be repeated multiple times to capture complex patterns. The attribute-wise message-passing networks are shared across all graphs, allowing knowledge transfer between different graphs.The probabilities of edges are estimated by the Euclidian distance between node embeddings. Experimental results on 14 real-world data sets demonstrate that the proposed method outperforms existing methods in edge prediction problems with sparse edge information.

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Meta-Learning for Graphs with Heterogeneous Node Attribute Spaces for Few-Shot Edge Predictions
Zhong Chuang
blong.chuang.. Sttunng.yws@kssnaiiie
Division of Information Science Nara Institute of Science and Technology
Yusuke Tanaka
ysk. tanaka Antt. com
NTT Commanication Science Laboratories, Kyoto, Japan
Tomoharu Iwata
tomoharu. winttarr.iwtta.oommmmm wwwta.ggy@hha. att..c..pp
NTT Communication Science Laboratories, Kyoto, Japan
Reviewed OpenReview: https: fttps://openrevieet net/ pormoo id= XXXX
Abstract
Prediction of edges between nodes in graph data is useful for many applications, such as social network analysis and knowledge graph completion. Existing graph neural network- based approaches have achieved notable advancements, but encounter significant difficulty in building an elfective model when there is an insufficient number of known edges in graphs. Although some meta-learning approaches were introduced to solve this problem, having an assumption that the nodes of training graphs and test graphs are in homogencous tribute spaces, which limits the flexibility of applications. In this paper, we proposed meta-learning method for edge prediction that can learn from graphs with nodes in hetero- geneous attribute spaces. The proposed model consists of attribute-wise networks that transform information between connected nodes for each attribute, resulting in autribute-specife node embeddings. The node embeddings are obtained by calculating the mean the attribute-specific node embeddings. The encoding operation can be repeated multiple times to capture complex patterns. The attribute-wise message-pases passsng networks are shared across all graphs, allowing knowledge transfer between different graphs. The probabilitics of edges are estimated by the Euclidian distance between node embeddings. Experimental results on 14 real-world data sets demonstrate that the proposed method outperforms existing methods in edge prediction problems with sparse edge information.
pvessage-passing
Introduction
Many real-world data can be described by graphs, such as social networks, knowledge networks, and protein- protein interactions. The nodes of graphs represent individuals, and edges denote the relations or interactions between nodes. Among many graph-related research problems, edge prediction is an essential problem that attempts to estimate the probability of the edges between two nodes. For example, odge prediction has been proven useful in discovering new protein-protein interactions, which are costly for blindly checking all possible interactions. In social networking services, edge predictions used to search for users' potential friends and provide recommendations.
Despite the early similarity-based and likelihood--aseed approaches, graph neural network-based approaches have received significant attention for their high performance on edge prediction tasks. The recent examples of Graph Convolutional Networks (GCN) applications include social networks (Rozemberczki & Sarkar (2021) and knowledge graphs [Lu al. 20021). GCN obtains node embeddings containing the graph's topology and node attribute information. It transforms node attributes such usage statistics of the

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social network members, the belonging species of proteins, and bag-of-words of the articles-inte latent space and aggregates messages from neighboring nodes. The node embeddings are then used to predict edges based on similarities. Nonetheless, GCN requires a tremendous number of observed edges for training (Ding ct al. 2022 Guo et al.) 2021), making them inapplicable for many real-world applications, such as newly released services or when data collection is costly.
Some meta-learning approaches for graph convolutional networks have been used in previous works (Mandal et al. 2021 Huang & Zitnik, 2020) to solve the insufficient data issue. With the other accessible training graphs, these meta-learning approaches try to improve edge prediction performance even when there is sparse odge information from test graphs. However, these meta-learning approaches require all training and test graphs to share a common attribute space. This assumption limits the models' ability to learn from diverse graphs, potentially missing valuable insights from graphs with nodes in heterogeneous spaces. Additionally, if the node attributes of the test graphs are unknown, these methods become inapplicable as it is impossible to collect training data.
This research aims to propose meta-learning model that can eliminate the limitation of node attribute spaces and achieve better performance in few-shot graph edge prediction problems. To fulfill this objective, we propose Heterogencous Graph Meta-Learning (HGML), which can learn from graphs with nodes in heterogeneous attribute spaces and improve edge prediction performance on unseen graphs with sparse edge information.
HGML comprises multiple layers of aatribute-wiss message-passinggg networks with average pooling. Attribute- wise wessage-passingg networks transform information from connecting nodes for each attribute to obtain attribute-specific node emboddings. The attributo-wisc messago-passiingg operation captures information from neighboring nodes and transforms graphs into a common latent space, accommodating graphs with heterogeneous node attributes. Since attribute-wise message-passing does not account for relationships between node attributes, we derive the node embeddings from the attribute-specific node embeddings using average pooling. The average pooling allows the inclusion all attribute-wise information nodes regardless of the number of attributes. By performing these two steps alternately, the node embeddings can include information from further nodes. The attribute-wise message-passee passing networks are shared for all graphs so the model can learn the common knowledge across different graphs. Unlike iterative updating procedures required in gradient-based meta-learning methods, such as model-agnostic meta-learning (Finn el al. 2017) or other macoder-decoder style meta-learning methods, such as neural processes (Garnelo et al. (0188)), which adapt to various tasks by only optimizing the parameters of neural networks using large training datasets, HGML can directly predict on new input graphs without local adaptations. We predict edge probabilities by Fuclidean distances between node embeddings. The model parameters are trained by minimizing the expected test edge prediction loss across graphs with sparse edge information. The contributions of this rescarch are summarized as follows:
We propose a graph neural network-based model where the parameters can be shared among graphs with nodes in heterogeneous attribute spaces.
We propose a meta-learning framework using our model to improve edge prediction performance with sparse edge information by learning from various graphs without bilevel gradient-based optimization.
We experimentally demonstrate that HGML outperforms existing meta-learning methods for edge prediction using 14 real-world graphs with nodes in heterogencous spaces.
This paper is organized as follows: Chapter 2 reviews previous research the edge prediction problem of graphs and existing approaches, including graph convolutional networks, and meta-learning on graph convolutional networks. Chapter 3 introduces the proposed method, including the problem sctting, the graph convolutional network-based model, and the mela-learning algorithm. Chapler 4 explains the details of the experimental setup, such as the dataset, comparison benchmarks, and the setup of training parameters. Chapter 5 presents the experimental results and discusses the effectiveness of the proposed method. Chapter concludes with the contributions and limitations of this research and discusses potential model extensions for future works.
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2 Related work
For edge prediction, many machine learning-based methods have been proposed. Started from graph con- volutional networks (Kipf & Welling 2017), the message passing-bar base methods have received significant rosults (Hamilton et al. 2018). These methods used in various applications, which include the knowl-
edge graph completion Ye et al.
2022 and the discovery of protein-protein interactions (Zhou et al. 2022
However, these message-passsngg -aased based approaches require a lot of edge information for training.
Some meta-learning approaches have been proposed to solve the issue of lacking training data. For instance, by splitting the training graphs into many subgraphs, the model can learn to predict new graphs with a few edges by subgraph sampled from the original graph (Huang & Zitnik 2020). Another approach is to perform model-agnostic meta-learning (Finn et al., 2017) on graph variational networks with an additional graph signature component for faster adaptation on graphs with small number of edges (Bose et al. 2020 However, these approaches can not handle graphs in heterogeneous attribute spaces the inputs.
A method for learning graphs in heterogencous attribute spaces has been proposed (Hassani 2022; where altributes in different graphs are padded to a fixed dimension. However, this method is only applicable when attributes of all training and test graphs are known at the meta-training phase. On the other hand, the proposed method in this paper can prodict the odges of unseen graphs that are not provided at the meta-training phase.
To extend the fiexibility of GNNs, the multi-domain generalized graph meta-learning (Lin et al. 2023 can be trained with graphs in heterogencous attribute spaces and make predictions on graphs in unknown attribute spaces. However, the bilevel optimization for the task-wise neural networks and prediction model makes it computationally expensive and hard to train. In contrast to MAML.-like meta-learning approaches, which learn initial meta-paramees for local adaptation, another meta-learnin approach based on encoder- decoder architectures (Garnelo et al.] 2018a) uses neural networks to encode data, enabling the prediction of new test tasks by meta-learning single set of parameters across diverse input graphs without requiring bilevel optimization. This kind of meta-learning approach optimizes the neural network to approximate the effect of fine-tuning. Although encoder-decoder meta-learning methods for tabular data have been proposed [wata & Kumagai 2020 they are not applicable for edge prediction in graph data.
Another solution is transfer lcarning(or domain adaptation), by learning the relationship between the source and larget domain, the model can learn to predict on test graphs even when few edges are available (Zheng) lt al., 2023; Mallick et al., 2020p. However, these approaches can only be applied to a pair of training and test graphs, and both the training and test graphs have to be available during the training phase. Different from the transfer learning approaches, we propose model that can learn from multiple training graphs and make predictions on multiple test graphs even when they are not available for training.
3 Method
3.1
Problem formulation
We illustrate the meta-learning process from graphs in heterogeneous attribute spaces in Figure 1 In the training phase, given multiple original graphs with nodes in heterogeneous attribute spaces G = (Gu) where 93 (X,, Ag) is the dth graph with Na nodes and Ta attributes. For any two original graphs Ga and GR, their attribute spaces and sizes may be different, Ia o Iar and their node sizes may be different Na & No. Although we assume undirected graphs for simplicity, the proposed method is straightforwardly applicable to directed graphs.
For each training step, the model is trained by the training graphs (G,)T_,, which are formed by sampling nodes and the corresponding edges from G. G, = (X,, At) have N₂ nodes and I, altributes, where X, e NiX,, is the attribute matrix, in which the rows represent the nodes, and the columns indicate the node attributes. A, E (0, 1] M.NN is the adjacency matrix where the rows and columns represent the nodes. A value of one indicates the presence of an edge between two nodes, while zero indicates the absence of an edge. For simplicity, we will ignore the subscript & in the following. In the test phase, test graph G* (X","7
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Training stage
Training
Test stage
Original graphs training
Training graph
Test graph with few edges
Sampling
f1
9
Support
Query edges
edges
22
Trained model
Node embeddings
Edge prediction
Go
Model
Loss
Edge probabilities
Backpropagation
Figure The mela-learning process of HGML.
with sparse edge information is given, where G* is different from any Ga and its node attributes differ from those in all training graphs. This research aims to predict the probability of edges in the test graph.
3.2
Model
HGML predicts the probability of edges between nodes from attribute matrix X and adjacency matrix A with nodes and / attributes. In the training phase, X and A are generated by sampling a subgraph from training graphs. In the test phase, they correspond to X and A of a test graph.
We demonstrate HGML Figure HGML implemented by repeatedly passing graphs into attributo-wiss cessage-passingg networks along with average pooling. With the attribute wise message- pesooppsssinggg networks and average pooling, we can obtain node embeddings containing node attributes and graph structure information, enabling HGML to learn graphs' common knowledge even when attribute spaces differ. The attribute- wise pussage-passing networks can be performed multiple times to learn from further neighbors. After transforming the node embeddings into a common space, we calculate the probability of edges using the final node embeddings.
3.2.1 Attribute-wise message- sassagg-ppssing networks
The attribute-specific node embedding of the nth node's ith attribute at the εth encoding layer vf. is calculated using the ith attribute values of the nth node and its neighboring nodes. Starting from the second layer, instead of the attribute values, we input the concatenation vector of attribute-specific node embeddings and node embeddings from the previous layer to the attribule-wise message- pasaagg networks.
EmErs f(lems)
for ==1
v.
(1)
nz
Will EmEN, fl 2 for l = L,
where Tmi E R. the ith attribute of the nth node, : K e 1), R (for E 2 2) are Feed-forward Neural Networks (FNNs), K is the output channel of PNNs at εth layer, Nr, is the index set of the neighboring nodes and wth node itself, |-1 indicates the element count in the set, [ is the concatenate operation, L is the numbers of encoding layers, and - is the node embedding of the nth node in the previous layer, which is calculated by taking the mean across attributes:
z
(2)
ni
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Z
Average pooling
V12
f 2,
Attribute-wise message passing network
Concatenation
z
Z
Node embeddings
z
Average pooling
Attribute-specffic node embeddings
Vin
Vi2
V21
22
V41
Vi2
t=1
V31
V32
(a)
Attribute- wisbb message passing network
X
X22
X11
X12
Node2
Attributes
X41
X42
Nodel
Attributed
X31
Attribute
Node4
Node3
Figure 2: attribute-wise cessago-passing networks' forward passing in HGML. The attributo-wisc message- passing networks can perform message- passigg regardless of the number of attributes, and the average pooling operation aggregates the relationships between these attributes.
For t= 1, Eq. represents the sum of transformed mossages from the neighbors and the second term accounts for the node's self-message. Eq. (1) based on message- message-passing networks (Kipl Welling 2017). However, unlike the existing networks, the attribute-wise message-passing networks can learn from graphs with various numbers of attributes with shared neural network due the attributo-wised operation. The average operation across sttribule-specific node embeddings the relationship between attributes regardless of the number of attributes but makes HGML permutation invariant network (Zaheer et al. 2017). which ensures that the model performs invariant even when node attributes are permuted.
Eq. 2 not only allows the model to learn
3.2.2 Edge prediction
The probability of edge existence between the nth and the mth nodes is represented as å,m, which can be estimated by the Euclidian distance between node embeddings:
@nm X, A, 4)) exp(- 1|. zm 1²,
(3)
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where & represents the parameter set of the neural networks: f for é = 1.2...., Zn and Zm are node embeddings, and ||. indicates the L.2 norm. We use the norm operation to evaluate the Euclidean distance between two node embeddings. The closer the node embeddings are, the higher the probability that an edge exists between them. The edge probabilitics are constrained to be between zero and one due to the negative exponent.
3.3 Meta-learning
We train the model by maximizing the following smoothed area under the ROC curve (AUC) (Hanley & McNeil 1
X(A) = 9A A
1
Σ A. "",m'EA"
Σ
o(-1lzn zml1² + I|zn' Zm 112)
(4)
where A is an adjacency matrix with support edges that are used to obtain node embeddings, A 9 is adjacency matrix with query edges that are different from support edges and used to calculate the modol's ovaluation loss, A indicate the node pairs with edges linked in A A are the negative samples, representing node pairs without edges linked A By maximizing Eq. 4 we make the distances bet ween nodes with linked edges close zero, when pulling the unlinked nodes as far as possible.
Numerous objective functions, such as binary cross-cntropy other pair-wised loss functions Zhu et al. 2022), are commonly used to optimize classification models. However, it has been shown that objective functions designed to minimize misclassification error may not necessarily maximize the AUC score (Cortes & Mohri 2003). Similar to the previous work [Iwata & Yamanaka 2019), which applicd the smoothed AUC ROC score as the objective function for an imbalanced classification problem. Consequently, we estimate the model parameters + with original graphs Ga by following expected test edge prediction smoothed AUC:
argmax Ea-nlEg- "AA
(5)
where Eg-D is the expectation over all original graphs, Eg is the expectation over all sampled training graphs and Ex--g is the expectation for edges in A The expectation is calculated by Monte Carlo sampling, We illustrate the proposed meta-learning model as Algorithm D In line 2, we reset the loss and its gradient as the beginning of an epoch. In lines 4-5, we randomly pick one of the original graphs Gd. uniformly random sample N nodes, and attributes for a training graph g = A). We sample the subgraphs with replacement and the order of the sampled attributes randomly shuffled. The isolated nodes of the subgraphs are removed. In line 6, we randomly split the edges in 9 with support edge ratio r to generate support adjacency matrix A and query adjacency matrix A In line 7, we input (X, into HGML's forward pass as described in Figuire for estimating edge probabilities {ánm ) mm.==1 In line 8, we calculate the loss with Eq. [ and add it to loss L. We repeat lines 3-9 for accumulating the loss and its gradient to L as a batch. In line 10 we update the model parameters with learning rate 7/
Although we did not impose specific conditions on the input graphs, we assumed an underlying common feature distribution across them. The proposed meta-learning algorithm in HGML enables the model meta-learn these common patterns from the input graphs.
4 Experimental Evaluation
4.1 Datasets
We evaluated our model with 14 real-world original graphs from 12 datasets: Amazon, Blogcatalog, Cora, CiteSeer, Coauthor, DeezerEurope, DBLP, Facebook, PubMed, Reddit, Twitch, and WikiCS.
Amazon (Shchur et al. 2018) includes two segments the Amazon co co-purchase graphs, where the nodes represent goods, the odges indicate that two goods are frequently bought together, and the node attributes are bag-of-worda encoded product reviews. This dataset has two independent graphs representing two categories of products: computers and photos.

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Algorithm 1 Training procedure of proposed model: Subgraph(G, N, randomly sample subgraph of N nodes and I attributes. RandomSplit(A,, (A, generate support and query adjacency matrix A A by randomly splitting edges from A with support edge ratio
Input: original graphs {9a]a-n. with batch size B, sample size N, number of sample attributes 4, and sampling rate of support adjacency matrix r, learning rate y
Output:
Trained model parameters
2: Initialize loss, L + 0.
3: for ..., B do Select graph from {1, 2,.,..., D}.
Sample training graph t Subgraphi (9d, N) Sample support adjacency matrix A A Random Split(,,tttt
Predict the edge probabilities {ānm IN n=m=1 by imput. X, A* described in Section 3.2
8: Calculate loss by Eq. 44 f - - JAA
9:
end for
10: Update model parameters + with loss C and its gradient with learning rate Ty
11: end while
BlogCatalog (Yang et. al. 2020) is a blogger-blogger interaction social network, where the nodes represent users and the edges represent friendship relationships. The node attributes are bag-of-wordss vectors con- taining the keywords of user profiles.
Cora McCallum et al. 2000) is citation network for scientific publications. The nodes are publications, and the edges represent their reference relationship. Each node is attributed by 0/1-valued word vector indicating the absence/presenn of the corresponding word from the dictionary. The dictionary consists of 1,433 unique words.
CiteSeer (Giles et al. 1998) is a citation network for scientific publications. The nodes represent the sci- entific publications, and the edges indicate the citation relationships between these publications. The node attributes are 0/1- 0/1-valued word vectors, indicating the absence or presence of the corresponding word from the dictionary, which consists of 3,703 unique words.
Coauthor (Shchur et al. 2018) are two co-author networks based on the Microsoft Academic Graph. Nodes are authors, edges represent the co-authorship of papers, and node attributes are 0/1-valued word vectors reprosenting the keywords for each paper. It includes two graphs from different rescarch fields: Physics and Computer Sciences (CS).
Durzer (Rozemberezki & Sarkar 2020) is a social network source from the music streaming service: Deezer. The nodes represent users, and the edges the friendships between users. The node attributes are the features associated with users, which can be derived from their activities and preferences.
DBLP Pan et al. 2016) is a citation network of papers in the computer sciences. The nodes represent the research papers, and the edges indicate the citation relationships between these papers. The node attributes are wordds representations of the papers' contents.
Faccbook (Rozemberezki ct al. 2021 is a network of Facebook pages where nodes correspond pages and edges correspond to mutual likes between these pages. The 128 numerical node attributes include 100-dimensional word embedding summarizing the page's textual content, relaved information, engagement metrics, and metadata.
Reddit (Hamilion et al. 2017) is a post-to-post graph dataset from Reddit posts made in September 2014. The nodes stand for posts and the edges exist if a user comments on both posts. For each post, two 300- dimensional GloVe CommonCravi word vectors (Pennington et al.] (2014) are used represent the average word embeddings of the post title and the post's comments. Adding on the post's score and the number of comments made, there 602 attributes in total.

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Table 1: Statistics of the graph datasets.
Graph
Network type
Attribute type
# NNodes
#Edges
# #Attr.
AmszonComputers
Co-purchase Social network
Bag-of-words
13,471
491,722
500
Blogcatalog
Bag-of-worde.
5196
343,486
500
A AmazonPhoto
Co-purchase
Bag-of-words
7,535
238,162
500
DBLP
Paper reference
Bag-of-wordh.
17,716
105,734
500
Coauthor CS
Corauth
Bag-of-words
18,333
163,788
500
Coauthor Physics
Co-authorship
Bag-of-wort
19,661
170,862
500
Europe
Social network
Numerical
28,281
185,504
128
Facebook
Pages-likes- likei--agesss
Numerical
22,470
341,646
128
CiteSeer
Paper reference
Bag-of-words
3,279
9,104
500
Cora
Paper reference
Bag-of-words
2,708
10,556
500
PubMed
Paper reference
Bag-of-wordh
19,717
88,648
500
Reddit
Post-to-post
Word embeddings
26,936
1,655,412
500
Twitch
Social network
Numerical
7,126
70,648
128
WikiCS
Page reference
Word embeddings
11,364
431,206
300
Twitch (Rozemberezki & Sarkar 2021 is a user-user network connected by mutual friendships, and attributes of games like, location, and streaming habits are included.
WikiCS (Mernyei & Cangea, 2020 an articles network derived from Wikipedia, where the nodes represent Wikipedia articles, and the edges represent hyperlinks between articles. The node attributes are multi- dimensional feature vectors that encapsulate the textual content of Wikipedia articles.
We uniformly sampled 30,000 nodes randomly for both the Reddit and CoauthorPhyyse datasets. To avoid sparse attributes, we only used the top 500 frequency words for bag-of-words for AmazonComputers Ama- Photo, Blogcatalog, DBLP, CoauthorCS, CoauthorPlysics CiteSeer, Cora, and Reddit. We normalized all attributes the range from zero to one. All graphs' edges were considered be undirocted. The statistics of these original graphs are listed in Table
4.2 Task
We randomly selected four original graphs, which were not used for training or validation, and sampled 100 subgraphs as test graphs. Each test graph was created by uniformly sampling 500 nodes and 70 attributes from the original graphs. For each sampling iteration, we replaced the sampled nodes and attributes, allowing the nodes and attributes repeat across test graphs. We randomly shuffled the order of attributes in the sampled test graphs to climinate any ordering information. The statisties of the sampled subgraphs are listed in Table 2
A portion of the graph edges is designated as known support edges, while the remaining edges are treated as query edges. The objective of the experiment is to predict the query edges in the test graphs by applying meta-learning on the remaining original graphs. We validated HGML and the baseline methods using three different support edge ratios (0.3, 0.5, 0.7) for various edge density situations.
4.3 Experimental Setup
We sampled subgraphs as training graphs to increase graph diversity, including variations in topological properties and combinations (or orders) of node attributes. The model can also be trained without sampling, but in that case, the training graphs would need to inherently exhibit diverse topological properties and node 70 from
attributes. We generated training graphs with the number nodes N 500 and attributes eight original graphs, which are not used for creating test graphs. The generation of training graphs is the that of the test graphs, the statistics of the sampled subgraph refer to Table 2 well.
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Table 2: Statistics of the sampled subgraphs. The reported values represent the mean and standard deviation derived from 100 sampling iterations.
Graph
#Nodes
#Edges
# Attr
AmazonComputerr
281.40=17.46
349.90160.90
70
AmazonPhoto
345.50=16.40
521.53++72.77
70
Blogcatalog
484.37 + 3.67
1,573.70 + 97.85
70
DBLP
69.27
42.77:17.69
70
CoauthorCS
98.13:112.77
60.37+10.09
70
CoauthorPhysice
86.60=11.91
52.33+7.84
70
DeezerEurope
54.43=111.14
30.87+7.05
70
Facebook
113.53+13.49
86.13+11.91
70
CiteSeer
164.00
108.03=13.21
70
Cora
234.93
199.27
70
PubMed
50.43++10.39
29.67+66888
70
Reddit
15..25
282.67+55..3
70
Twitch
182.17:166.6
177.33+44.500
70
WikiCS
423.37163.36
70
Three-layered feed-forward neural nerworks are used to J The model encoder layer L set to three, and the number of hidden units and output channels K are set to 64 for all l. Rectified linear units, (eLU(z)= x)), are applied as activation. Optimization is performed using Adam (Kingma & Ba 2015), with learning rate y 10-3 and dropout rate 10-1 We train the model for 30,000 epochs. The batch size B is set to 50.
The validation graphs were used for early stopping. We sampled 100 validation graphs from two original graphs with the same method as creating the test graphs. The original graphs used to create the validation graphs are not used for generating testing or training graphs. We evaluated the model performance using the area under the ROC curve (AUC) (Hanley & McNeil, 1982) by calculating the mcan score across all test graphs. The selection of original graphs for generating training, validation, and lest graphs was redone each time. We ran 10 experiments for each setting and took the mean results. The experiments were implemented with Pytorch (Paszke et al. (017)) in Python 3.11.3 and conducted on a computer with Xcon Platinum 8180 2.5GHz CPU, Nvidia Volta100, and 384GB memory, rumning the 64-bit Ubuntu 22.04.1 LTS.
4.4 Comparative methods
We compared HGML with five baseline methods. For the meta-learning method, We combined DeepSets ZZa- heer ct al. 2017) and GCN (DSGCN), and MAMLGCN. MAMLGCN is a single method that applics model- agnostic meta-learning (MAML) to GCN. We used standard GCN as the prediction model and optimized the meta-parameters through a few task-specific local adaptations, following the original MAML. approach. Because MAMLGCN is a meta-learning model that can not work on graphs with nodes in heterogeneous attribute spaces, We trained MAMLGCN without using node attributes. For non non-meta-learning comparative methods, Neural Networks (NN), GCN, and Graph ATtention networks (GAT) (Veličković al. 2018 were trained for each test graph only with the support edges. We did not implement the finc-tuned version of the comparative methods because the previous work (Iwata & Kumagai| 2020)) similarly encodes attribute- specific information into a latent space and decodes it into prediction values. Their results demonstrated that this encoder-decoder meta-learning approach can outperform existing approaches that rely on fine-tuning.
For all neural network-based benchmark approaches, we set the number of hidden units and output channels to 64, the dropout rate to 10-1, and used rectified linear units, ReLU(z) = max(0, æ), as activation function. The edge probabilities between any node pair fn. m) for the comparative methods are estimated using the inner product of the node embeddings. DSGCN contains two neural network components: the feature extractor and GCN. First, we input the node attribute vectors into the feature extractor to convert. the
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Table 3: Performance HGML and the comparable methods under different support edge rates r. Bold text indicates the highest mean AUC scores. The asterisk (*) denotes results significantly higher than all other comparative methods, as determined by paired t-test with a p-value of less than 0.05.
Model
r -= 0.3
7 0.5
r 0.7
HGML
0.633-10.031
0.687
0.719=10.050
DSGCN
0.519=0.019
0.526=00058
0,584+0.033.
MAMLGCN
0.492=0.044
0.008
0.620:0.015
NN
0.590=0.013
0.593=0.010
0.605=10.016
GCN
0.604=000017
0.603+00.023
0.637+00.027
GAT
0.617=0.022
0.618=0.028
0.652+0.027
attributes to a latent space x', = Ei are FNN with three hidden layers. Then, we input the converted attributes and the adjacency matrix into the GCN to obtain the node embeddings. We trained DSGCN for 30,000 epochs with the lcarming rale 10-3, and the parameters were updated every batch for 50 training graphs. The training graphs are resampled every epoch. MAMLGCN is comprised of two graph convolutional layers and three linear output layers. We trained MAMLGGN without using node attributes because MAML. can not deal with attributes in heterogeneous spaces. Unlike HGML and DSGCN, we trained the MAMLGCN with 50 training graphs without resampling every epoch. We set the local adaptation steps to 10, the learning rate 10-3 for the local adaptation, and the learning rate 10-3 for meta-parameteer optimization. We trained MAMLGCN for 500 epochs. NN contained a five-layer FNN and trained for 500 epochs with the learning rate 10-3 on cach meta-lest graph. GCN is comprised of two graph convolutional layers and three linear output layers. It trained for 500 epochs with the learning rate 10-3 each meta-test graph. GAT is an extension approach of GCN, which implements the attention mechanism on message-passing operations. We trained GAT on each test graph for 500 epochs with the learning rate 10-3
is the ith attribute of the nth node, and g.
5 Results
5.1 Performance
Table 3 presents the results of the experiments, which includes the mean AUC score along with the standard deviation across 10 times of experiments. The proposed method, HGML, has superior performance compared to the other comparative methods. DSGCN does not surpass the proposed HGML bocause cannot use edge information for encoding attributes. In contrast, HGML's attribule-wise message- message-passing network simultaneously considers node attributes and neighbor information. This allows to learn enhanced attribute reprosentations. MAMLGCN has the worst performance among all approaches because it cannot obtain node embeddings with attribute information from heterogeneous attribute graphs, and there is insufficient edge data to learn the edge patterns from various graphs. The three non-meta-learning models cannot. reach better performance because they cannot learn from additional graphs. While NN performs better than GCN and GAT at the support rate r = 0.3, 0.5, GCN and GAT outperform NN when more support edges are available under the setting of 0.7. GAT did not outperform GCN due to little information the training graphs to support its more complex model structure.
Table 4 presents the number of parameters, average training time for meta-learning, and inference time. The inference time refers to the time required for the model to process query graph and generate predictions for the query edges, including the local adaptations of MAMLGCN and the ro- ro-training required for NN, GCN, and GAT. To evaluate inference time, we sample three different graph sizes: N = 500, 5,000, 20,000 from Reddit, ensuring that each sampled graph contains N nodes and N edges to simulate the few-shot scenario. HGML achieves better performance while maintaining similar model complexity and training time compared to DSGCN and MAMLGCN. MAMLGCN and the non-meta-learning approaches have higher inference time. In contrast, HGML can be applied to new graphs with reasonable inference time.
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Table 4: The average training time for meta-learning, inference time on graphs in size of N, and the number of parameters HGML and the comparable methods.
Inference times (ms)
Model
# Parameters (K)
Training time (hours)
500
N 5,000
20,000
HGML
23.2
11.1
24
25
104
DSGCN
29.2
13.8
3
33
22
MAMLGON
20.9
10.4
493
579
3,215
NN
21.2
840
840
840
GCN
21.2
1562
1563
1575
GAT
21.6
4202
4204
4215
Table 5: Performance HGML using different numbers of datasets for training.
# Datasets for training
= 0.3
0.5
7 = 0.7
0.623
0.663
0.72410.043
0.621+:0.035
0.678=0.026
0.730=0.033
0.633::0.031
0.687=0.025
0.719+0.050
We evaluated HGML's ability to learn from diverse datasets by reducing the number of training datasets. The results are listed as Table 5 When used all eight datasets for training, the model performed better under the support rate r = 0.3, 0.5. At the support rate = 0.7, the results demonstrate that using 5 datasets for training may have better performance. This is likely because the model performs well with certain specific combinations of training datasets relative to the test datasets. However, using more datasets for training HGMT, generally results in better performance. Although we used data from various fields, they have some similar graph structures, and meta-learning can identify and learn useful common patterns shared among them. Unlike previous meta-learning methods, our model is not constrained by heterogeneous attribute spaces across graphs. In experiments, demonstrated that adding more graphs to the training set lcads to better performance, even with high proportion of SNS graphs in the data. We will test the model by adjusting the proportion of each category to better understand the impact of similarity between training and testing graphs.
Besides the neural network-basse basod approaches described in this section, we also applied classic graph com- pletion algorithms, such as Singular Value Decomposition (SVD), our prediction tasks. However, the performance was close to random guessing that chose not to compare it with approach.
5.2 Ablation study and
analysis
We perform ablation studies to verify the effectiveness of each element in HGML. The result is listed Table 6 (a) we removed the message-passing from attributo-wised mossage-passing networks that the altribule-specific node embeddings are obtained without using the information of neighboring nodes:
(xni)) / (0,,,,,--11 f for l = 22....,,
for é t= =
(6)
The model failed learn the pattern of the edges, and the prediction results are close random guesses. (b) trained HGML by minimizing the binary cross-entropy loss, which is commonly used in existing research for graph edge prediction, rather than maximizing the smoothed AUC as proposed in our method. The results demonstrate that using the proposed smoothed AUC as the loss can reach better performances under all three support rate setups.
In the hyrer-parameters analysis, we compared the models with different encoder layers, hidden units, and the ratio of negative samples. First, we analyze the effect of the encoder layer L. The results are demonstrated in Figure 3 aa.. Under the support rate 0.3, performance did not significantly improve increased
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Table 6: Ablation study.
-= 0.3
f= 0.5
T T= 0.7
HGML
0.633:10.031 0.518#0.014
0.687
0.719:10.050
(a) Wathut pressage-passilee operation (b)Trained using binary cross-entropy loss
0.517=0.017
0.521=0.012
0.616+0.018
0.622+00.099
0.656+0..025
0.80
Support rate
0.80
Susport rate
0.80
Support
0.3
0.5
0.3
0.5
0.5
0,5
0.1
0.75
0./
0.70
0.70
0.70
0.65
0.65-
0.65
16
32
100%
200%
300%
400%
(a) # Encodding layers L
(b) #Hidden units
(c) Times of negative samples
Figure AUC results for the experiments under different selups.
the number of encoding layers. However, when 0.5, 0.7, the model performed better using two and four encoding layers. This suggests that additional encoder layers might have greater potential to learn more complex patterns in specific situations. Next, we adjust the hidden units of neural network components f. The results are demonstrated in Figure 3(). The model performed better when increasing the hidden units of the neural networks under all three support/quee the model required more hidden units to achieve better results due the increased information the input graphs. Finally, we verified HGML by adding more negative samples for training. In the original setup for training HGML, the number of negative samples matched the number of support edges for calculating the loss and gradients. We increased the negative samples to two to four times the support edges in this experiment. The results are demonstrated in Figure 3 Cc.. Similar to the experiments of adjusting the encoding layers, the performances did not change significantly when r = 0.3, 0.5. However, under the support rate r = 0.7, the models performed better when we increased the amount of negative samples.
settings. Under the setting of support rate r = 0.7,
6 Conclusion
In this research, we proposed a novel approach, HGML,, that addresses the few-shot edge prediction problem for graphs. The proposed attribute-wise message-pasiing networks can be shared and learn common patterns from graphs with heterogencous node attributes. The proposed meta-learning algorithm allows the model to learn from various subgraphs and apply them to new test graphs with sparse edge data. In our experiments, HGML outperformed the existing approaches on 14 real-world graph datascts. HGML has the potential be applied to many real-world applications. For instance, it can be used build prediction models on newly launched SNS or when data collection is costly, such discovering protein- protin--rotein interaction. HGML can be trained with publicly available data regardless of differences in data attributes.
HGML can be exlended in several directions. First, HGML is developed based on basic graph convolutional networks (Kipf & Welling 2017). Incorporating recent advanced approaches could further improve perfor- mance. Second, the current model can only handle graphs with a single node type. Extending the model to deal with graphs with multiple types of nodes could enhance its flexibility for world applications. Third, we aim to evaluate the proposed method using more graphs from various sources. Further testing
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more diverse datasets will be part of future work. Fourth, while the combination of multiple non-linear layers and average pooling enables the model to learn from diverse graphs, it also reduces interpretability. Finally, due to subgraph re-sampling for each epoch and graph optimization, training HGML is computa- tionally expensive. Efficiently searching for training graphs may shorten training time and make HGML more robust.
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15


Reviews:
[{"review_id": "U6QBlFXtwS", "reviewer": "Reviewer_Sn7r", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strength\n\n- The proposed method is a flexible framework that can be applied to graphs with heterogeneous node attributes. The proposed method can work when some node attributes are unknown during training and testing in reasonable runtime.\n- Throughout the experimental results, the proposed method consistently shows higher AUCs than existing methods.\n- Experiments have been conducted on real-world graphs. The experimental results suggest that the proposed method shows promising performance on real data, supporting its real-world applicability.\n\n## Weakness\n\n- The graphs used in the experiment covered SNS, Citation and EC, with a particularly high proportion of SNS graphs. As such graphs are known to be scale-free, the structure of the graphs used in the experiment is likely to be similar. Therefore, the effectiveness of proposed method for graphs with heterogeneous attributes and structures should be clarified in the future.\n- When comparing the performance of the proposed and existing methods, do we need to consider differences in model size (number of parameters)? In a comparison of the runtime with the existing methods, the authors state that the proposed method requires a longer computation time than the existing methods due to the higher number of layers in the proposed method.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This research addresses improving the accuracy of link prediction for graphs with heterogeneous node attributes. The real-world graphs subject to edge prediction are very sparse and the number of training data is limited. To cope with the small amount of data, a meta-learning framework is introduced. Existing meta-learning frameworks target tasks where all node attributes are known during training and testing. Another existing approach is very time-consuming. The proposed method is capable of dealing with unknown node attributes. Through numerical experiments on 14 real-world datasets, the effectiveness and versatility of the proposed method is demonstrated.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please see the weaknesss above.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "iaw8Qij1bz", "reviewer": "Reviewer_qJhD", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1.) Existing literature often limits meta-learning on graphs to homogeneous attribute spaces, restricting models to graphs where nodes share similar attributes. The HGML model in this paper, however, introduces attribute-wise message-passing networks that allow the model to process and learn from graphs with heterogeneous attributes.\n\n2.) Prior models, including GCNs and GATs (Veličković et al., 2018), often depend on dense edge data for effective learning, making them less applicable to real-world scenarios where edge information may be sparse or costly to obtain. This paper’s focus on few-shot edge prediction addresses these constraints by enabling the model to generalize from sparse edge data. This few-shot learning approach relates to works like Huang & Zitnik (2020), which also aim to improve performance with limited data. However, HGML’s attribute-wise message-passing networks give it an edge in handling sparsity across varied attribute spaces.\n\n3.) The paper supports its contributions with a robust experimental setup across 14 graph types, demonstrating HGML’s superior performance against both traditional GNNs and newer meta-learning models. This empirical validation not only supports the model’s effectiveness but also addresses gaps in existing literature where heterogeneous graph datasets have been underexplored.\n\nWeaknesses:\n1.) The model’s training time is notably longer than that of other comparative methods, especially due to repeated subgraph resampling and additional encoding layers. This may limit its practicality in real-time applications or settings with limited computational resources, as noted in the results where HGML took longer to train compared to simpler models like GCN and GAT\n\n2.) Although the attribute-wise message-passing design could contribute to model interpretability, the paper does not explore or evaluate this aspect in depth. Without specific interpretability analyses, the practical advantage of interpretability remains speculative, missing an opportunity to provide insights into how attribute-specific embeddings contribute to edge predictions in heterogeneous graphs.\n\n3.)Although the model performs well on a variety of mid-sized datasets, its suitability for much larger graphs (e.g., millions of nodes) is unclear. The computational demands of the attribute-wise message-passing and repeated encoding layers may become prohibitive as dataset size increases, potentially limiting the model’s scalability for very large graph applications like large social networks or web-scale knowledge graphs.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper titled \"Meta-Learning for Graphs with Heterogeneous Node Attribute Spaces for Few-Shot Edge Predictions\" introduces a new meta-learning model aimed at improving edge prediction in graphs, specifically when available data is sparse and the nodes possess heterogeneous attributes. The authors propose the Heterogeneous Graph Meta-Learning (HGML) model, which features an attribute-wise message-passing network to transform information across nodes and generate embeddings tailored for diverse attribute spaces. This design enables HGML to share parameters across different graphs, promoting knowledge transfer and enhancing edge prediction accuracy, even when test graphs vary significantly from training ones.\n\n1.) A graph neural network-based model that can share parameters among graphs with nodes in heterogeneous attribute spaces. This allows the model to learn from and make predictions on graphs with different types and numbers of node attributes.\n2.) A meta-learning framework that improves edge prediction performance with sparse edge information by learning from various graphs without requiring bilevel gradient-based optimization. This enables the model to generalize to new unseen graphs with limited edge data.\n3.) An attribute-wise message-passing network architecture combined with average pooling, which allows the model to process graphs with different numbers of attributes and learn relationships between attributes.\n4.) The ability to make predictions on new input graphs without local adaptations, unlike some other meta-learning approaches that require fine-tuning.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1.) Better Interpretability\n2.) While HGML’s ability to predict without fine-tuning is positioned as a strength, this approach could be a double-edged sword. Without task-specific adaptation, the model may not fully optimize its performance on new graphs, especially those with highly distinct structures or attribute distributions from the training set. In classic meta-learning, some level of task-specific adaptation often enhances performance on new tasks, which HGML bypasses. Maybe I am understanding this wrong but I would like to understand the meta-learning aspect vis-a-vis task-specific fine-tuning.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "RWl5H8wdlv", "reviewer": "Reviewer_PM1y", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. The paper is written well and is easy to understand.\n\n2. The studied problem is very important.\n\n3. The results seem to outperform state-of-the-art.\n\nWeaknesses:\n\n1. could the authors try more ablations on the support edge rates, to test the robustness of the proposed algorithm?\n\n2. Could the authors inlcude more recent meta-learning baselines for comparison? There are multuiple related papers working on this.\n\n3. Could the authors try to compare with non-GNN related methods? There are some classific graph completion algorithms by low-rank approximation available in literature. It is better to observe the robustness of these staistical approaches in the few-shot setting.\n\n4. Is it possible to estimate the edge probabilty by the cosine similarity?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposed a meta-learning method for edge prediction that can learn from graphs with nodes in heterogeneous attribute spaces. The proposed model consists of attribute-wise message-passing networks that transform information between connected nodes for each attribute, resulting in attribute-specific node embeddings. The node embeddings are obtained by calculating the mean of the attribute specific node embeddings. The encoding operation can be repeated multiple times to capture complex patterns. The attribute-wise message-passing networks are shared across all graphs, allowing knowledge transfer between different graphs.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "see above", "broader_impact_concerns": "na", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "QbJPNYIhJU", "reviewer": "Reviewer_91Y2", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n1. Designing graph neural networks for heterogenous node features seems like an important problem.\n2. More than 10 graph datasets were used for the experiments, demonstrating the superiority of the proposed method.\n3. The average performance, standard deviation, and training time are well reported in the experiments.\n\nWeaknesses\n1. Meta-learning is an essential keyword of this work, but the proposed method does not seem like meta-learning. From my understanding, the loss is computed for each sample and then just summed. Where are meta-parameters of the proposed method?\n2. I’m not sure why we need to sample subgraphs and use them in the experiments instead of using the original graphs. How can we guarantee that the sampled graphs preserve the original topological properties? Is the proposed approach applicable only with sampling?\n3. The concepts of support and query edges seem to be from previous work (Huang & Zitnik, 2020), but not sufficient description is given in the paper. Please describe their roles and why we need them in more detail.\n4. The proposed method does not require any meta-data for the features, e.g., their distributions, min, max, etc. How can this work? Does the data preprocessing play an essential role in this perspective?\n5. The authors use the objective function which approximates the AUC score in a differentiable manner. There are many recent variants of Eq. (4) particularly for contrastive learning. I hope the authors can strengthen the discussion on the choice of an objective function, in relation to recent studies.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "1. The authors propose a graph neural network-based model for graphs with nodes in heterogeneous attribute spaces.\n2. They propose a meta-learning framework to improve edge prediction performance with sparse edge information without bilevel gradient-based optimization.\n3. They show that the proposed method outperforms existing meta-learning methods for edge prediction using 14 real-world graphs with nodes in heterogeneous spaces.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please revise the paper based on the weaknesses above. Minor comments are given below:\n- I’m not sure if we need Algorithm 1, which is straightforward, in the paper.\n- In Section 4, the citations for datasets are in a wrong format.", "broader_impact_concerns": "I have no concerns regarding the broader impact.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "5EufYSd0Wk", "reviewer": "Reviewer_CJpF", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**  \n-  This paper is well-written and easy to understand\n-  The method is easy to follow.\n\n**Weakness**\n- The running time is much longer than other baseline methods. The scalability is not that good, especially on large-scale graphs. The performance gains aren't significant compared to the extra time.\n- The chosen baselines seem out-of-date. The results are not that convincing.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposed a novel meta-learning method that aims to solve two problems in previous graph meta-learning methods: (i) training graphs and test graphs share different attribute space; and (i) no known information about the test graph's information. Extensive experiments show the effectiveness of the proposed method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I have some questions. \n- Is MAMLGCN (model-agnostic meta-learning) defined in 4.3 Comparative methods a method or a series of methods? In my opinion, it is a series of methods but it is only one line in your table which looks like just a single method. Besides, no citations are provided in 4.3 so I am a little confused. I am not sure what method it is.\n- What is the difference between graph domain adaptation methods on link prediction and the proposed method?", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The authors did a good job with their explanations and they mostly addressed all the concerns that the reviewers had. Still, the recommendations are rather mixed, with one reviewer recommending a reject decision. I see the same issue the latter had: the fact that the proposed method requires significantly longer execution times and has significantly more complex architectures than other learning approaches that it was compared to. This leads to the question of fairness of comparisons, especially on larger graphs (such as knowledge graphs used in recommender systems and biomedical research, where heterogeneity may be an issue). 

I am requesting that the reviewers compare methods in a way that the execution times, number of layers ( or model complexity) etc are all comparable. Otherwise, the utility of the method is rather mute. I also reserve the right to reverse my decision to reject if the comparisons are not adequately implemented. Out goal should always be to accurately investigate the pros and cons of all methods in an unbiased manner.
Decision: Accept (poster)