SHADOWCAST: Controllable Graph Generation with Explainability
Authors: Wesley Joon-Wie Tann
Ee-Chien Chang
Bryan Hooi
Venue:  (2021)
Keywords: Controllable Graph Generation
Explainability
Conditional Generative Adversarial Network

Abstract: We introduce the problem of explaining graph generation, formulated as controlling the generative process to produce desired graphs with explainable structures. By directing this generative process, we can explain the observed outcomes. We propose SHADOWCAST, a controllable generative model capable of mimicking networks and directing the generation, as an approach to this novel problem. The proposed model is based on a conditional generative adversarial network for graph data. We design it with the capability to control the conditions using a simple and transparent Markov model. Comprehensive experiments on three real-world network datasets demonstrate our model's competitive performance in the graph generation task. Furthermore, we control SHADOWCAST to generate graphs of different structures to show its effective controllability and explainability. As the first work to pose the problem of explaining generated graphs by controlling the generation, SHADOWCAST paves the way for future research in this exciting area.

Under review as a conference paper at ICLR 2021
SHADOWCAST: CONTROLLABLE GRAPH GENERA- TION WITH EXPLAINABILITY
Anonymous authors Paper under double-blind review
ABSTRACT
We introduce the problem of explaining graph generation, formulated control- ling the generative process to produce desired graphs with explainable structures. By directing this generative process, we can explain the observed outcomes. We propose SHADOWCAST, controllable generative model capable of mimicking networks and directing the generation, as an approach this novel problem. The proposed model is based on conditional generative adversarial network for graph data. We design it with the capability to control the conditions using a simple and transparent Markov model. Comprehensive experiments three real-world network datasets demonstrate our model's competitive performance in the graph generation task. Furthermore, different structures to show its effective controllability and explainability. As the first work to pose the problem of explaining generated graphs by controlling the generation, SHADOWCAST paves the way for future research in this exciting area.
control SHADOW to generate graphs of
INTRODUCTION
In many real-world networks, including but not limited to communication, financial, and social networks, graph generative models are applied to model relationships among actors. It is crucial that the models not only mimic the structure of observed networks but also generate graphs with desired properties because it allows for an increased understanding of these relationships. Currently, there are no such methods for explaining graph generation.
Meaningful interactions between agents are often investigated under different what-if scenarios, which determines the feasibility of the interactions under abnormal and unforeseen cireumstances. In such investigations. instead of using actual data, we can generate synthetic data to study and test the systems (Barse et al. 2003 Skopik et al. 2014). However, there are many challenges. (1) Data is not accessible by direct measurement of the system. (2) Data is not available. (3) Data produced by generative models cannot be explained. To address these challenges, we have to answer a natural and meaningful question: Can we control the generative process to shape and explain the generated graphs?
In this work, introduce the novel problem of explaining graph generation. The goal is gener- ate graphs of desired shapes by learning to control the associated graph properties and structure to influence the generative process. We provide an illustrative case study email communications in an organization with two departments (Figure [. where interactions of the employees follow a regu- lar pattern during normal operations. Due to limited data, previously observed network information may be missing scenarios of intra-departma counting departments. When such situations are required for analyzing the system, an ideal model should generate graphs that reflect these scenarios (see box in Figure I while maintaining the orga- nizational structure, By effectively controlling the generative process, SHADOW CAST allows users to generate designed graphs that meet conditions resembling wide range of possibilities. Overall, this is a meaningful problem because controlling the generative process to explain generated net- works proves be valuable in many applications such as anomaly detection and data augmentation.
email surge within either the Human Resources or Ac-
Existing graph generative models aim to mimic the structure of given networks, but they cannot easily shape graphs into other desired states. These works either directly capture the graph struc- ture (Cao & Kipf 2018 Liu et al., 2017 Tavakoli et al. 2017]] Zhou et al.) 2019 Ma et al., 2018 You et al. 2018. Simonovsky & Komodakis 2018 Bojchevski al. 2018 model node feature

---

Under review as a conference paper at ICLR 2021
Reg llar mail traffic between two deparbments
Controllable Graph Generation
Generated Graph
Generated Graph
SHaDOWCAST
? Intra-department email surge
Accounting
Humen
Figure I: Case study illustration explaining controlled generation: Many times, data of various situations are not available in observed real-world networks. SHADOWCAST allows to generate graphs of desired structures and provide explanations for the generations.
information (Kipf & Welling 2016 Wang et al. 2018 Grover et al. 2019 Zou & Lerman 2019)
Most of them adopt implicit model approaches, such as the popular generative adversarial networks (GANs) (Goodfellow) (016). Only very recent advances (Li et al. 2018: Yang et al. 2019) in net- work generation have started injecting auxiliary information into the model by adding graph-level conditions as additional inputs. However, none of them allow direct control over the generative process, which addresses the fundamental challenge of generating explainable graphs.
While there are existing methods for explaining graph generation, studies of explainability in other AI methods are increasing popularity. One family of work, proxy methods (Huysmans et al. 2011: AAugssta & Kathirvalavakumar 2011: Zilke et al. 2016 Lakkaraju et al. 2017), learns to approximate model predictions with simpler surrogate models. Another line of work (Adadi & Berrada 2018: Guidotti et al. 2018 Koh & Liang 2017) treats models black-boxes and carefully queries them for relevant information to form interpretations of the results. The works closest to problem in interpretable Graph Neural Network (GNN) models, where models predict and assign values to edges via attention mechanisms (Veličković et al., (2018) Neil et al. [0018] Xie & Grossman 2018). Notably, even the latest work (Ying et al. 2019), which considers both graph structure and node feature information, still only explains predictions of individual nodes but cannot produce explanations for entire graphs.
We propose SASDOWCAST, an approach for explaining graph generation, which addresses the chal- lenge of generating graphs with user-desired structures. achieved by using easy-to- aasytto-understand node properties that are intended to capture graph semantics in an explicable way. These proper- ties form the shadow that we control in order to guide the graph generative process. The model architecture is essentially based on conditional GANs (Mirza & Osindero 2014). The model intro- duces control by leveraging the conditions, which we manage with a transparent Markov model, as control vector to influence the generative process. It allows for user-specified parameters such as density distributions to generate designed graphs that are explainable. Finally, the generator captures essential graph structures while exploring myriad of other possibilities in multifarious networks.
We first evaluate SHADOWCAST on three real-world social and information networks to demonstrate its competitive performance against several mate-of-the--ad graph generation methods in mimicking given graphs. Our model achieves impressive results that are superior in most datasets. In addition, demonstrate the capability of SHADOWWAST produce customizable synthetic graphs through tunable parameters, which existing generative models are incapable of performing.
EXPLAINABLE GRAPH GENERATION
In this section, we describe the explainable graph generation problem. The core idea of the prob- lem lies in generating graphs of desired structures through control of node properties as form of explainability. We define these properties and its structure as a shadow and introduce our approach SHADOWCAST. Since it is challenge directly control the generation of graphs due to their com- plex interconnected nature, we model them through shadows, which can be manipulated to control the graph generation. We depict the problem and our approach in detail below (Sections 2.1 and
2

---

Under review as a conference paper at ICLR 2021
2.1 PROBLEM FORMULATION
We focus on the novel problem of explaining graph generation. Let G = (V, denote a graph with N nodes i; E V and E edges (v,,,y) E. Each node is associated with some identity information, e.g., the employee ID. In addition, we induce another graph with N nodes and the same edge connections as in G. by the node properties, which we define as shadow S. Fach node in the shadow is associated with some property label k3 E K, e.g., the employee's department, and it "shadows" the corresponding node in G. Every node in G can be uniquely identified by the identity, whereas the label of each node in S is not necessarily unique. Shadow nodes provide important explanatory information that is useful in understanding the generated graphs. We note that there could be other properties of interest, e.g., degree distribution, shadow with different connectivity than G. We leave the inclusion of additional properties as extensions for future work.
In this work, aim to develop explainable network graph generative model. By training the model @ on a graph G and its shadow S, the model would then monitor the generative process and subject the generation to direction-aiding in the explainability of the generated graphs. Let us define the Explainable Graph Generation (X2G) problem as such:
Given graph & and key node properties of G. induce another graph by these properties, defined as shadow S: train model @ learn representation S of the shadow and control S to generate graphs I's with explainable structures.
Following this process, we can leverage node properties such as ground-trun labels and other node attributes, valuable in understanding the model-generated results, control vector to guide the graph generation.
2.2 PROPOSED MODEL
Generative Process
Generated graph shadow walk
Sampledi shadow
Geneeitoe shadow wilk
Shadow Daster
Ganerator
G
Disarimiation
D
D
Original graph
shadow
Real
Fike
Sampled shadow
Figure 2: The SHSDOWCAST architecture proposed in this paper.
We propose SASDOWCAST, an explainable generative approach that leverages both conditional modeling and GANs generate graph-structured data. Our approach is inspired by the recent work (Bojchevski et al. 2018) that poses the graph generation problem as learning a distribution of biased random walks over the input graph, which captures the underlying distribution of graph where nodes belong in some ground-trutt communities. Similar to any archetypal generative ad- versarial nets, SHADOWCAST consists of two 'adversaries" -a generative model G and a discrimi- native model D. In addition, our approach consists of a shadow caster model S that takes in some sequences sampled from the shadow and produces shadow walks that directly influence the gener- ator G. The goal of G is to capture the distribution over the data and generate synthetic graph random walks and conditions that are similar to the real walks. At the same time, D) estimates the probability that graph random walk and its conditions came from the real graph rather than G, to distinguish between the synthetic and real walks. We provide details of our model architecture (Figure 2 and design choices below.
Using the conditional GAN framework, we train both G and D conditioned on some extra information- shadow walks from the shadow S. By allowing our model to consider
3

---

Under review as a conference paper at ICLR 2021
any auxiliary information such ground-truth communities or data from other sources, the model can (1) leverage extra information from different data modalities, and (2) directly control the data generation process. For example, by using contextual information in the social communications of an organization, we learn semantically meaningful graph representations. We can then explicitly generate networks of any given context.
Following Mirza & Osindero (2014), we introduce the conditional GAN training for graph shadow random walks and define the loss as:
Legan log(D(# 8)) log(1 D(G(= 8)))
where NO Ia) is latent noise from multivariate standard normal distribution. We rep- resent a social transaction network as an input graph of N nodes as a binary adjacency matrix A E (0, } J.N We then sample sets of random walks of length 7 from A to use training data for our model. Following Bojchevski et al. (2018). we use biased second-order random walk sam- pling strategy (Grover & Leskovec 2016) one of the advantageous properties of random walks is their invariance under node reordering in order to better capture both global and local graph structures. Another advantage of random walks is that the walks only include connected nodes, which efficiently exploits the sparsity of real-world graphs by including nonzero values of the adja- cency matrix A. In the rest this section, we describe in detail each stage of the SHAADWWCSSS generation process and formally present the procedure (Algorithm D.
Algorithm Minibatch stochustic gradient descent training of explainable graph generative adver- sarial nets. The number of steps to apply to the generator, w. is a hyperparumeter. We used w 3.
I: for number of training iterations de
2: Sample minibatch of m samples {a("),.... ........m)) (x))) from data distribution Pdata
3: Sample the respective m shadow walks (s(1) s(m))
4: Update S model weights:
5:
8 log S(s(01)
6: Generate minibatch of m shadow walks (8(1) s(m) with model S
7:
Sample minibatch of m noise samples {2(1). 2m)) from (O00, [g) Update C' model weights:
8:
9:
Σ Dog(1 D(C(=!) (())
10:
for w steps de
11:
Update D model weights:
Vo. 1 Σ log ((x 1 + log(1 | [())
1=1
13: end for end for
Shadow Caster The shadow caster S is a sequence-to-sequenee model that learns arrays of con- tiguous node properties from sampled shadow walks on the shadow. The network predicts quence of inputs one at time when some sequence is observed. We model S with a long short-term memory (LSTM) (Hochreiter & Schmidhuber (997) neural network. Given sampled sequences of shadow walks ($1,..... from the shadow as inputs, the shadow caster S then generates synthetic shadow walks ($1...., šT) to mimic the sampled walks.
Generator
The generator G is probabilistic sequential learning model that generates conditional graph random walks (#),..., VT) ~ G. We model G using another parameterized I. I.STM network fe. At each step t, fe takes input the previous memory state m, of the LSTM model, the current additional information 8,, and the last node v,-1- The model produces two values (p:: m.), where pa denotes the probability distribution over the current node and m, the current memory state. Next, the current node i, is sampled from a categorical distribution v. ~ Cat(a(pi)) using a one-hot vector representation, where o(-) is the softmax function.
In order to initialize the model, we draw a latent noise from a multivariate standard normal distri- bution AO0 Ia) and pass it through hyperbolic tangent function go (2) to compute memory
4

---

Under review as a conference paper at ICLR 2021
state my. Generator G takes as inputs the noise z and sampled shadow walks s, and outputs graph random walks (U1....,yy) Through this process, we generate fake random walks.
At this point, we find that our model is closely related to the recently introduced random walk graph generative model (Bojchevski et al. 2018). In addition to random noise model initialization, the gen- erator greatly benefits from the auxiliary information $t, modeling more accurate representation of the original graph (see Appendix for details).
Discriminator The discriminator D is binary classification LSTM model. The goal of D is to discriminate between real walks sampled from walking on the original graph and fake walks generated by G. At each time-step f, the discriminator takes two inputs: the current node v, and the associated shadow St, both represented as one-hot vectors. After processing each presented sequence of shadow and graph walks, D outputs a score between 0 and 1, indicating the probability of real walk.
After training the model, we have a shadow caster S and generator G that can produce synthetic graphs. The shadow caster first constructs shadow walks ($1,.... .......,.. 8T) of some user-defined class distribution (a relatively small number of shadow walks, e.g., 10,000), The generator then takes (B)...., BT) and generates a large set of random graph walks (a much larger number of random walks than for training, e.g., 10M). We construct score matrix S by counting how often an edge appears in the set of graph walks. Next, we convert S into binary adjacency matrix Å by first to get a symmetric matrix. Next, we could use simple binariza-
setting 8ij = 85z = max($i,, tion strategies such as thresholding choosing top-k entries. However, we follow probabilistic strategy, introduced in [BBocchvvkki et al. (2018), that mitigates the issue of leaving out the low-degree nodes and producing singletons because the starting nodes of every walk is random.
2.3 EXPLAINING GENERATED GRAPIIS
Different from existing approaches, our model takes shadow walks-a series of random walks on the node properties graph as inputs to the generator, and creates graphs with various densities. To answer questions like: "Why did the model generate such graphs? Could we modify it to our desire?", generate graphs that are more explainable by controlling these shadow walk inputs. Our goal is to provide insight into how black-box generative models produce graphs. For any desired graph, we first build a Markov chain model and construct sequences of node properties based on some user-specified transition distribution. These sequences are then injected into the shadow caster S to generate shadow walks (.,,..., 8r) that mimic the original shadow. Next, given trained ShadoWCAst model θ and the shadow walks ($1..... 3 the generator G produces desired graphs G's. Through this process, one can control the shadow distributions and study the generated graphs by comparing the results.
3 RELATED WORK
Although many existing works study the generalizability of graph generation methods, explaining generated graphs remains an open question. From a broader point of view, we can consider the related problems of (1) constructing generative models for graph-structured data and (2) interpreting machine learning models and understanding their results.
Graph Generation Most existing graph generation models are designed to generate graphs mim- icking the structure of observed graphs. So far, no generative method that shapes graphs into new desired states have been proposed. In general, we can group these graph generative models into two main families those that directly model the graph structure (Cao & Kipf 2018 Liu et al. 2017] Tavakoli et al.) 2017 Zhou et al. 2019 Ma et al. 2018 Simonovsky & Komodakis 2018) and oth- ers that study the graph in the context of node representations (Kipf & Welling 2016 Wang et al.) 2018 Grover et al.) 2019 Zou & Lerman 2019). While modeling of graph structures approximates the distribution of graphs with minimal assumptions about their structure, modeling node embed- ding estimates the probabilities of each edge's 's existence, which effectively models the relational structure of large graphs. Another series of tangential work, graph translation (Guo et al.) 2019 Jin et al. 2019 Guo et al. 2018), attempts to learn translation mapping from the input domain the
5

---

Under review as a conference paper at ICLR 2021
target domain graph. However, the methods are designed to mainly generate graphs that match the structural characteristics of any given graph.
Recently, some works in graph generation have started exploring network structures of various ditions. These works employ graph-level condition information. In one work. Li et al. (2018) produce some conditional generation results, where the conditions are graph properties such as the number of nodes and edges. Another work, CondGEN (Yang et al. 2019), injects semantics into the graphs by conditioning the model on supplementary contextual information. The model mainly con- siders multiple small graphs, each with an accompanying semantic condition to learn a distribution over graphs. While GraphRNN YYou et al., 2018) is not a direct conditional model, it decomposes the generative process into sequences of nodes and edges, which potentially allows for explicit con- ditioning. However, these methods only generate graphs mimicking the observed graphs.
To allow state manipulation and controllable graph generation, our model borrows the concept from NetGAN (Bojehevski et al., 2018)). which adapts the standard LSTM to learn a distribution of random walks and exploit sparsity in real-world graphs. In contrast to NetGAN, we integrate condition-bad -baeed control mechanism to learn a model that generates explainable graphs. Due to the challenging nature of the problem, to the best of our knowledge, no work has definitively considered shaping graphs into new desired states.
Explainable AI Explainable AI studies the task of improving the interpretability of Al systems. While proxy model methods (Huysmans et al.) 2011 Augasta & Kathirvalavakumar 2011 Zilke
et a 2016 Lakkaraju et al. (0177) often resort to learning local approximations of predictions using sets of rules in applying conditions on the prediction, advances in interpretability methods (Adadi & Berrada 2018 Guidotti et al. 2018 Koh & Liang] 2017) treat black-box models as such and query them for information. Among the many recently developed interpretable models, Graph Neu- ral Network (GNN) models have been studied to explain predictions on graph-structured data via attention mechanisms VVelčkkoić et al. 2018 Neil et al.) 2018 Xie & Grossman 2018). These ap- proaches learn important graph structures by predicting and assigning attention values to the edges. The attention values are the same for all nodes in the same structure, limiting the predictive power.
Moreover, these models cannot explain predictions by combining node feature information with the graph structure. To circumvent the limitations of attention-based GNN models, GNNEx- plainer (Ying et al. 2019) considers both graph structure and node features to explain predictions. However, explainable GŇN models identify explanations in graph structures and node features, which are suitable for link prediction, node/graph classification tasks but not graph generation.
4 EXPERIMENTS
In this section, we first compare and evaluate our approach with other baseline graph generation methods on three datasets to establish our model's ability to generate high-quality graphs of complex networks. Next, we demonstrate the explainability of SHADOW CAST by controlling the generative process create graphs according to specification. Note that generating graphs mimicking any given graph as closely as possible is not our goal. Our objective is to introduce a more explainable graph generative approach. Through our experiments, we not only demonstrate that SHaDOWCAST exhibits competitive performance in the task of graph generation, but we also show that our model can generate graphs of different density distributions by controlling the shadows.
Datasets We consider three real-world graphs in social and information networks, where each node belongs to one of the ground truth communities. Two of the datasets are email communication networks EUcore-top (N = 348, E = 3342, K = 5) and Enron (N 154, F 1843, K = 3). The other dataset Cora-ML (N 2810, F. = 7981, K = 7)) is a commonly used subset of a large author citation dataset. We provide the links to datasets used in our experiments (see Appendix for details).
We study communication networks: (1) EUcore-top is a network that consists of the top five largest departments in the EUcore email dataset that was created using anonymized emails from a large European research institution. (2) Enron is a dataset of the Enron email corpus where nodes are employees labeled according to their department information. The citation network: (3) Cora-ML is a popular benchmark citation dataset. Nodes labeled according to their paper topic are authors, and edges between them indicate that author cited another author's paper.

---

Under review as a conference paper at ICLR 2021
Baselines Since controlling the generative process provide explainable graph generation is novel task, and no such method is developed, we compare our approach against four current state- of-the-art graph generation baseline methods GraphRNN You et al. 2018), GVAE (Simonovsky & Komodakis 2018), NetGAN (Bojchevski et al., 2018), and CondGEN Yang et al., 2019). We randomly select 85% of the edges in each graph for training and use the remaining 15% for validation and testing. We refer readers to the Appendix for more details about the model implementation settings, baseline models, datasets, and explainable generated visualizations.
Performance We evaluate SHADOW against existing benchmark generative models (You et al. 2018 Simonovsky & Komodakis 2018 Bojchevski et al. 2018 Yang et al. (019) and present the comparison statistics (Table D. By comparing the statisties of the real graphs and those gen- erated by each method, closer mean values indicate greater resemblance to the original graphs, thus better performance. In general, baseline methods succeed at replicating the graphs that are directly modeled. Unsurprisingly. GVAE, designed for generating small graphs. performs well in the smaller Enron and EUcore-opp datasets. However, it does not recover statistics of the larger graph Cora-ML well. On the other hand, our model captures all graph properties of the datasets, especially excelling in preserving properties of larger graphs, as shown in its generation of the Cora-MI. dataset.
Graph
Model Real
ASST
CLUST
CPL
GINI
MD
TC
27,075
0.00227
3,630
0.483
241.0
2890
GraphRNN
0.0624553e- Sc-4
0.00121=2.2--
1892=3.70-3
0.119:119c4
507.4+2.7
9023.82
17.8
GVAE
-0.324-6.1e-33
0.01294=4.2o-4
1.4
0.825+1
121.647.0
15513.0+ 186,
Cors-ML
NetGAN
-0.055=1.56-3
0.001:40:2.8-55
4.943=9.50-3
1.40
223.6+2.11
1034.6:118. 18.7
CondGEN
4.52412.0e-2
0.00524-9.0-4
2.168=177-2
0.94611..e33
404.01:7.00
958434424780.4
SHADOWCAST
4.081=3.1e-3
0.00191=1.5e-
5.187=1.062
0.459+1.3e-3
229.6:7777
1713.6+26.4
40003
0:03300
2.154
0.287
74.0
4784.0
GraphRNN
0.028
0.02154:3.1e4
5.97
0.11612.00
30.1008
12216633444
GVAE
0.1124221e-2
0.04625+11.0e.
2.165-69e-3
0.288447.26-3
45.241..
5439 2-+-8.77
Enron
NetGAN
0.1231122:2 0.13051
2,105
0.244
55.8.11.4
3486.0-157.9
CondGEN
0.28772.76-2
0.04074-1.56-3
2.10242.3-2
0,46347.
70441.77
9619.6-183.7
SAST
-..004=4.6e-3
0.03483=7.8--
2.214=62203
0.278+188-3
73.2+2,6
$262.2+442.8
Real
-0.085
0,03105
2,885
0.433
65.0
8133.0
GraphRNN
0.005 18.66 3
0,00891 1.le
5.128
0.11819.66
41.0-0.84
3.39.
GVAE
0.257::1.2e-2
0.02
2.579=7.0e-3
4--3
68.842.3
9025 2::
9025.2::127
EUcore top
NeiGAN
0.028.11.0e 2
0.02335
2.642.1..0-
1.3
62.0.1222
4639.8.1286
CondGEN
0.3778:3.8e-2
0.01880=1.96-3
2.101=1:2--2
0.72013.6e-3
147.0:110.0
26106441126,4
SHADOWCAST
-0.034 1.le-2
0.02847.1.4e2
2.843 1.0-2
0.436
66.2.1.11
7414.4199388
Table Performance statistics (mean and standard error) of the graphs generated by SHADOWCAST and the baseline models, computed over five runs. We indicate the mean values of the generated statistics closest to the real graphs. SHaDOWCASt most closely matches original graphs in the statistics when compared with the baseline models.
SHADOWCAST, conditional generative model that considers meaningful auxiliary information (e.g.. node labels) of given graphs on top of learning the graph structure, naturally outperforms methods that take an unconditional approach. The baseline methods are designed to generate graphs unconditionally, with the exception of CondGEN. However, CondGEN performs conditional gen- eration with graph-level conditions, which not informative as the node-level information inject into SHADOW CAST. This rich supplementary node information enables our model to learn better representations of graphs. Hence, SHADOWCAST achieves the best performance results.
Explaining Generated Graphs In addition recreating graphs that closely match statistics of the input graphs, we demonstrate our model's ability to generate desired graphs by controlling parameters of the shadows. The controlled generation is good way to gain insight into how graphs are generated and provide form of explainability. We influence the generative process by constructing shadow walks of preferred distribution using shadow caster S. First, we create sequences of node ground- truth labels by specifying the parameters of a transparent and straightfor- ward Markov model: (1) initial probability distribution over K labels ा = (T1, T2, TK) ). where t, is the probability that the Markov chain will start from label and (2) transition probability ma- aRR), where each a.j represents the probability of moving from label i
trix A = (a11412
4kl
Statistics measuring properties of the datasets and the graphs generated by SHADOWCAST and the base- lines include ASST (assortativity), CLUST (clustering coefficient). CPI. (character path length), GINT (Gini index), MD (maximum node degree), and TC (triangle count).
7

---

Under review as a conference paper at ICLR 2021
to label j. Next, input these constructed sequences into shadow caster S. which returns model- generated shadow walks. Finally, by injecting these designed shadows into our trained generator G, generate explainable graphs of different structures.
400
(a) Observed: Enron normal operations
(b) Generated: Legal (red) intemnll surge
Genemttd:: Finance (green) internal surge
Generated: Trading (blue) outgoing surge
Figure 3: SHADOWCAST generated explainable graphs of the Enron email network.
In Figure we show controlled generation examples of the Enron email network, where each em- ployee represented by a node belongs one of three departments (e.g.. Legal, Trading, and Finance offices in the organization). Figure 3a is an observed instance of interactions between the depart- ments during normal operations. Due limited observations, network data of some unprecedented, extraordinary situations may be unavailable. To simulate such occurrences, bution of the Legal (red), Trading (blue), and Finance (green) departments with parameters (л, A) control the generative process. Distribution configurations likely sequence model- seeerraeee shadow walks start from a particular department, while the transition probability matrix A [[110122 ... 031 ... 033) determines the probability of moving from one department to another. Various configurations (πr, A) correspond to different cases such as (Figure 3b) internal communication surge in the legal team during court pre-trial period, (Figure 3ch internal surge in the finance department during financial accounts reporting period, and (Figure 3d) increased outgoing communication between the trading team and the other departments when purchasing subsidiary trading firm. Thus, by specifying these parameters, we can control and explain the structure of the generated graphs (see Appendix for the specific parameter settings).
set the distri-
(T1, 22, Ts) correspond to how
Following the example in Figure 3b] one could argue that we naively remove the legal (red) inter- department edges and add random intra-department edges to create the effect of an internal email surge. While the random graph constructed could appear legitimate, it is not clear if this newly formed graph (1) follows the dynamics the original network, and (2) has an explainable structure. In contrast, approach follows simple and transparent Markov model, providing the needed explainability for generated graphs that are modeled on the original graph. This intuitive approach allows for increased understanding of the generated graphs.
CONCLUSION
In this work, we present SHADOWCAST, novel controllable graph generative model, which gen- crates graphs that are explainable. To the best of our knowledge, this method the first its kind to address the unique problem of controlling the generative process to explain the structures of gen- erated graphs. Our model demonstrates how it can leverage graph properties as controls and allow for adjustable parameters to direct the generative process. By introducing explainability in graph generation, a meaningful problem for better understanding of generated graph data, we hope to encourage further investigation in this line of work and expand its applications in different areas.
8

---

Under review as a conference paper at ICLR 2021
REFERENCES
A. Adadi and M. Berrada. Peeking inside the black-box: A survey on explainable artificial intelli- genee (XAI). IEEE Access, 0552138-52160 2018.
M. Gethsiyal Augasta and T. Kathirvalavakumar Reverse engineering the neural networks for rule extraction classification problems. Neural Processing Letters, 35:131-150, 2011.
Emilie Lundin Barse, Häkan Kvarnström, and Erland Jonsson. Synthesizing test data for fraud detection systems. In ACSAC, 2003.
Aleksandar Bojchevski and Stephan Günnemann. Deep gaussian embedding of graphs: Unsuper- vised inductive learning via ranking. In International Conference on Learning Representations, 2018.
Aleksandar Bojehevski, Oleksandr Shchur, Daniel Zügner, and Stephan Günnemann. NetGAN: Generating graphs via random walks. In ICML, 2018.
Nicola De Cao and Thomas Kipf. MolGAN: An implicit generative model for small molecular graphs. arXiv preprint, arx: 1805.1 1973, 2018.
Ian Goodfellow. NIPS 2016 tutorial: Generative adversarial networks. arXiv preprint, arXiv: 1701.00160, 2016.
Aditya Grover and Jure Leskovec. Node2vec: Scalable feature learning for networks. In KDD, 2016.
Aditya Grover, Aaron Zweig, and Stefano Ermon. Graphite: Iterative generative modeling of graphs. In ICML, 2019.
Riccardo Guidotti, Anna Monreale, Salvatore Ruggieri, Franco Turini, Fosca Giannotti, and Dino Pedreschi. A survey of methods for explaining black box models. ACM Comput. Surv., 51(5), 2018.
X. Guo, L. Zhao, C. Nowzari, Rafatirad, H. Homayoun, and S. M. Pudukotai Dinakarrao. Deep multi-attributed graph translation with node-edge co-evolution. In 2019 IEEE International Con- ference on Data Mining (ICDM), 2019.
Xiaojie Guo, Lingfei Wu, and Liang Zhao. Deep graph translation. arXiv preprint, arXiv: 1805.09980, 2018.
Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural Comput., 9(8): 1785-1780, 1997.
Johan Huysmans, Karel Dejaeger, Christophe Mues, Jan Vanthienen. and Bart Baesens. An empir- ical evaluation of the comprehensibility of decision table, tree and rule based predictive models. Decision Support Systems, 51(1):141 154, 2011.
Wengong Jin, Kevin Yang. Regina Barzilay, and Tommi Jaakkola. Learning multimodal graph-to- graph translation for molecule optimization. In International Conference on Learning Represen- tations, 2019.
Thomas N. Kipf and Max Welling. Variational graph auto-encoders. arXiv preprint, arXiv: 1611.07308, 2016.
Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence functions. In ICML, 2017.
Himabindu Lakkaraju, Ece Kamar, Rich Caruana, and Jure Leskovec. Interpretable & explorable approximations of black box models. arXiv preprint, arXiv: 170.00114, 2017.
Jure Leskovec, Jon Kleinberg, and Christos Faloutsos. Graph evolution: Densification and shrinking diameters. ACM transactions on Knowledge Discovery from Data (TKDD), 1(1):-ess, 2007.

---

Under review as a conference paper at ICLR 2021
Yujia Li, Oriol Vinyals, Chris Dyer, Razvan Pascanu, and Peter Battaglia. Learning deep generative models of graphs. arXiv preprint, arXiv:1803.03324 2018.
Weiyi Liu, Pun-Yu Chen, Hal Cooper, Min Hwan Oh, Sailung Yeung, and Toyotaro Suzumura. Can
GAN learn topological features of graph? arXiv preprint, 1oXiv:1707.061111 2017.
Tengfei Ma, Jie Chen, and Cao Xiao. Constrained generation of semantically valid graphs via regularizing variational autoencoders. In NeurlPS, 2018.
Mchdi Mirza and Simon Osindero. Conditional generative adversarial nets. arXiv preprint, arXiv: 1411.1784, 2014.
Daniel Neil, Joss Briody, Alix Lacoste, Aaron Sim, Paidi Creed, and Amir Saffari. Interpretable graph convolutional neural networks for inference noisy knowledge graphs. arXiv preprint, arXiv:1812.00279, 2018.
Patrick O. Perry and Patrick J. Wolfe. Point process modelling for directed interaction networks. Journal of the Royal Statistical Society: Series (Statistical Methodology), 75(5):821-849, 2013.
Martin Simonovsky and Nikos Komodakis. GraphVAE: Towards generation of small graphs using variational autoencoders. In ICANN, 2018.
F. Skopik, G. Settanni, R. Fiedler, and I. Friedberg. Semi-synthetic data generation for security software evaluation. In PST, 2014.
Sahar Tavakoli, Alireza Hajibagheri, and Gita Sukthankar. Learning social graph topologies using generative adversarial neural networks. SBP, 2017.
Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks. In ICLR, 2018.
Hongwei Wang. Jia Wang, Jialin Wang, Miao Zhao, Weinan Zhang, Fuzheng Zhang, Xing Xie, and Minyi Guo. GraphGAN: Graph representation learning with generative adversarial nets. In AAAI, 2018.
Tian Xie and Jeffrey C. Grossman. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett., 120:145301, 2018.
Carl Yang, Peiye Zhuang, Wenhan Shi, Alan Luu, and Pan Li. Conditional structure generation through graph variational generative adversarial nets. In NeurIPS, 2019.
Zhitao Ying, Dylan Bourgeois, Jiaxuan You, Marinka Zitnik, and Jure Leskovec, GNNExplainer: Generating explanations for graph neural networks. In NeurlPS, 2019.
Jiaxuan You, Rex Ying, Xiang Ren, William Hamilton, and Jure Leskovec. GraphRNN: Gener- ating realistic graphs with deep auto-regressive models. In ICML, 2018.
Dawei Zhou, Lecheng Zheng, Jiejun Xu, and Jingrui He. Misc-GAN: A multi-scale generative model for graphs. Frontiers Big Data, 2:3, 2019.
Jan Ruben Zilke, Eneldo Loza Mencía, and Frederik Janssen. DeepRED - rule extraction from deep neural networks. In Discovery Science, 2016.
Dongmian Zou and Gilad Lerman. Encoding robust representation for graph generation. IJCNV, 2019.
10

---

Under review as a conference paper at ICLR 2021
APPENDIX
A. IMPLEMENTATION DETAILS
The SHADOWCAST model incorporates sequence- serpueenne----squunnee (Seq2Seq) learner, generator, and a discriminator.
Shadow Caster (Seq2Seq) In the sequence-to-sequenee model, for all three datasets. The input of this LSTM batch shadow walk sequences length n and dimension d, where the batch size is 128, walk length 16, and dimension is set the number of classes K in each dataset (128 x 16 x d). We select the walk length as 16 because it should capture structures of most graphs of different sizes. The LSTM hidden layer with 10 memory units should be more than sufficient to learn this problem. A dense layer with Softmax activation is connected to the LSTM layer, and the generated output is batch of sequences with size (128 x 16 x d).
an LSTM with 10 cells
Generator In the generator, we use a conditional LSTM with 50 layers. We follow a similar ar- chitecture NetGAN to generate sequences of walks the graph nodes. Different from NetGAN, our generator not only initializes the model with Gaussian noise, but also takes the shadow walks conditions each step of the process. Interestingly, sensitive to the input conditions than hyperparameters for performance. Hence, the set of hyperpa- rameters for the generator is the same for all the datasets. We summarize the generative process of G' in the box below. We note that the conditional generative process is similar to the unconditional process of NetGAN, with the addition of conditions & in each timestep.
notice that the LSTM generator is more
~~ N0 Ia)
mg (x)
fo(mo, (Pi.m.). m.).
1 Cat(ar(pi)
[a(m: 82, vn) = (p2, me).
by ~ Cat(a(pa))
fo(me 1.81, By my):
By ~ Cat(a((r))
Discriminator Our discriminator is an LSTM with 40 layers. The inputs are sequences of graph nodes concatenated with the respective conditions. The discriminator has similar architecture the shadow caster, where they are LSTM models that take sequences as inputs, expect that the LSTM layer is connected to final dense layer. The output is a single value between O and 1, which distinguishes real sequences from generated ones.
In the SHADOW training, we use Adam optimizers for all the models. The learning rate of the shadow caster use learning rate of 0.0002.
training is 0.01, while both the generator and the discriminator
B. BASELINES
CondGEN, We use the official PyTorch implementation
Kelestz/ C/nddGen). However, CondGEN is designed to leam distribution over mul- tiple small graphs. To ensure a fair comparison, we modify it to train on randomly selected 85% of the edges in graph, validate on the remaining 15%, and generate graphs
GraphRNN. We use the official PyTorch implementation (https: /i htt//gttuuieee thub.com/ of GraphRNN. The default hyperparameter set- tings were used in all our experiments.
JiaxuanYou/ Sataxuuanoougrrahhhaaaaa http://aaaaagggggaigooooo
GVAE. To compare with Graph VAE (no public code available), we adapt the reference implementation provided by Yang et al. (2019) in their experiments for single graph and use the suggested hyperparameter settings.
NetGAN, We use the official TensorFlow implementation provided by the authors bttips://github..cmm www.ro/daaineeeneneaeeee //et following the recommended hyperparameter settings. We set random walk length to 16, learning rate to 0.0003, generator L2 penalty to le-7, and discriminatos L2 penalty to 5e-5.
11

---

Under review as a conference paper at ICLR 2021
C. DATASETS
Details of the datasets are listed below (see Table 2
Dataset
Naer
Exce::
K classes
K distribution
Coro-Mi
2810
7981
?
EU top
348
3342
5
Table 2: Statistics of datasets. In the largest connected component (LCC) of each dataset, Nr.co: is the number of nodes, Eycc the edges, and K number of total classes. The distribution of the classes is shown in the corresponding histograms.
EUcore-top: An email communication network we created that consists of the top five largest departments in the EU-core dataset (Leskovec et al. (007). For all nodes in the graph, a person i sends at least one email to person J. then there exists an edge (i.j) between the two nodes. Each node belongs exactly one department. We sort the data by the intra-department email counts in descending order. The list of top five departments is {14, 4, 1, Link here: http://snap.stanforddeee dat a /emmaimllll..... core.html
Enron: It is the Enron Corporation email corpus dataset (Perry & Wolle 2013), where edge exists between any two nodes long they share at least one email. Link here: http:://ihhaab..ccooo/pprtrtrter
ftrec/msster/data/ennoo
Cora-ML: A scientific publication citation dataset (Bojchevski & Günnemann 2018 consisting of machine learning papers. Link here:
abo
D. EXPLAINING GENERATED GRAPHS
We provide the Markov model parameters, initial probability distribution π (x1, T2, Ts) and transition probability matrix A (011012... O31 ... Azs). used in our experiments.
10
00
-30
-05
85
85
10
Observed: Enron normal operations
12

---

Under review as a conference paper at ICLR 2021
65
-05
-15
Generated:
Legal (red) internal surge
Initial probability distribution: π
[0.9. 0.05, 0.05]
Transition probability matrix:
[0.9, 0.05, 0.05,, [0.1, 0.6, 0.3), [0.0, 0.1,
10
00-
-10
-10
-05
60
05
10
Generated:
Finance (green) internal surge
Initial probability distribution: π [0.05, 0.05, 0.9
Transition probability matrix: A 0.1,0.6, 0.3), [0.05, 0.05, 0.9]]
-10
-10
05
65
65
16
Generated:
Trading (blue) outgoing surge
Initial probability distribution: π [0.05, 0.9, 0.05
Transition probability matrix: [0.9,0.1,0.0, [0.25, 0...0... 0.250. [0.0, 0.1, 0.9]
13


Reviews:
[{"review_id": "zmJjXVJNrVF", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper introduces a graph generation method that aims at mimicking the structure of a given graph but meanwhile maintaining the possibility of altering it (\"controllable\" in the authors' wording).\n\nThere appears a strong footprint of NetGAN (Bojchevski et al., 2018) in the proposed method. NetGAN learns a distribution of random walks on the given graph, so that synthetic walks are generated and assembled to form a new graph. This paper differs from NetGAN in that the sampling of the walks is conditioned on certain \"shadow\" information outside the graph structure (e.g., community labels).\n\nOne weakness of this paper is that the presentation is rather verbose but still not to the point. For example, the authors heavily use several concepts that are vague and whose meanings are not clear until deep into the paper. These concepts include \"explaining graph generation\", \"controlling the generative process\", and \"shadow\". As another example, the definition of \"explainable graph generation\" in page 3 is nearly a verbatim copy of the prior sentence, while leaving the reader wondering what \"generate explainable graphs\" actually means. I also doubt if it is worthwhile to state two future works in the problem formulation section.\n\nWhile the authors have done a reasonable job to show that their method generates a realistic graph (which is expected because the core of the method is NetGAN) when the controlled condition comes from the original data, it is concerning what actually happens when the condition is altered (e.g., favoring more links among a certain community). It is challenging to measure the effectiveness and the reader has not been convinced yet the proposed method shows advantage. For example, following Figure 3(b), to generate the effect of \"legal (red) internal surge\", how does the proposed method compare with naively adding random edges to the \"legal\" cluster? What is missing is a convincing account of why the proposed method makes sense and outperforms others.\n\nMinor comments:\n\n- Replace Table 1 by Table 3 in the appendix. Standard errors are important.\n\n- What the proposed method can control appears to be exogenous of the graph structure (e.g., node attributes). Hence, it appears unlikely that one can use the graph structure as the controllable condition. For example, I am skeptical that the proposed method can generate a graph that leans toward a desired degree distribution.", "extra_scores": {}, "extra_text": {}}, {"review_id": "T97Qo4W-U-I", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper is clearly written, ideas are well presented, and it is easy to follow the pipeline of the method. One highlight of the paper is the shadow network, which can carry multi-modal auxiliary information. Not only semantic features but also graph statistics can be considered during the generating process, and explainable graphs are constructed accordingly. As a minor comment, I would suggest the authors giving more details on the proposed Shadow Cast part and fewer details on the generator and discriminator part, as they are quite similar to the NetGAN setting. \n\nHowever, there are three major concerns of the paper:\n1.\tIn the proposed model, synthetic shadow walks are directly translated from real sampled shadow walks. Since both input and output sequences carry the homogeneous information, it could be easy and less challenging for the seq2seq model to mimic the original shadow walk. It would be interesting to see the shadow walk is predicted from some prediction function (e.g., predict from a set of real shadow walks). \n2.\tIn the experiment part, baseline methods are mostly designed for generating graphs unconditionally except for CondGen. These baselines may indeed not be comparable in the conditional generation task. In addition, there are other conditional graph generative methods [1, 2] proposed in recent years. The authors should consider to add them as baseline methods to validate their performance. \n3.\tFollowing the second concern, the survey of the related work is not comprehensive. There are other lines of works trying to generate the node and edge attributes of the target graph conditioning on input graphs. Authors may consider further address the difference of the proposed model.\n\nTo conclude, the contribution of the paper seems to be limited if the shadow network is constructed only on node class. It would be more comprehensive to leverage other node properties to build shadow network and generate graphs.   \n\n[1] Guo, Xiaojie, et al. \"Deep Multi-attributed Graph Translation with Node-Edge Co-evolution.\" 2019 IEEE International Conference on Data Mining (ICDM). IEEE, 2019.\n[2] Jin, Wengong, et al. \"Learning multimodal graph-to-graph translation for molecular optimization.\" arXiv preprint arXiv:1812.01070 (2018).\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "LlWHDeC9cL1", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper proposes a novel problem - explainable graph generation,  and proposed a controllable generative model to mimic network structures as well as network properties. In particular, the proposed model, SHADOWCAST, is developed based on the recent proposed graph generative model NetGAN, and exploits the auxiliary information to guide the generation process. Experimental results on a bunch of real-world networks show the performance of the proposed algorithm. In general, I believe the problem is novel, and the paper is well-motivated and well-written.  My major concern is the paper lacks some insightful discussion to support the rationality of the proposed model. Here are the detailed comments: \n\n[Novelty] The studied problem of this paper - explainable graph generation - is novel. However, it seems the proposed algorithm is more about the generation of attributed networks (Please correct me here if I am wrong). If yes, I believe there are a series of attributed graph generators in the literature, ranging from random graph models to deep graph generative models. \n\n[Literature Review] I am not sure whether it is a standard way for ICLR that the paper can be presented without a section of related work. Two of my review paper have the same problem,  but I am not a fan of it. It would largely help reviewers with less background knowledge to appreciate your work and shed light on the connection between your proposed model to the existing methods. \n\n[Algorithm] In general, I feel the architecture of the proposed model is highly similar to NetGAN. Moreover, on Page 5, it seems the box showing the generative process is directly copied from NetGAN, which is not very professional. \n\n[Experiments] According to Tabel 1 in the experiments, the proposed method achieves the best performance across 3 datasets and 6 network properties. It is interesting to me why the proposed method can outperform NetGAN with a large margin. Some insightful discussions shall be provided. \n\nOverall, I still lean positive to this paper for its novel problem and strong results. But, without clear my concerns above. I vote for weak rejection. \n\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "20DP2kTpDH9", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Strengths: \n1. The motivation of this paper that controls the graph generation is interesting.\n2. Most recent papers on graph generation are listed.\n\nWeakness:\n1. In the vanilla GAN, the generator only takes standard normal distribution as the input to generate the synthetic data and it gradually learns the data distribution by back-propagation. However, the generator in this paper takes the shadow information \\hat{S_t} and standard normal distribution as the inputs and generate the synthesized random walks. I am worried that the generator might learn the data distribution directly from the shadow information rather than through the adversarial training. In other word, I am curious whether it is due to the additional information or the shadow information that the generator could generate the synthesized random walks as genuine as the real random walks. \n2. This paper is similar to NetGAN in terms of both generator and discriminator, and thus, the novelty of this paper is limited.\n3. There is a trade-off between the controllability of the graph generation and the quality of the synthesized graph. When we try to control the graph generation to achieve the desired structure, then the quality of the synthesized graph diminishes, because the desired graph might be very different from the original graph. However, it seems that in the experiment, the synthesized graph generated by proposed method is the closest to the statistics of the original graph, which is not well justified.", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposed a conditional graph generative model closely following the unconditional generative model NetGAN and extending it by adding conditioning on extra information available for graph generation (“shadow” node attributes as the authors call it).  Overall this is an extension over NetGAN and gives this class of models the ability to utilize extra information when generating graphs.

However, all reviewers lean toward the reject side and the concerns raised by the reviewers range from limited novelty to the could-be-improved writing.

I want to highlight two issues.  The first is, is the GAN formulation really necessary?  Could you directly learn using a likelihood objective, e.g. treat the sampled random walks as sequence data, and learn an autoregressive sequence generative model on these data (as a language model for example)?  You could then also generate sample walks from your model.  The benefit is training would be much simpler and more stable.  I believe this could also be related to R2’s concern that the model might be learning the distribution from s alone, as that is entirely possible and potentially easier (not with the GAN formulation proposed here, though).

The second issue is that I encourage the authors to dig deeper into explainability.  The notion of explainability is obviously important but it is not very well defined.  Does controllability equal explainability?  Is a visualization sufficient to demonstrate explainability (and further, is this sufficient to show this method offers more explainability than alternatives)?  Also intuitively random walk models are not very explainable due to the large amount of randomness in the generation process, compared to e.g. autoregressive graph generative models that generate graphs part-by-part (related to R1’s concern).  If explainability is the main motivation, maybe other alternatives can be more competitive.

Overall I would recommend a reject at this time but encourage the authors to improve the paper further.
Decision: Reject