Inf-VAE: A Variational Autoencoder Framework to IntegrateHomophily and Influence in Diffusion Prediction

Aravind Sankar, Xinyang Zhang, Adit Krishnan, Jiawei Han

University of Illinois at Urbana-Champaign, IL, USA

{asankar3, xz43, aditk2, hanj}@illinois.edu

ABSTRACTRecent years have witnessed tremendous interest in understanding

and predicting information spread on social media platforms such

as Twitter, Facebook, etc. Existing diffusion prediction methods pri-

marily exploit the sequential order of influenced users by projecting

diffusion cascades onto their local social neighborhoods. However,

this fails to capture global social structures that do not explicitly

manifest in any of the cascades, resulting in poor performance for

inactive users with limited historical activities.

In this paper, we present a novel variational autoencoder frame-

work (Inf-VAE) to jointly embed homophily and influence throughproximity-preserving social and position-encoded temporal latentvariables. To model social homophily, Inf-VAE utilizes powerful

graph neural network architectures to learn social variables that

selectively exploit the social connections of users. Given a sequence

of seed user activations, Inf-VAE uses a novel expressive co-attentivefusion network that jointly attends over their social and temporal

variables to predict the set of all influenced users. Our experimental

results on multiple real-world social network datasets, including

Digg, Weibo, and Stack-Exchanges demonstrate significant gains

(22% MAP@10) for Inf-VAE over state-of-the-art diffusion predic-

tion models; we achieve massive gains for users with sparse activi-

ties, and users who lack direct social neighbors in seed sets.

CCS CONCEPTS• Information systems→ Social networks; •Computingmethod-ologies → Neural networks;

KEYWORDSSocial Network, Diffusion, Deep Learning, Autoencoder, Attention

ACM Reference Format:Aravind Sankar, Xinyang Zhang, Adit Krishnan, Jiawei Han. 2020. Inf-VAE: A

Variational Autoencoder Framework to Integrate Homophily and Influence

in Diffusion Prediction. In The Thirteenth ACM International Conference onWeb Search and Data Mining (WSDM ’20), February 3–7, 2020, Houston, TX,USA. ACM, New York, NY, USA, 9 pages. https://doi.org/10.1145/3336191.

3371811

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1 INTRODUCTIONIn social media, information disseminates or diffuses to a large num-

ber of users through posting or re-sharing behavior, resulting in

a cascade of user activations, e.g., a user voting a news story on

Digg (a social news sharing website) triggers a series of votes from

multiple users, who may be his friends or other users interested in

the same story. Given a set of activated seed users, diffusion models

aim to predict the set of all influenced users. Diffusion modeling

has widespread social media applications, including viral market-

ing [24], recommendations [22, 23], and popularity prediction [51].

The diffusion prediction problem has received significant atten-

tion in the research community. Unlike pre-defined propagation

hypotheses [18], recent methods learn data-driven diffusion models

from collections of user activation sequences (diffusion cascades).Existing diffusion models broadly fall into two categories.

Probabilistic generative cascade models use hand-crafted features

including roles [47], communities [4], topics [3], and structural pat-

terns [49]. Such methods rely on feature engineering that requires

manual effort and extensive domain knowledge, and are limited by

the modeling capacity of carefully chosen probability distributions.

Representation learning methods avoid feature extraction by

learning user embeddings characterizing their influencing abil-

ity and conformity [7, 9]. State-of-the-art methods project cas-

cades onto local social neighborhoods to generate Directed Acyclic

Graphs (DAGs), and propose extensions of Recurrent Neural Net-

works (RNNs). In particular, DAG-structured LSTMs [41] explicitly

operate on the induced DAG, while attention-based RNNs [17, 43,

44] implicitly consider cross-dependence for diffusion prediction.

Prior works only consider the sequence or projected social struc-

ture (induced DAG) of previously influenced users while ignoring

social structures that do not manifest in cascades. As a result, theyonly capture the temporal correlation of diffusion behaviors among

users, which is also known as temporal influence or contagion [37].

Consider a Twitter user with interests in politics, who is likely to

follow famous political leaders and join interest groups that induce

transitive connections to other users; however, these connections

may not appear in cascades unless she re-tweets or posts content.

Social homophily [27] suggests that ties are more likely between

users with shared traits or interests, which can induce correlated

diffusion behaviors without direct causal influence. Since a vast

majority of social media users seldom post content and thus rarely

appear in cascades, it is critical to exploit their social neighborhood

structures to characterize social homophily accurately.

However, homophilous diffusion and contagion can result in sig-

nificantly different dynamics, e.g., contagions are self-reinforcingand viral while homophily hinges on users’ preferences or traits.

Real-world cascades are often a complex combination of both as-

pects with user-specific variations. Indeed, it is well known that

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social homophily and temporal influence are fundamentally con-

founded in observational studies [37]. Thus, we propose a data-

driven framework to contextually model their joint effect when

predicting user-level diffusion behaviors. Therefore, our key ob-

jective is to develop a principled neural framework to unify socialhomophily and temporal influence in diffusion prediction.

Our architecture Inf-VAE jointly models homophily through so-cial embeddings preserving social network proximity and influencethrough temporal embeddings encoding the relative sequential

order of user activations. Motivated by the recent successes of vari-

ational autoencoders (VAEs) [19] in characterizing sparse users via

Gaussian priors [26], and the expressive power of graph neural net-

works [14, 21], we adopt VAEs to model social homophily. We learn

structure-preserving social embeddings through a VAE framework

that supports a wide range of graph neural network architectures

as encoders and decoders. Given an initial set of seed user acti-

vations, Inf-VAE utilizes an expressive co-attentive fusion networkthat captures complex non-linear correlations between social and

temporal embeddings, to model their joint effect on predicting the

set of all influenced users. We make the following contributions:

• GeneralizableVariationalAutoencoder Framework: Unlikeexisting diffusion prediction methods that only consider local

induced propagation structures, Inf-VAE is a generalizable VAE

framework that models social homophily through graph neu-

ral network architectures of arbitrary complexity, to selectively

exploit the rich global network of social connections.

• Efficient Homophily and Influence Integration: To the bestof our knowledge, ours is the first work to comprehensively

exploit social homophily and temporal influence in diffusion pre-

diction. Given a sequence of seed user activations, Inf-VAE em-

ploys an expressive co-attentive fusion network to jointly attend

over their social and temporal embeddings to predict the set of

all influenced users. Inf-VAE with co-attentions is faster than

state-of-the-art recurrent methods by an order of magnitude.

• Robust Experimental Results: Our experiments on multiple

real-world social networks, including Digg, Weibo, and Stack-

Exchanges, demonstrate significant gains for Inf-VAE over state-

of-the-art models. Modeling social homophily through VAEs

enables massive gains for users with sparse activities, and users

who lack direct social neighbors in seed sets. An ablation analysis

of various modeling choices further highlights the synergistic

effects of jointly modeling homophily and temporal influence.

2 RELATEDWORKWe discuss existing work on diffusion modeling followed by related

work on network representation learning and co-attentions.

Information diffusion overview.Historically, information dif-

fusion has been studied through two seminal models: Independent

Cascade (IC) [18] and Linear Threshold (LT) [11]. Three distinct

applications emerged, namely: network inference [10], which in-

fers the underlying social network that best explains the observed

cascades; cascade prediction [25], which predicts macroscopic prop-

erties of cascades, including size, growth, and shape; and diffusionprediction [41], which learns a model from social links and cascade

sequences, to predict the set of influenced users given a seed set of

activated users. In this paper, we focus on diffusion prediction.

Diffusion prediction. The earliest data-driven methods pro-

pose several extensions of IC and LT incorporating topics [3], con-

tinuous timestamps [31], user profiles [32], and community struc-

ture [4]. A few techniques explore probabilistic generative models

via latent topics and communities [16, 50]. Most recent studies focus

on learning representations to overcome feature engineering or pre-

defined hypotheses in diffusion modeling [6, 7, 9, 30, 41–44]. Emb-

IC [7], Inf2vec [9] embed user influencing capability and suscepti-

bility in diffusion. Topo-LSTM [41], CYAN-RNN [43], SNIDSA [44],

and DeepDiffuse [17] project the diffusion cascades on local social

neighborhoods and model the resulting DAG propagation struc-

tures with RNNs. These techniques outperform classical approaches

by significant margins in diffusion prediction. Our key observation

is that these projected DAGs could ignore social structures that

do not appear in any observed cascade. In contrast, our model Inf-

VAE can account for unobserved social connections in the user

activation process by modeling social homophily through VAEs.

A related problem is social influence prediction, which aims to

classify social media users based on the activation status of their

ego-network [30, 48]. Direct extensions to predict the set of all in-

fluenced users (diffusion prediction) entails reapplying their models

on each candidate inactive user in the social network, resulting in

prohibitive inference costs, hence preventing a comparison.

Network representation learning: This line of work capturesvaried notions of structural node proximity [12, 33] in networks

via low-dimensional vectors. Notably, graph neural networks have

achieved great success in node classification and link prediction [13,

21, 28, 34–36, 39]. Graph Autoencoders [20, 40] employ various en-

coding and decoding architectures to embed network structure and

learn unsupervised node embeddings. Hamilton et al. [14] unify

a large family of network embedding methods in an autoencoder

framework. However, general-purpose embeddings modeling struc-

tural proximity are not directly suited to diffusion modeling.

Co-attentional models: Our work also leverages recent ad-

vances in neural attention mechanisms, especially in Natural Lan-

guage Processing [2]. Specifically, co-attention has achieved great

success in modeling relationships between pairs of sequences, e.g.,question-answer [45], etc. Co-attentional methods compute inter-

action weights between data modalities, learning fine-grained non-

linear correlations. In our work, we develop a co-attentive fusion

network to capture the contextual interplay of users’ social and

temporal representations for diffusion prediction.

3 PROBLEM DEFINITIONWe study diffusion prediction where the goal is to predict the set of

all influenced users, given temporally ordered seed user activations.

Definition 3.1. Social Network: The social network is repre-

sented as a graph G = (V, E) where V = {vi }Ni=1 is the set of Nusers and E = {ei j }Ni, j=1 is the set of links. We denote the adjacency

matrix of G by A ∈ RN×Nwhere Ai, j = 1 if ei, j ∈ E otherwise 0.

Definition 3.2. Diffusion cascade: A diffusion cascade Di is an

ordered sequence of user activations in ascending order of time

denoted by: Di = {(vik , tk ) | vik ∈ V, tk ∈ [0,∞), k = 1 . . .K},eachvik is a distinct user inV (no repeats) and tk is non-decreasing,

i.e., tk ≤ tk+1. The kth

user activation is recorded as tuple (vik , tk ),referring the activated user and activation time.

We represent cascades by delay-agnostic relative activation or-

ders similar to [7, 9, 41], i.e., a cascade is equivalently written as

D = {(vik ,k) | vik ∈ V}Kk=1. We do not assume the availability of

explicit re-share links between users in cascades; this corresponds

to the simplest yet most general setting of diffusion [9, 41]. Though

timestamps may be easily used as input features, we leave genera-

tion of continuous timestamps as future work.

Definition 3.3. Diffusion prediction: Given a social networkGand a collection of cascade sequences D = {Di , 1 ≤ i ≤ |D|}, learndiffusion modelM to predict the future set of influenced users in a

cascadewith the seed activation sequence I = {(vi1 , 1), . . . , (vik ,k)}of k seed users. Diffusion prediction estimates the probability of

influencing each inactive user: PΘ(v | I ) ∀v ∈ V − I , inducing a

ranking of activation likelihoods over the set of inactive users.

We create a training set T of diffusion episodes containing (seed

activations, activated users) tuples from the cascade collection D,by randomly splitting each cascade D ∈ D of length K at each time

step 2 ≤ k ≤ K − 1. Specifically, a split at time step k ≥ 2, creates a

training episode (Ik ,Ck ) where Ik = {(vi j , j); 1 ≤ j ≤ k} is the seedset consisting of the cascade sliced at k and Ck = {vik+1 , . . . ,viK }is the set of influenced users after time step k . Thus, we denote thetraining set by T = {(Ii ,Ci ) 1 ≤ i ≤ |T|}.

4 INFLUENCE VARIATIONALAUTOENCODER

In this section, we describe our proposed Influence Variational

Autoencoder (Inf-VAE) for predicting information diffusion.

4.1 Model DescriptionWe describe the latent variables modeling social homophily and

temporal influence, followed by our generative network Inf-VAE.

4.1.1 Social Homophily. Our objective is to define latent socialvariables for users that capture social homophily. The homophily

principle stipulates that users with similar interests are more likely

to be connected. In the absence of explicit user attributes, we posit

that highly interconnected users in social communities share ho-

mophilous relationships. We model social homophily through la-

tent social variables designed to encourage users with shared social

neighborhoods to have similar latent representations.

Specifically, we assign a latent social variable zi for uservi , wherethe prior for zi is chosen to be a unit normal distribution, in linewith

standard assumptions in VAEs. Normal distributions are chosen

in VAE frameworks due to their flexibility to support arbitrary

functional parameterizations by isolating sampling stochasticity

to facilitate back-propagation [19]. We assume the latent social

variables Z to collectively generate the social network G, through a

graph generation neural network fdec(Z ) parameterized by θ . Thecorresponding generative process is given by:

zi ∼ N(0, ID ) G ∼ pθ (G | Z ) = pθ (G | fdec(Z )) (1)

where ID ∈ RD×Dis an identity matrix of D dimensions. Here, the

graph generation neural network fdec(Z ) can be instantiated to

preserve an arbitrary notion of structural proximity in the social

network G (Sec 4.3). In the above equation, we abuse the notation

of G to denote an appropriate representational form of the social

Symbol Description

Z Social variables modeling network proximity, for all users VVS Sender variables for all users VVR Receiver variables for all users VVT Temporal influence variables for all users VVP User-specific popularity variables for all users VPK Position-encoded temporal embeddings for all time steps K

Table 1: Notations

network structure, which can take multiple forms, including the

adjacency matrix, random walks sampled from G, etc.

While homophily characterizes peer-to-peer interest similarity,

its impact on user behaviors tends to asymmetric since users who

share interests may drastically differ in their posting rates, e.g., cer-tain users are naturally predisposed to be socially active and hence

more influential in comparison to others. Thus, it is necessary to dif-

ferentiate user roles when modeling the effect of social homophily

on diffusion behaviors. Similar concepts have been examined in

social influence literature to characterize users by their influencing

capability and conformity [7–9, 41, 42].

We associate each user vi ∈ V with a sender vsi ∈ RD and

receiver vri ∈ RD latent variable. Our key innovation lies in condi-

tioning the information sending and receiving capabilities of users

on their homophilous traits. We use normal distributions centered

at zi to define the sender and receiver variables for user vi as:

vsi ∼ N(zi , λ−1s ID ) vri ∼ N(zi , λ−1r ID ) (2)

where λs , λr are hyper-parameters controlling the degree of varia-

tion or uncertainty for vsi and vri w.r.t. zi . LetVS andVR denote the

set of all sender and receiver variables respectively for all users.

4.1.2 Temporal Influence. Now, we define latent temporal influ-ence variables to describe the varying influence effects of seed usersdepending on the relative sequential order of activations. There

are two interesting factors at play: activation orders and popularity

effects. A majority of social media users adopt more recent infor-

mation while often ignoring old and obsolete content [46]. On the

other hand, social status impacts the influencing power of seed users

independent of their activation order and social neighbors, e.g., fa-mous media figures naturally exert significant influence. Thus, we

consider both the relative sequential order of user activations and

popularity effects of seed users to model temporal influence.

To quantify the temporal influence exerted by a seed user activa-

tion (vik ,k) of user vik at time step k (1 ≤ k ≤ K ), we first encodethe relative position k through positional-encodings [38] to obtain

temporal embeddings pk . Since we expect the variation in popu-

larity effects to be quite small, we draw user-specific popularity

variables from a zero-mean normal distribution to serve as offsets

to the temporal embeddings. Specifically, the temporal influencevariable for activation (vik ,k) denoted by vtik , is given by:

vpik ∼ N(0, λ−1p ID ) pk = PE(k) vtik = vpik + pk (3)

PE(k)2d = sin(k/100002d/D ) PE(k)

2d+1 = cos(k/100002d/D )where λp is a hyper-parameter to control the popularity effects, and

1 ≤ d ≤ D/2 denotes the dimension in the temporal embedding

pk . Note that the popularity variable vpik is user-specific, while

temporal embedding pk only depends on the activation step k . The

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co-attention

Variational Graph Autoencoder Co-attentive Diffusion Prediction Predicted Users

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vtik

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Receiver

Sender

Social

Figure 1: Neural Architecture of Inf-VAE depicting latent variable interactions. The left side indicates the VAE framework tomodel social homophily; right side denotes the co-attentive fusion network to integrate the social and temporal variables.

set of all latent user popularity variables are denoted by VP , whilePK represents the set of position-encoded temporal embeddings.

4.1.3 Co-attentive Diffusion Episode Generation. Let us con-sider a single diffusion episode (I ,C) ∈ T, with seed activations I ={(vi1 , 1), . . . , (vik ,k)} and influenced usersC = {vik+1 , . . . ,viK }. Adiffusion model aims to predict the set of influenced users C given

seed activations I . Since diffusion is always conditioned on I , wepropose a conditional generative process to sample C given I .

Let us denote the set of seed users by IU = {vi1 , . . . ,vik }. Ourobjective is to jointly model the effects of social homophily and

temporal influence exerted by seed users IU , which can be summa-

rized by: sender sequence (vsi1 , vsi2, . . . , vsiK

); and temporal influencesequence (vti1 , v

ti2, . . . , vtiK

). To model complex correlations between

the sender and temporal influence sequences, we propose an expres-

sive co-attentive fusion strategy to learn attention scores for each

seed user by modeling interactions between the two sequences. We

describe the conditional generative process in two steps:

• The social homophily and temporal influence aspects of seed

users, are integrated into an aggregate seed set representation hI .The co-attentive fusion network Gdiff(·) performs homophily-

guided temporal attention, i.e., attends over the temporal influ-

ence variables by computing co-attentional weights that jointly

depend on both homophily and temporal influence characteris-

tics. As illustrated in Figure 1, the sender and temporal influence

variables of seed users feed into a fusion networkGdiff(vsik , vtik).

The aggregate seed representation hI is computed as:

αk =exp(Gdiff(vsik , v

tik(k)))

K∑j=1

exp(Gdiff(vsi j , vti j(j)))

hI =K∑j=1

α jvti j (j) (4)

Each α j is the normalized co-attentional coefficient for seed user

vik denoting its contribution in computing the aggregate repre-

sentation hI . To model the co-dependence between vsi , vti , we de-

fine the co-attentive functionGdiff(vsik , vtik) = tanh(vsik

TW vtik )as a bi-linear product parameterized byW ∈ RD×D

.

• The probability of influencing an inactive uservj depends on the

sending capacity of seed users (embedded in hI ) and her receivingcapability (encoded by receiver variable vrj ). We quantify the

likelihood of influencing vj by hTI vrj . For each inactive user vj ∈

V− IU , we draw a binary variable Cj ∈ {0, 1} indicating whetheruser vj is influenced by set users IU or not, given by:

Cj ∼ Ber (σ (hTI vrj )) ∀vj ∈ V − {vi1 , . . . ,viK } (5)

where σ (·) is the sigmoid function and Ber (·) is the Bernoulli dis-tribution. The corresponding logistic log-likelihood of generating

a single diffusion episode (I ,C) is given by:

Ldiff

I,C = logpθ (C | I ,VS ,VR ,VP ) (6)

=∑v ∈C

η log(σ (hTI vri )) +

∑vn ∈V−C−IU

log(1 − σ (hTI vrn ))

Here, η re-weights positive examples since the actual number of

influenced users is much smaller than the total number of users.

4.2 Model LikelihoodDue to the intractability of analytically computing the latent poste-

rior distribution p(VS ,VR ,VP ,Z |G,T), we use variational inferenceto factorize the posterior with a mean-field approximation:

q(VS ,VR ,VP ,Z |G) = q(VS )q(VR )q(VP )q(Z |G) (7)

The variational distributions of variables VS ,VR , and VP follow

normal distributions while the social variablesZ are conditioned on

G through a structure-encoding inference network [19]. Specifically,

the variational distribution of Z denoted by qϕ (Z |G), is a diagonalnormal distribution parameterized by fenc(G) defined as:

fenc(G) ≡ [µϕ (G), logσ 2

ϕ (G)] qϕ (Z |G) = N(µϕ (G),diaд(σ 2

ϕ (G)))

The inference network outputs the parameters, µϕ (G),σϕ (G) ofthe variational distribution qϕ (Z |G), which is designed to approxi-

mate the corresponding posterior p(Z |G). The inference networkfenc(G) endows the model with added flexibility to incorporate

arbitrary neighborhood aggregation functions such as graph convo-

lutions [21], attentions [39], etc. The variational structure distribu-

tion qϕ (Z |G) and the structure generative model pθ (G|Z ) (Eqn. 1)together constitutes a variational graph autoencoder [20].

4.3 Neural Graph Autoencoder DetailsIn this section, we describe functions fenc(G) and fdec(Z ) whichdescribe the graph structure inference and generative networks

of Inf-VAE. The encoder summarizes local social neighborhoods

into latent vectors, which are subsequently transformed by the de-coder into high-dimensional structural information (e.g., adjacencymatrix). Hamilton et al. [14] present an encoder-decoder framework

to conceptually unify a large family of graph embedding methods.

Encoder architectures fall into three major categories: embedding

lookups [12, 29], neighborhood vector encoding [40], and neighbor-

hood aggregation [13], while decoders comprise unary and pairwise

variants. In Inf-VAE, we explore two representative choices:

• MLP + MLP: We use a Multi-Layer Perceptron (MLP) to both

encode and decode the laplacian matrix of G, given by L =

D−1/2AD−1/2. The neighborhood vector for user vi , denoted by

ai , is the ith row of L = [a1, . . . , aN ]T . The encoder is an MLP

network fenc(ai ) which encodes ai into zi , while the decoderfdec(zi ) strives to reconstruct ai from zi . We introduce a re-

weighting vector bi = {bi j }Nj=1 where bi j = 1 if Li j = 0 and

bi j = β > 1 when Li j > 0. β is a confidence parameter that re-

weights the positive terms (Li j > 0) to balance the unobserved 0′s

which far outnumber the observed links in real-world networks.

The generative process to obtain ai from zi is given by:

ai ∼ pθ (ai |zi ) = N(fdec(zi ),diaд(bi ))where diaд(bi ) is a diagonal matrix with non-zero entries from

vector bi . The corresponding Gaussian log-likelihood is given by:

logpθ (A|Z ) =N∑i=1

logpθ (ai |zi ) =N∑i=1

bi ⊙ (ai − fdec(zi )) 2

• GCN + Inner Product: We use a Graph Convolutional Network

(GCN) as the encoder and an inner product decoder that maps

pairs of user embeddings to a binary indicator of link existence

in G. The GCN network comprises multiple stacked graph con-

volutional layers to extract features from higher-order structural

neighborhoods. The input to a layer is a user feature (or embed-

ding) matrix X ∈ RN×Fand a normalized adjacency matrix

ˆA,where each GCN layer computes the function:

fenc(A) = σ ( ˆAXW ) ˆA = D−1/2AD−1/2 + IN

whereX is an identity matrix encoding user identities. Each entry

Ai j of adjacency matrix A is generated according to:

Ai j ∼ pθ (Ai j |zi , zj ) = Ber (σ (zTi zj ))Similar to above, we re-weight the positive entries of A with a

confidence parameter β . The logistic log-likelihood is given by:

logpθ (A|Z ) =∑

(i, j)∈Eβ log(σ (zTi zj )) +

∑(i, j)<E

log(1 − σ (zTi zj ))

As an alternative to re-weighting positive entries, negative sam-

pling [29] can scale this objective to large-scale networks.

4.4 Model InferenceThe overall objective maximizes a lower bound on the marginal log

likelihood, also named evidence lower bound (ELBO) [5], given by:

Lq = Eq [logp(G,T,VS ,VR ,VP ,Z ) − logq(VS ,VR ,VP ,Z |G)] (8)

Note that Lq is a function of both generative (θ ) and variational

(ϕ) parameters. However, an analytical computation of the expec-

tation with respect to qϕ (Z |G) is intractable, while Monte Carlo

Algorithm 1 Inf-VAE training with block coordinate ascent.

Input: Social Network (G), Training episodes (T)Output: MAP estimates of VS ,VR ,VP and parameters θ ,ϕ.1: Initialize latent variables from a standard normal distribution.

2: Pre-training: Train fdec(G|Z ) and fenc(Z |G) on G using a

VAE with log-likelihood:

LVAE = Eqϕ (Z |G) logpθ (G|Z ) − DKL(qϕ (Z |G),p(Z ))3: while not converged do▷ Optimize over social network G

4: for each batch of usersU ⊆ V do5: Fix VS ,VR ,VP ,Gdiff(·) and update weights of fenc(G)

and fdec(Z ) using mini-batch gradient ascent (Eqn. 9)

▷ Optimize over diffusion episodes T6: for each batch of diffusion episodes B ⊆ T do7: Fix Z , fenc(G), fdec(Z ) and update VS ,VR ,VP , and

Gdiff(.) using mini-batch gradient ascent. (Eqn. 9)

sampling prevents gradient back-propagation to the neural param-

eters of fenc(G). With the reparametrization trick [19], we instead

sample ϵ ∼ N(0, IN×D ) and form samples ofZ = µϕ (G)+ϵ⊙σϕ (G).This isolates the stochasticity during sampling and the gradient

with respect to ϕ can be back-propagated through the sampled Z .

4.4.1 Optimization. Since bayesian methods to infer latent pos-

teriors incur high computational costs, and considering our goal

of making good predictions rather than explanations, we resort

to MAP (Maximum A Posteriori) estimation. Thus, we sample Zfrom qϕ (Z |G) using point estimates for VS ,VR and VP . We maxi-

mize the joint log-likelihood with MAP estimates of latent variables

VS ,VR ,VP , inference and generative network parameters θ ,ϕ, andobservations T and G, given hyper-parameters λs , λr , λp :

LMAP = Eqϕ [logpθ (G|Z )] − DKL(qϕ ,p(Z )) +∑

(I ,C )∈T

Ldiff

I,C (9)

−N∑i=1

(λs2

Eqϕ ∥vsi − zi ∥2 +

λr2

Eqϕ ∥vri − zi ∥2 +

λp

2

∥vpi ∥2

)where qϕ is a shorthand for qϕ (Z |G), and Eqϕ (Z |G)[Z ] is equal

to µϕ (G) output by the inference network. To optimize this objec-

tive, we employ block coordinate ascent with two sets of variables,

{ fenc(G), fdec(Z )} and {VS ,VR ,VP ,Gdiff}. As illustrated in Alg 1,

each iteration of the algorithm proceeds in two steps, by alternating

optimization over the social network and diffusion cascades.

4.4.2 Diffusion Prediction. After learning the (locally) optimal

model parameters and MAP estimates of latent variables, the like-

lihood of influencing user vj given seed activations I is given by:

p(vj |I ) = σ (hTI vrj ) (10)

4.4.3 Complexity. The cost per iteration comprises two parts: (a)

optimizing over social network G givesO(|E | ·F 2+ |E | ·D) assuming

GCN + Inner Product (b) optimizing over diffusion episodes is

O(|T| ·D ·N )where F is the maximum layer dimension in fenc. Theoverall complexity per iteration isO(|E | · F 2 + |E | ·D + |T| ·D · N ).

Social Networks Stack-Exchange Networks

Dataset Digg Weibo Android Christianity Travel

# Users 8,602 5,000 9,958 2,897 8,726

# Links 173,489 123,691 48,573 35,624 76,555

# Cascades 968 23,475 679 589 711

Avg. cascade len 100.0 23.6 33.3 22.9 26.8

Table 2: Statistics of datasets used in our experiments

5 EXPERIMENTSIn this section, we present our experimental results on multiple

datasets from real-world social networks and public Stack-Exchanges1.

We examine two popular social networks Digg and Weibo.

• Digg [15]: A social platform where users vote on news stories.

The sequence of votes on each story constitutes a diffusion cas-

cade, while the social network comprises friendship links among

voters. We retain only users who have voted on at least 40 stories.

• Weibo [48]: A Chinese micro-blogging platform, where the so-

cial network consists of follower links, and cascades reflect re-

tweeting behavior. We choose the 5000 most popular users.

Stack-Exchanges: Community Q&A websites where users post

questions and answers on a wide range of topics. The inter-user

knowledge-exchanges on various interaction channels (e.g., ques-tion, answer, comment, upvote, etc.), constitute the social network.

Cascades correspond to chronologically ordered series of posts as-

sociated with the same tag, e.g., “google-pixel-2" on Android. We

choose three Stack-Exchanges, Android, Christianity and Travel,

spanning diverse themes. Dataset statistics are provided in Table 2.

5.1 BaselinesWe compare Inf-VAE against state-of-the-art representation learn-

ing methods for diffusion prediction since they have been shown to

significantly outperform classical models (e.g., IC and LT) [9, 41].

• CDK [6]: an embedding method that models information spread

as a heat diffusion process in the representation space of users.

• Emb-IC [7]: an embedded cascade model that generalizes IC to

learn user representations from partial orders of user activations.

• Inf2vec [9]: an influence embedding method that combines local

propagation structure and user co-occurrence in cascades.

• DeepDiffuse [17]: an attention-based RNN that operates on just

the sequence of previously influenced users, to predict diffusion.

• CYAN-RNN [43]: a sequence-based RNN that uses an attention

mechanism to capture cross-dependence among seed users.

• SNIDSA [44]: an RNN-based model to compute structure atten-

tion over the local propagation structure of a cascade.

• Topo-LSTM [41]: a recurrent model that exploits the local prop-

agation structure of a cascade through a dynamic DAG-LSTM.

5.2 Experimental SetupWedenote our twomodel variants with GCN andMLP architectures,

by Inf-VAE+GCN and Inf-VAE+MLP respectively. We randomly

sample 70% of the cascades for training, 10% for validation and

remaining 20% for testing. We consider the task of predicting the

set of all influenced users as a retrieval problem [7, 9, 41, 43]. The

1https://archive.org/details/stackexchange

fraction of users sampled from each test cascade to serve as the seed

set is defined as seed set percentage, which is varied from 10% to

50% to create a large evaluation test-bed spanning diverse cascade

lengths. The likelihood of influencing an inactive user determines

its rank (Eqn. 10). We use MAP@K (Mean Average Precision) and

Recall@K as evaluation metrics. Note that MAP@K considers both

the existence and position of ground-truth target users in the rank

list, while Recall@K only reports occurrence within top-K ranks.

Hyper-parameters are tuned by evaluating MAP@10 on the val-

idation set. Since Emb-IC generalizes IC, we use 1000 Monte Carlo

simulations to estimate influence probabilities. Since the recurrent

neural models (e.g., Topo-LSTM) are trained for next user predic-

tion, we use the ranking induced by user activation probabilities for

diffusion prediction, which we found to significantly outperform

a similar simulation approach. For Inf2vec, we examine several

seed influence aggregation functions (Ave, Sum, Max, and Latest)

to report the best results. Our reported results are averaged over

10 independent runs with different random weight initializations.

Our implementation of Inf-VAE is publicly available2.

5.3 Experimental ResultsWe note the following key observations from our experimental

results comparing Inf-VAE against competing baselines (Table 3).

Methods that do not explicitly model sequential activation orders

(e.g., CDK and Emb-IC), perform markedly worse than their coun-

terparts. Modeling local projected cascade structures with neural

recurrent models results in improvements (e.g., Topo-LSTM and

others). Jointly modeling social homophily derived from global net-

work structure and temporal influence by our model Inf-VAE yields

significant relative gains of 22% (MAP@10) on average across all

datasets. Inf-VAE+GCN consistently beats the MLP variant, vali-

dating the power of graph convolutional networks in effectively

propagating higher-order local neighborhood features.

Figure 2 depicts the variation in recall with size of rank list K . Asexpected, recall increases with K , however, the relative differencesacross methods is much smaller. Inf-VAE consistently outperforms

baselines across a wide range of K values. For instance, the Chris-

tianity dataset has seed sets with 2-10 users, and corresponding tar-

get sets with 10-15 users out of a possible 3000. Here, a recall@100

of 0.45 for Inf-VAE is quite impressive, especially considering the

absence of explicit re-share links and the noise associated with

real-world diffusion processes. We restrict our remaining analyses

to Inf-VAE+GCN since it consistently beats the MLP variant.

5.4 Impact of Social and Behavior SparsityIn this section, we analyze the benefits of explicitly modeling social

homophily through VAEs, in comparison to the best baseline (Topo-

LSTM) that only considers local propagation structures.

• Users with sparse diffusion activities. We divide users into

quartiles by their activity levels, which is the number of partici-

pating cascades per user. We evaluate target recall@100 for each

user u, defined as the fraction of times u was predicted correctly

within top-100 ranks. In Figure 3(a), we depict both recall scores

and relative gains (over Topo-LSTM) across activity quartiles.

2https://github.com/aravindsankar28/Inf-VAE

Method Digg Weibo Android Christianity Travel

MAP @10 @50 @100 @10 @50 @100 @10 @50 @100 @10 @50 @100 @10 @50 @100

CDK 0.0437 0.0222 0.0228 0.0130 0.0106 0.0123 0.0319 0.0121 0.0125 0.0876 0.0531 0.0578 0.0650 0.0333 0.0341

Emb-IC 0.0862 0.0431 0.0431 0.0140 0.0116 0.0131 0.0505 0.0248 0.0267 0.1340 0.0905 0.0962 0.0924 0.0584 0.0609

Inf2vec 0.1189 0.0554 0.0546 0.0156 0.0103 0.0121 0.0412 0.0141 0.0150 0.1824 0.0790 0.0852 0.1245 0.0495 0.0529

DeepDiffuse 0.0919 0.0460 0.0471 0.0291 0.0186 0.0213 0.0437 0.0228 0.0250 0.1632 0.0828 0.0831 0.1220 0.0675 0.0693

CYAN-RNN 0.1188 0.0479 0.0427 0.0296 0.0207 0.0234 0.0520 0.0276 0.0296 0.1971 0.1229 0.1304 0.1551 0.0791 0.0799

SNIDSA 0.0941 0.0363 0.0348 0.0224 0.0146 0.0169 0.0397 0.0207 0.0222 0.1233 0.0699 0.0781 0.0857 0.0562 0.0585

Topo-LSTM 0.1193 0.0577 0.0587 0.0325 0.0226 0.0247 0.0595 0.0283 0.0289 0.1811 0.0989 0.0991 0.1393 0.0773 0.0783

Inf-VAE+MLP 0.1587 0.0774 0.0719 0.0322 0.0211 0.0234 0.0584 0.0272 0.0285 0.2549 0.1355 0.1402 0.1865 0.0897 0.0913Inf-VAE+GCN 0.1642 0.0779 0.0724 0.0373 0.0230 0.0257 0.0601 0.0290 0.0304 0.2594 0.1413 0.1461 0.1924 0.0906 0.0910

Table 3: Experimental results for diffusion prediction on 5 datasets (MAP@K scores forK = 10, 50 and 100), the seed set percentagevaries in the range to 10 to 50% users in each test cascade. 22% relative gains in MAP@10 (on average) over the best baseline.

0 20 40 60 80 100Size of rank list (K)

0.00

0.04

0.08

0.12

0.16

Rec

all@

K

Android

0 20 40 60 80 100Size of rank list (K)

0.0

0.1

0.2

0.3

0.4

0.5Christianity

0 20 40 60 80 100Size of rank list (K)

0.00

0.08

0.16

0.24

0.32

Travel

0 20 40 60 80 100Size of rank list (K)

0.00

0.06

0.12

0.18

0.24Digg

0 20 40 60 80 100Size of rank list (K)

0.00

0.03

0.06

0.09

0.12

0.15Weibo

CDK Emb-IC Inf2vec DeepDiffuse CYAN-RNN SNIDSA Topo-LSTM Inf-VAE+GCN

Figure 2: Experimental results for diffusion prediction on 5 datasets, Recall@K scores on varying size of the rank list K

Q1 Q2 Q3 Q4# actions per target user (activity level)

0.00

0.05

0.10

0.15

0.20

Rec

all@

100

Recall@100 Inf-VAE

Q1 Q2 Q3 Q4Fraction of social neighbors in seed set

0.00

0.05

0.10

0.15

0.20

Recall@100 Inf-VAE

0%

50%

100%

150%

200%Relative gains over Topo-LSTM

0%

10%

20%

30%

40%

50%

Rel

ativ

e ga

ins

over

Top

o-LS

TM

Relative gains over Topo-LSTM

Figure 3: Performance across user quartiles on diffusion ac-tivity level, and seed neighbor fraction (Q1: lowest, Q4: high-est). Inf-VAEhas higher gains for userswith sparse activitiesand lacking direct neighbors in seed sets (quartiles Q1-Q3).

While target recall increases with activity levels, Inf-VAE signifi-

cantly improves performance for inactive users (quartiles Q1-Q3).

Thus, modeling social homophily through VAEs contributes to

massive gains for users with sparse diffusion activities. Interest-ingly, Topo-LSTM performs comparably on the most active users

(quartile Q4), which indicates the potential of purely local se-

quential modeling techniques for highly active users.

• Users that lack direct social neighbors in seed sets.We sep-

arate users into quartiles by seed neighbor fraction, which is com-

puted as the fraction of seed users that are direct social neighbors,

averaged over the training examples. We similarly report target

recall@K and relative gains across quartiles (Figure 3(b)).

As expected, performance increases with seed neighbor fraction.

Note higher relative gains over Topo-LSTM for users that lack

direct neighbors in the seed set (quartiles Q1-Q3). This demon-

strates the ability of Inf-VAE to implicitly regularize seed user

representations based on higher-order social neighborhoods cap-

tured by GCN-based autoencoders. Again, we find that local

sequential models suffice for users with large seed neighbor frac-

tions, as evidenced by the results of Topo-LSTM in quartile Q4.

Metric Weibo Android

MAP @10 @50 @100 @10 @50 @100

(0) Default 0.0373 0.0230 0.0257 0.0601 0.0290 0.0304(1)VS = VR ̸⊥⊥ Z 0.0353 0.0220 0.0248 0.0558 0.0275 0.0287

(2)VS ⊥⊥ Z 0.0351 0.0213 0.0240 0.0595 0.0285 0.0301

(3)VR ⊥⊥ Z 0.0326 0.0217 0.0241 0.0567 0.0276 0.0291

(4)VS ⊥⊥ Z , VR ⊥⊥ Z 0.0313 0.0205 0.0235 0.0542 0.0274 0.0289

(5) Remove Coattention 0.0307 0.0207 0.0233 0.0553 0.0270 0.0284

(6) Separate Attentions 0.0293 0.0217 0.0192 0.0570 0.0277 0.0291

(7) Static-Pretrain 0.0342 0.0203 0.0226 0.0606 0.0281 0.0292

Table 4: Ablation study on architecture design (MAP@Kscores for K = 10, 50, 100), ⊥⊥ denotes variable independence

5.5 Ablation Study and Sensitivity AnalysisIn this section, we first present an ablation study followed by a

sensitivity analysis on seed set percentage and hyper-parameters.

5.5.1 Ablation Study. We analyze model design choices includ-

ing homophily via VAEs and co-attention, in Android and Weibo.

Social Homophily: We examine ways to condition VS , VR on Z :(1) VS andVR are identical and are conditioned onZ through hyper-

parameter λs (= λr ), i.e.,VS = VR ̸⊥⊥ Z (note that this is different

from setting λs = λr without enforcing VS = VR ).(2) VS is a free variable conditionally independent ofZ , i.e.,VS ⊥⊥ Z ,

which is equivalent to setting λs = 0.

(3) VR is a free variable, i.e., VR ⊥⊥ Z , which is the inverse of (3).

(4) VS and VR are both free variables conditionally independent of

Z (λs = λr = 0), i.e., VS ⊥⊥ Z ,VR ⊥⊥ Z .Independent conditioning of VS and VR on Z (default) achieves

best results. Enforcing VS = VR (row 1) is clearly inferior, which

validates the choice of differentiating user roles. Notably, allowing

VS to be a free variable results in minor performance degradation

10-20% 21-30% 31-40% 41-50%Seed Set Percentage (measured as percentage of cascade length)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

Rec

all@

10

CDK Emb-IC Inf2vec DeepDiffuse CYAN-RNN Topo-LSTM Inf-VAE

Figure 4: Impact of seed set percentage in Weibo. Inf-VAE achieves higher gains for larger seed set fractions.

(row 2), while the drop is significant when VR is independent of Z(row 3). As expected, setting both VS and VR as free variables (row

4), performs the worst due to lack of social homophily signals.

Co-attention:We conduct two ablation studies defined by:

(5) Replace co-attention with meanpool over concatenated sender

and temporal influence vectors, followed by a dense layer.

(6) Replace co-attention with two separate attentions on the sender

and temporal influence sequences, followed by concatenation.

Learning co-attentional weights (default) consistently outperforms

mean pooling (5), illustrating the benefits of assigning variable con-

tributions to seed users. Using separate attentions (6) significantly

deteriorates results, which indicates the existence of complex non-

linear correlations between the social and temporal latent factors.

Joint Training: In (2), we replace joint block-coordinate optimiza-

tion (Alg 1) with a single step over cascades with pre-trained user

embeddings (line 2), i.e., Z is not updated based on cascades.

Joint training is beneficial when social interactions are noisy (e.g.,Weibo) in comparison to focused stack-exchanges such as Android.

5.5.2 Impact of Seed Set Percentage. We divide the test set

into quartiles based on seed set percentage, and report performance

per quartile. Since we require a sizable number of test examples per

quartile to obtain unbiased estimates, we use the Weibo dataset.

Figure 4 depicts Recall@10 scores in different ranges. First, re-

call scores increase with seed set percentage since larger seed sets

enable better model predictions; and target set size reduces with in-

crease in seed set percentage. Second, relative gains of Inf-VAE over

baselines increase with seed set percentage. This highlights the

capability of co-attention in focusing on relevant users based on

both social homophily and temporal influence factors.

5.5.3 Impact of λs and λr . Hyper-parameters λs and λr control

the degree of dependence of the sender and receiver variablesVS ,VRon the social variables Z . Figure 5 depicts performance (MAP@10)

on Android and Weibo datasets. The performance is sensitive to

variations in λr with best values around 0.01 and 0.1, while λs re-sults in minimal variations. Furthermore, the best values of λs , λrare stable in a broad range of values that transfer across datasets, in-

dicating that Inf-VAE requires minimal tuning in practice. Since λphas minimal performance impact, we exclude it from our analysis.

5.5.4 Runtime Analysis. In our experiments, all methods con-

verge within 50 epochs with similar convergence rates. For the sake

of brevity, we only compare runtime per epoch, which includes one

step over the social network and cascades for Inf-VAE.

0.001 0.01 0.1 1.0 10.0 100.0

λr

0.001

0.01

0.1

1.0

10.0

100.0

λ s

Weibo

0.001 0.01 0.1 1.0 10.0 100.0

λr

0.001

0.01

0.1

1.0

10.0

100.0

Android

0.012

0.018

0.024

0.030

0.036

0.052

0.054

0.056

0.058

0.060

0.062

Figure 5:MAP@10 on varying λs , λr over Android andWeibo.Performance is more sensitive to variations in λr than λs .

Weibo Android10−2

10−1

100

101

102

103

Tim

e pe

r Epo

ch (s

ecs)

Inf2vec CYAN-RNN Topo-LSTM Inf-VAE

(a) Runtime on Weibo and Android

10 20 30 40 50Cascade Length

0

4

8

12

16

20

Tim

e pe

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ch (s

ecs) Inf2vec

CYAN-RNNTopo-LSTMInf-VAE

(b) Scalability on synthetic dataset

Figure 6: Running time and scalability comparison of Inf-VAE with several baselines. Inf-VAE is faster than recurrentmodels (Topo-LSTM, CYANRNN) by an order of magnitude.

From figure 6(a), Inf2vec is the fastest while Inf-VAE comes sec-

ond. Thus, Inf-VAE achieves a good trade-off between expensive

recurrent models (e.g., Topo-LSTM) and simpler embedding meth-

ods (e.g., Inf2vec), with consistently superior results.

5.5.5 Scalability Analysis. We analyze scalability on cascade

sequences of varying lengths. Since real-world datasets possess

heavily biased length distributions, we instead synthetically gen-

erate a Barabasi-Albert [1] network of 2000 users and simulate

diffusion cascades using an IC model. We compare training times

per epoch for each cascade length (l ) in the range of 10 to 50.

Figure 6(b) depicts linear scaling for Inf-VAE and Inf2vec wrtcascade length. Recurrent methods scale poorly due to the sequen-

tial nature of back-propagation through time (BPTT), resulting in

prohibitive costs for long cascade sequences. On the other hand, Inf-

VAE avoids BPTT through efficient parallelizable co-attentions.

6 CONCLUSIONIn this paper, we present a novel variational autoencoder framework

(Inf-VAE) to jointly embed homophily and influence in diffusion pre-

diction. Given a sequence of seed user activations, Inf-VAE employs

an expressive co-attentive fusion mechanism to jointly attend over

their social and temporal variables, capturing complex correlations.

Our experimental results on two social networks and three stack-

exchanges indicate significant gains over state-of-the-art methods.

In future, Inf-VAE can be extended to include multi-faceted user

attributes owing to the generalizable nature of our VAE framework.

While the current implementation employs GCN networks, we fore-

see direct extensions with neighborhood sampling [13] to enable

scalability to social networks with millions of users. We also plan

to explore neural point processes to predict user activation times.

Finally, similar frameworks may be examined for joint temporal

co-evolution of social network and diffusion cascades.

7 ACKNOWLEDGEMENTSResearch was sponsored in part by U.S. Army Research Lab. under

Cooperative Agreement No. W911NF-09-2-0053 (NSCTA), DARPA

under Agreements No. W911NF-17-C-0099 and FA8750-19-2-1004,

National Science Foundation IIS 16-18481, IIS 17-04532, and IIS-17-

41317, and DTRA HDTRA11810026.

REFERENCES[1] Réka Albert and Albert-László Barabási. 2002. Statistical mechanics of complex

networks. Reviews of modern physics 74, 1 (2002), 47.[2] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 2015. Neural machine

translation by jointly learning to align and translate. In ICLR.[3] Nicola Barbieri, Francesco Bonchi, and Giuseppe Manco. 2012. Topic-aware

social influence propagation models. In ICDM. IEEE, 81–90.

[4] Nicola Barbieri, Francesco Bonchi, and Giuseppe Manco. 2013. Influence-based

network-oblivious community detection. In ICDM. IEEE, 955–960.

[5] David M Blei, Alp Kucukelbir, and Jon D McAuliffe. 2017. Variational inference:

A review for statisticians. J. Amer. Statist. Assoc. 112, 518 (2017), 859–877.[6] Simon Bourigault, Cedric Lagnier, Sylvain Lamprier, Ludovic Denoyer, and Patrick

Gallinari. 2014. Learning social network embeddings for predicting information

diffusion. In Proceedings of the 7th ACM international conference on Web searchand data mining. ACM, 393–402.

[7] Simon Bourigault, Sylvain Lamprier, and Patrick Gallinari. 2016. Representation

learning for information diffusion through social networks: an embedded cascade

model. In Proceedings of the Ninth ACM International Conference on Web Searchand Data Mining. ACM, 573–582.

[8] Robert B Cialdini and Noah J Goldstein. 2004. Social influence: Compliance and

conformity. Annu. Rev. Psychol. 55 (2004), 591–621.[9] Shanshan Feng, Gao Cong, Arijit Khan, Xiucheng Li, Yong Liu, and Yeow Meng

Chee. 2018. Inf2vec: Latent Representation Model for Social Influence Embedding.

In ICDE. IEEE, 941–952.[10] Manuel Gomez-Rodriguez, Jure Leskovec, and Andreas Krause. 2012. Inferring

networks of diffusion and influence. ACM Transactions on Knowledge Discoveryfrom Data (TKDD) 5, 4 (2012), 21.

[11] Mark Granovetter. 1978. Threshold models of collective behavior. Americanjournal of sociology 83, 6 (1978), 1420–1443.

[12] Aditya Grover and Jure Leskovec. 2016. node2vec: Scalable feature learning for

networks. In Proceedings of the 22nd ACM SIGKDD international conference onKnowledge discovery and data mining. ACM, 855–864.

[13] Will Hamilton, Zhitao Ying, and Jure Leskovec. 2017. Inductive representation

learning on large graphs. In Advances in Neural Information Processing Systems.1024–1034.

[14] William L Hamilton, Rex Ying, and Jure Leskovec. 2017. Representation learning

on graphs: Methods and applications. arXiv preprint arXiv:1709.05584 (2017).[15] Tad Hogg and Kristina Lerman. 2012. Social dynamics of digg. EPJ Data Science

1, 1 (2012), 5.

[16] Zhiting Hu, Junjie Yao, Bin Cui, and Eric Xing. 2015. Community level diffusion

extraction. In SIGMOD 2015. ACM, 1555–1569.

[17] Mohammad Raihanul Islam, Sathappan Muthiah, Bijaya Adhikari, B Aditya

Prakash, and Naren Ramakrishnan. 2018. DeepDiffuse: Predicting

the’Who’and’When’in Cascades. In ICDM. IEEE, 1055–1060.

[18] David Kempe, Jon Kleinberg, and Éva Tardos. 2003. Maximizing the spread of

influence through a social network. In Proceedings of the ninth ACM SIGKDDinternational conference on Knowledge discovery and data mining. ACM, 137–146.

[19] Diederik P Kingma and Max Welling. 2013. Auto-encoding variational bayes.

arXiv preprint arXiv:1312.6114 (2013).[20] Thomas N Kipf and Max Welling. 2016. Variational Graph Auto-Encoders. NIPS

Workshop on Bayesian Deep Learning (2016).

[21] Thomas N Kipf and MaxWelling. 2017. Semi-supervised classification with graph

convolutional networks. In ICLR.[22] Adit Krishnan, Hari Cheruvu, Cheng Tao, and Hari Sundaram. 2019. A Modular

Adversarial Approach to Social Recommendation. In Proceedings of the 28thACM International Conference on Information and Knowledge Management. ACM,

1753–1762.

[23] Adit Krishnan, Ashish Sharma, Aravind Sankar, and Hari Sundaram. 2018. An

Adversarial Approach to Improve Long-Tail Performance in Neural Collaborative

Filtering. In Proceedings of the 27th ACM International Conference on Informationand Knowledge Management. ACM, 1491–1494.

[24] Jure Leskovec, Lada A Adamic, and Bernardo A Huberman. 2007. The dynamics

of viral marketing. ACM Transactions on the Web (TWEB) 1, 1 (2007), 5.[25] Cheng Li, Jiaqi Ma, Xiaoxiao Guo, and Qiaozhu Mei. 2017. DeepCas: An end-to-

end predictor of information cascades. In Proceedings of the 26th InternationalConference on World Wide Web. 577–586.

[26] Dawen Liang, Rahul G Krishnan, Matthew D Hoffman, and Tony Jebara. 2018.

Variational autoencoders for collaborative filtering. In Proceedings of the 2018World Wide Web Conference. 689–698.

[27] Miller McPherson, Lynn Smith-Lovin, and James M Cook. 2001. Birds of a feather:

Homophily in social networks. Annual review of sociology 27, 1 (2001), 415–444.

[28] Kanika Narang, Chaoqi Yang, Adit Krishnan, Junting Wang, Hari Sundaram, and

Carolyn Sutter. 2019. An Induced Multi-Relational Framework for Answer Selec-

tion in Community Question Answer Platforms. arXiv preprint arXiv:1911.06957(2019).

[29] Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. 2014. Deepwalk: Online learning

of social representations. In Proceedings of the 20th ACM SIGKDD internationalconference on Knowledge discovery and data mining. ACM, 701–710.

[30] Jiezhong Qiu, Jian Tang, Hao Ma, Yuxiao Dong, Kuansan Wang, and Jie Tang.

2018. DeepInf: Social Influence Prediction with Deep Learning. In Proceedings ofthe 24th ACM SIGKDD International Conference on Knowledge Discovery and DataMining (KDD’18).

[31] Kazumi Saito, Masahiro Kimura, Kouzou Ohara, and Hiroshi Motoda. 2009. Learn-

ing continuous-time information diffusion model for social behavioral data anal-

ysis. Advances in Machine Learning (2009), 322–337.

[32] Kazumi Saito, Kouzou Ohara, Yuki Yamagishi, Masahiro Kimura, and Hiroshi

Motoda. 2011. Learning diffusion probability based on node attributes in social

networks. In International Symposium on Methodologies for Intelligent Systems.Springer, 153–162.

[33] Aravind Sankar, Adit Krishnan, Zongjian He, and Carl Yang. 2019. Rase: Rela-

tionship aware social embedding. In IJCNN. IEEE, 1–8.[34] Aravind Sankar, Yanhong Wu, Liang Gou, Wei Zhang, and Hao Yang. 2018.

Dynamic Graph Representation Learning via Self-Attention Networks. arXivpreprint arXiv:1812.09430 (2018).

[35] Aravind Sankar, Xinyang Zhang, and Kevin Chen-Chuan Chang. 2017. Motif-

based Convolutional Neural Network on Graphs. arXiv preprint arXiv:1711.05697(2017).

[36] Aravind Sankar, Xinyang Zhang, and Kevin Chen-Chuan Chang. 2019. Meta-

GNN: Metagraph Neural Network for Semi-supervised learning in Attributed

Heterogeneous Information Networks. In ASONAM. IEEE, 137–144.

[37] Cosma Rohilla Shalizi and Andrew C Thomas. 2011. Homophily and contagion

are generically confounded in observational social network studies. Sociologicalmethods & research 40, 2 (2011), 211–239.

[38] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones,

Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is all

you need. In Advances in Neural Information Processing Systems. 5998–6008.[39] Petar Velickovic, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro

Lio, and Yoshua Bengio. 2018. Graph attention networks. In ICLR.[40] Daixin Wang, Peng Cui, and Wenwu Zhu. 2016. Structural deep network em-

bedding. In Proceedings of the 22nd ACM SIGKDD international conference onKnowledge discovery and data mining. ACM, 1225–1234.

[41] Jia Wang, Vincent Zheng, Zemin Liu, and Kevin Chen-Chuan Chang. 2017. Topo-

logical Recurrent Neural Network for Diffusion Prediction. In ICDM. 475–484.

[42] Yongqing Wang, Huawei Shen, Shenghua Liu, and Xueqi Cheng. 2015. Learning

User-Specific Latent Influence and Susceptibility from Information Cascades. In

Twenty-Ninth AAAI Conference on Artificial Intelligence.[43] YongqingWang, Huawei Shen, Shenghua Liu, Jinhua Gao, and Xueqi Cheng. 2017.

Cascade Dynamics Modeling with Attention-based Recurrent Neural Network..

In IJCAI. 2985–2991.[44] Zhitao Wang, Chengyao Chen, and Wenjie Li. 2018. A Sequential Neural In-

formation Diffusion Model with Structure Attention. In Proceedings of the 27thACM International Conference on Information and Knowledge Management. ACM,

1795–1798.

[45] Caiming Xiong, Victor Zhong, and Richard Socher. 2017. Dynamic coattention

networks for question answering. In ICLR.[46] Jaewon Yang and Jure Leskovec. 2010. Modeling information diffusion in implicit

networks. In ICDM. IEEE, 599–608.

[47] Yang Yang, Jie Tang, Cane Wing-ki Leung, Yizhou Sun, Qicong Chen, Juanzi Li,

and Qiang Yang. 2015. RAIN: Social Role-Aware Information Diffusion.. In AAAI.367–373.

[48] Jing Zhang, Biao Liu, Jie Tang, Ting Chen, and Juanzi Li. 2013. Social influence

locality for modeling retweeting behaviors. In IJCAI.[49] Jing Zhang, Jie Tang, Yuanyi Zhong, Yuchen Mo, Juanzi Li, Guojie Song, Wendy

Hall, and Jimeng Sun. 2017. StructInf: Mining Structural Influence from Social

Streams.. In AAAI. 73–80.[50] Yuan Zhang, Tianshu Lyu, and Yan Zhang. 2017. Hierarchical community-level

information diffusion modeling in social networks. In Proceedings of the 40thInternational ACM SIGIR Conference on Research and Development in InformationRetrieval. ACM, 753–762.

[51] Qingyuan Zhao, Murat A Erdogdu, Hera Y He, Anand Rajaraman, and Jure

Leskovec. 2015. Seismic: A self-exciting point process model for predicting tweet

popularity. In Proceedings of the 21th ACM SIGKDD International Conference onKnowledge Discovery and Data Mining. ACM, 1513–1522.