PaperlayerView exact revision on arXiv

Source-linked AI summary

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

Aravind Sankar, Xinyang Zhang, Adit Krishnan, Jiawei Han

arXiv:2001.00132v1cs.SIcs.LG

TL;DR

Cascade-based diffusion methods can miss social structures absent from observed cascades, limiting their evidence about users with sparse activity. Inf-VAE jointly models social homophily and temporal influence through social and temporal embeddings with co-attentive fusion. It reports 22% relative gains in MAP@10 on average across datasets over state-of-the-art models.

  • Problem

    Cascade-projection methods overlook social structures that do not appear in observed cascades, while many users have limited activity in cascades.

    Source: §1 · p. 1

  • Method

    Inf-VAE combines proximity-preserving social embeddings and activation-order temporal embeddings, using co-attentive fusion to predict influenced users.

    Source: §1 · p. 2

  • Results

    22% relative gains in MAP@10 on average across all datasets are reported for Inf-VAE over state-of-the-art models.

    Source: §5.3 · p. 6

  • Takeaways & Limitations

    The paper reports massive gains for users with sparse activity and for users whose seed sets lack direct social neighbors.

    Source: §1 · p. 2

    The formulation uses relative activation order without explicit re-share links and leaves continuous timestamp generation for future work.

    Source: §3 · p. 3

Abstract

from arXiv · show

Recent years have witnessed tremendous interest in understanding and predicting information spread on social media platforms such as Twitter, Facebook, etc. Existing diffusion prediction methods primarily 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 framework (Inf-VAE) to jointly embed homophily and influence through proximity-preserving social and position-encoded temporal latent variables. 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-attentive fusion 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 prediction models; we achieve massive gains for users with sparse activities, and users who lack direct social neighbors in seed sets.

1 INTRODUCTION

Diffusion prediction estimates which users will be influenced from activated seeds, but cascade-based methods can miss social structures absent from observed cascades. Inf-VAE addresses this by jointly modeling social homophily and temporal influence.

Motivation

  • Cascade models using hand-crafted features require manual effort and domain knowledge, while cascade-projection methods miss social structures not manifested in cascades.These omissions matter for users who seldom post and rarely appear in cascades.Source: §1 · p. 1
  • Homophily and contagion have different dynamics and are fundamentally confounded in observational studies, motivating a framework that models their joint effect.Homophily reflects shared traits or preferences, whereas contagion is self-reinforcing and viral.Source: §1 · pp. 1–2

Inf-VAE

  • Inf-VAE uses proximity-preserving social embeddings and activation-order temporal embeddings, then co-attentively fuses them to predict influenced users.Its VAE supports graph neural network encoders and decoders for modeling social homophily.Source: §1 · p. 2

Contributions

  • Inf-VAE combines global social connections with temporal influence, and its co-attention model is reported faster than state-of-the-art recurrent methods by an order of magnitude.The introduction also reports gains for users with sparse activity and users whose seed sets lack direct social neighbors.Source: §1 · p. 2

2 RELATED WORK

Prior diffusion work ranges from hand-designed propagation models to learned representations of cascades and networks. This paper’s related-work discussion identifies unobserved social structure and the interplay of social and temporal representations as central gaps.

Information diffusion overview

  • Diffusion prediction estimates influenced users from social links and cascade sequences, distinct from inferring networks or predicting aggregate cascade properties.The overview identifies Independent Cascade and Linear Threshold as seminal diffusion models.Source: §2 · p. 2

Diffusion prediction

  • Data-driven methods progress from feature-augmented propagation models to learned representations, including RNNs over cascade-projected DAGs that may omit social structures absent from observed cascades.The paper contrasts these methods with Inf-VAE’s use of VAEs to model social homophily from unobserved social connections.Source: §2 · p. 2
  • Ego-network social-influence classifiers are not directly compared because predicting all influenced users would require rerunning them for each inactive candidate.Source: §2 · p. 2

Network representation learning

  • Network representation learning captures structural proximity, but the related-work discussion says general-purpose embeddings are not directly suited to diffusion modeling.Graph autoencoders learn unsupervised node embeddings by encoding and decoding network structure.Source: §2 · p. 2

Co-attentional models

  • Co-attention computes interaction weights between modalities; Inf-VAE applies it to contextual interplay between users’ social and temporal representations.Source: §2 · p. 2

3 PROBLEM DEFINITION

The problem is to rank inactive users by their likelihood of becoming influenced, given a social network and temporally ordered seed activations. Cascades are represented by relative activation order, and training episodes are formed by splitting cascades into seed and subsequent-user sets.

Social network

  • The social network is represented as a graph G = (V, E) over users, with an adjacency matrix whose entries indicate whether an edge exists.Source: §3 · p. 2

Cascade definition

  • A cascade is an ordered sequence of distinct user activations with non-decreasing activation times.Source: §3 · p. 2

Cascade representation

  • The formulation uses delay-agnostic relative activation orders and does not assume explicit re-share links; generating continuous timestamps is left for future work.Source: §3 · p. 3

Task definition

  • Diffusion prediction estimates each inactive user’s probability of activation from the seed sequence, inducing a ranking over inactive users.Source: §3 · pp. 2–3

Training set

  • Training episodes are created by splitting each cascade at successive time steps into a seed prefix and the users activated afterward.Source: §3 · p. 3

4 INFLUENCE VARIATIONAL AUTOENCODER

Inf-VAE models diffusion using social and temporal latent variables and fuses seed-user signals to predict influenced users.

4.1 Model Description

  • Social homophily is encoded by proximity-preserving latent user variables, with sender and receiver distributions centered on each user's social variable.The graph-generation network can preserve different structural proximity representations, including adjacency matrices or sampled random walks.Source: §4.1.1 · p. 3
  • Temporal influence combines activation position and user-specific popularity offsets to represent both activation order and popularity effects.The positional embedding depends on the activation step, whereas the popularity variable is user-specific.Source: §4.1.2 · p. 3
  • Given seed activations, Inf-VAE predicts influenced users by modeling each inactive user's binary influence outcome from aggregate seed and receiver representations.Positive examples are re-weighted because influenced users are much fewer than the total user population.Source: §4.1.3 · p. 4
  • Co-attentive fusion weights each seed user's temporal influence using interactions between that user's social and temporal characteristics.The normalized co-attentional coefficients determine each seed user's contribution to the aggregate representation.Source: §4.1.3 · p. 4

4.2 Model Likelihood

  • Variational inference approximates latent posteriors with a mean-field factorization, while the graph encoder and decoder form a variational graph autoencoder trained to maximize an ELBO.The expectation under the variational distribution is analytically intractable.Source: §4.2 · p. 4, §4.4 · p. 5

4.3 Neural Graph Autoencoder Details

  • Graph autoencoder options include MLP reconstruction of normalized-Laplacian neighborhoods and GCN encoding with an inner-product link decoder.The GCN uses stacked layers to extract features from higher-order structural neighborhoods.Source: §4.3 · p. 5

4.4 Model Inference

  • Training uses MAP estimates and alternating block-coordinate updates over social-network and diffusion variables; GCN-based iterations have complexity O(|E| · F^2 + |E| · D + |T| · D · N).The stated complexity assumes a GCN with an inner-product decoder.Source: §4.4.1 · p. 5, §4.4.3 · p. 5

5 EXPERIMENTS

Across five datasets, Inf-VAE improves diffusion prediction over the best baseline, with especially strong gains for users with sparse activity or few seed neighbors. Ablations and efficiency analyses examine the model’s design choices, sensitivity, and scaling.

5 EXPERIMENTS

  • The experiments use Digg, Weibo, and three Stack-Exchange communities, with cascades drawn from voting, retweeting, and topic-associated posts.The Stack-Exchange datasets are Android, Christianity, and Travel.Source: §5 · p. 6

5.1 Baselines

  • Baselines include embedding models and recurrent models that use activation sequences or local cascade structures.The comparison includes CDK, Emb-IC, Inf2vec, DeepDiffuse, CYAN-RNN, SNIDSA, and Topo-LSTM.Source: §5.1 · p. 6

5.2 Experimental Setup

  • Cascades are split into 70% training, 10% validation, and 20% testing, and prediction is evaluated as a retrieval task using MAP@K and Recall@K.Seed set percentage varies from 10% to 50%; reported results are averaged over 10 runs with different random initializations.Source: §5.2 · p. 6

5.3 Experimental Results

  • Inf-VAE achieves 22% relative gains in MAP@10 on average over the best baseline across five datasets.It also consistently outperforms baselines across a wide range of Recall@K values.Source: §5.3 · p. 6, Table 3 · p. 7

5.4 Impact of Social and Behavior Sparsity

  • Inf-VAE improves performance for users in activity quartiles Q1–Q3 and for users with few direct seed neighbors, while Topo-LSTM performs comparably in Q4.The figure reports performance across activity and seed-neighbor-fraction quartiles.Source: §5.4 · pp. 6–7, Figure 3 · p. 7

5.5 Ablation Study and Sensitivity Analysis

  • Independent conditioning of sender and receiver variables on social variables performs best; co-attention outperforms mean pooling and separate attentions, and joint training helps on noisy Weibo.Making the receiver variable independent of social variables causes a significant drop, while making both variables free performs worst.Source: §5.5.1 · pp. 7–8
  • Inf-VAE gains more as seed-set percentage increases; MAP@10 is more sensitive to λr than λs, and the best hyperparameter values transfer across Android and Weibo.The sensitivity analysis reports best values around 0.01 and 0.1 for λr and minimal variation with λs.Source: §5.5.2 · p. 8, §5.5.3 · p. 8, Figure 4 · p. 8
  • Inf-VAE is second-fastest per epoch behind Inf2vec and scales linearly with cascade length, unlike recurrent methods that scale poorly.Its parallelizable co-attentions avoid back-propagation through time; the figure reports it is an order of magnitude faster than Topo-LSTM and CYAN-RNN.Source: §5.5.4 · p. 8, §5.5.5 · p. 8, Figure 6 · p. 8

6 CONCLUSION

Inf-VAE jointly models homophily and influence through a variational autoencoder framework with co-attentive fusion. Experiments on two social networks and three Stack Exchanges indicate gains over state-of-the-art methods.

6 CONCLUSION

  • Experiments on two social networks and three Stack Exchanges indicate significant gains over state-of-the-art methods.Source: §6 · p. 8
  • Inf-VAE jointly embeds homophily and influence, using co-attention over social and temporal variables to capture complex correlations.Source: §6 · p. 8
  • Future work includes adding multifaceted user attributes, improving scalability, predicting activation times, and modeling temporal co-evolution of networks and cascades.The authors propose neighborhood sampling to enable scalability to networks with millions of users.Source: §6 · p. 8

Related papers

Loading 2001.00132v1…