[Paper Review] Learning Influence-Receptivity Network Structure with Guarantee

Ming Yu, Varun Gupta+1 more|arXiv (Cornell University)|Jun 14, 2018

Complex Network Analysis Techniques36 references3 citations

TL;DR

This paper proposes a novel influence-receptivity network model that learns node-specific influence and receptivity vectors across multiple topics to explain time-varying network structures from observed adjacency matrices. It provides theoretical guarantees on estimation error and outperforms state-of-the-art methods in synthetic and real-world data, demonstrating superior generalization and interpretability by capturing topic-dependent connectivity patterns.

ABSTRACT

Traditional works on community detection from observations of information cascade assume that a single adjacency matrix parametrizes all the observed cascades. However, in reality the connection structure usually does not stay the same across cascades. For example, different people have different topics of interest, therefore the connection structure depends on the information/topic content of the cascade. In this paper we consider the case where we observe a sequence of noisy adjacency matrices triggered by information/event with different topic distributions. We propose a novel latent model using the intuition that a connection is more likely to exist between two nodes if they are interested in similar topics, which are common with the information/event. Specifically, we endow each node with two node-topic vectors: an influence vector that measures how influential/authoritative they are on each topic; and a receptivity vector that measures how receptive/susceptible they are to each topic. We show how these two node-topic structures can be estimated from observed adjacency matrices with theoretical guarantee on estimation error, in cases where the topic distributions of the information/event are known, as well as when they are unknown. Experiments on synthetic and real data demonstrate the effectiveness of our model and superior performance compared to state-of-the-art methods.

Motivation & Objective

• To address the limitation of static adjacency matrices in modeling time-varying network structures where connections depend on topic-specific interests.
• To model networks where node connectivity varies based on topic distributions, using influence and receptivity vectors per node per topic.
• To estimate the influence and receptivity vectors from noisy, observed adjacency matrices with theoretical error bounds.
• To provide a more interpretable and generalizable alternative to traditional network models that assume a single fixed adjacency matrix.
• To extend the model to cases where topic distributions are either known or unknown, with provable convergence guarantees.

Proposed method

• Model each node as having two latent vectors: an influence vector (how authoritative they are on each topic) and a receptivity vector (how susceptible they are to each topic).
• Define the probability of a directed edge from node i to j as the inner product of i's influence vector and j's receptivity vector, weighted by the topic distribution of the observed cascade.
• Use a low-rank matrix factorization framework to estimate the influence and receptivity matrices from multiple observed adjacency matrices under different topic distributions.
• Formulate the estimation problem as a convex optimization program with nuclear norm regularization to promote low-rank solutions and ensure identifiability.
• Provide theoretical guarantees on estimation error under both known and unknown topic distribution settings, showing convergence to the true parameters up to statistical error.
• Apply alternating minimization and spectral initialization techniques to solve the optimization problem efficiently in practice.

Experimental results

Research questions

• RQ1 Can we model time-varying network structures where node connectivity depends on topic-specific interests using a single, unified latent structure?
• RQ2 How can we estimate influence and receptivity vectors for each node across topics from multiple noisy adjacency matrices with theoretical error bounds?
• RQ3 What is the performance gain of using topic-dependent influence-receptivity modeling compared to static network models or standard community detection?
• RQ4 How does the model perform when topic distributions are unknown, and can we still achieve consistent estimation with theoretical guarantees?
• RQ5 To what extent does the proposed model improve generalization and interpretability in real-world network data?

Key findings

• The proposed model achieves the best test error on synthetic data, significantly outperforming baseline methods that overfit due to higher parameter counts.
• On the citation network dataset, the model achieves a test link prediction error of 8.217, outperforming the one-matrix method (8.223) and the K-matrix method (8.415) despite having far fewer parameters (2400 vs. 40,000 and 240,000).
• The model's low training error (8.259) and high test generalization indicate it avoids overfitting, unlike the other two methods which suffer from overfitting due to higher model complexity.
• The influence and receptivity matrices learned from the citation dataset show meaningful patterns: for example, Edward Witten has high receptivity in string theory and supersymmetric field theory, aligning with his known research profile.
• The model's theoretical analysis shows that estimation error converges to the statistical minimax rate, confirming consistency under both known and unknown topic distribution settings.
• The influence-receptivity structure provides better interpretability than dense adjacency matrices, enabling targeted recommendations and insights into node roles across topics.