[Paper Review] Latent Point Process Models for Spatial-Temporal Networks

Yoon-Sik Cho, Aram Galstyan+2 more|arXiv (Cornell University)|Feb 12, 2013

Human Mobility and Location-Based Analysis23 references13 citations

TL;DR

This paper proposes a spatial-temporal latent point process model to infer unobserved participants in incomplete interaction events using only location and time data. It employs an approximate variational EM algorithm to jointly infer missing identities and predict future events, demonstrating strong performance on identity inference and forecasting tasks using synthetic and real-world data.

ABSTRACT

Social network data is generally incomplete with missing information about nodes and their interactions. Here we propose a spatial-temporal latent point process model that describes geographically distributed interac-tions between pairs of entities. In contrast to most existing approaches, we assume that interactions are not fully observable, and certain interaction events lack information about participants. Instead, this information needs to be inferred from the available obser-vations. We develop an efficient approximate algorithm based on variational expectation-maximization to infer unknown participants in an event given the location and the time of the event. We validate the model on syn-thetic as well as real–world data, and ob-tain very promising results on the identity-inference task. We also use our model to predict the timing and participants of future events, and demonstrate that it compares fa-vorably with a baseline approach. 1

Motivation & Objective

• To address the challenge of incomplete social network data where interaction participants are unobserved or missing.
• To model geographically distributed interactions between entity pairs with incomplete observation of participants.
• To develop an efficient inference method that jointly estimates missing identities and predicts future events.
• To validate the model on both synthetic and real-world datasets for identity inference and event prediction.

Proposed method

• The model uses a spatial-temporal point process to represent interactions as events in continuous time and space.
• It assumes that interaction participants are latent variables, unobserved in the data, and must be inferred from event locations and timestamps.
• An approximate inference algorithm based on variational expectation-maximization (VEM) is developed to handle the intractable posterior over latent participants.
• The VEM approach iteratively optimizes variational parameters to approximate the true posterior distribution over unobserved participants.
• The model jointly learns the intensity function of event occurrences and the participant identity distribution using observed event metadata.
• The framework enables both identity inference and future event prediction through a unified probabilistic generative process.

Experimental results

Research questions

• RQ1 Can a latent point process model effectively infer missing participants in spatial-temporal social interactions using only location and time data?
• RQ2 How well does the proposed model perform in reconstructing unobserved interaction identities compared to baseline methods?
• RQ3 To what extent can the model predict the timing and participants of future events with incomplete data?
• RQ4 How robust is the model to data sparsity and missing participant information in real-world social networks?

Key findings

• The model achieves strong performance on the identity-inference task, outperforming baseline approaches on both synthetic and real-world datasets.
• The variational EM algorithm enables efficient and scalable inference over latent participant identities in large-scale spatial-temporal networks.
• The model demonstrates favorable predictive performance for future event timing and participant prediction compared to baseline methods.
• Results on synthetic data validate the model's ability to recover true underlying interaction patterns despite missing participant information.
• The approach effectively handles data incompleteness by leveraging spatial and temporal dependencies to infer unobserved entities.
• The model's joint inference framework improves both identity recovery and forecasting accuracy by modeling interactions as a unified generative process.