[Paper Review] Network Inference from Temporal-Dependent Grouped Observations

Yunpeng Zhao|arXiv (Cornell University)|Aug 25, 2018

Complex Network Analysis Techniques3 citations

TL;DR

This paper proposes a novel model for inferring latent social networks from temporally dependent grouped observations, where group leaders follow a Markov chain and adjacent groups exhibit correlation. Using an EM algorithm with a polynomial-time E-step based on the forward-backward algorithm, the method improves network inference over independent group assumptions, validated through simulations and applied to chimpanzee social data with enhanced accuracy.

ABSTRACT

In social network analysis, the observed data is usually some social behavior, such as the formation of groups, rather than an explicit network structure. Zhao and Weko (2017) propose a model-based approach called the hub model to infer implicit networks from grouped observations. The hub model assumes independence between groups, which sometimes is not valid in practice. In this article, we generalize the idea of the hub model into the case of grouped observations with temporal dependence. As in the hub model, we assume that the group at each time point is gathered by one leader. Unlike in the hub model, the group leaders are not sampled independently but follow a Markov chain, and other members in adjacent groups can also be correlated. An expectation-maximization (EM) algorithm is developed for this model and a polynomial-time algorithm is proposed for the E-step. The performance of the new model is evaluated under different simulation settings. We apply this model to a data set of the Kibale Chimpanzee Project.

Motivation & Objective

• To address the limitation of existing network inference methods that assume independence between grouped observations in social network analysis.
• To model temporal dependence in grouped data by allowing group leaders to follow a Markov chain, capturing dynamic social structures.
• To develop a computationally efficient inference procedure for latent network estimation under temporal dependence.
• To extend the hub model to incorporate correlation between adjacent groups, improving realism in network reconstruction.
• To validate the model on both simulated data and real-world animal grouping behavior, such as the Kibale Chimpanzee Project.

Proposed method

• Models grouped observations using a latent Markov chain for group leaders, allowing temporal dependence in network structure.
• Introduces a hierarchical model where each group is led by one individual, and other members are conditionally dependent on the leader and prior group states.
• Employs an expectation-maximization (EM) algorithm for parameter estimation, with a polynomial-time E-step using the forward-backward algorithm for hidden Markov models.
• Derives sufficient statistics for the E-step, including counts of leader transitions and co-occurrences across time points.
• Uses logistic regression-like link functions to model edge probabilities, incorporating parameters for leader influence, inter-group correlation, and edge strength.
• Derives closed-form expressions for first and second-order derivatives of the complete-data log-likelihood to enable Newton-Raphson optimization in the M-step.

Experimental results

Research questions

• RQ1 Can temporal dependence in grouped observations be effectively modeled to improve latent network inference beyond i.i.d. assumptions?
• RQ2 How does incorporating a Markov chain for group leaders enhance the accuracy of inferred social networks?
• RQ3 What is the computational feasibility of performing network inference under temporal dependence using an EM algorithm with a tractable E-step?
• RQ4 How do correlations between adjacent groups affect the quality of network estimation compared to independent group models?
• RQ5 Can the proposed model successfully recover known social structures in real-world animal grouping data, such as chimpanzee associations?

Key findings

• The proposed model significantly improves network inference accuracy over the independent hub model in simulation settings with temporal dependence.
• The EM algorithm with the forward-backward E-step achieves polynomial-time complexity, making the method scalable to large networks.
• The model successfully captures temporal dynamics in the Kibale Chimpanzee Project data, revealing more realistic social structure than i.i.d. models.
• The inclusion of leader Markov dependence and inter-group correlation leads to more stable and interpretable network estimates.
• The derived derivatives enable efficient optimization via Newton-Raphson, ensuring convergence in practical time.
• The model outperforms co-occurrence and half-weight index methods in recovering ground-truth network structures under temporal dependence.