New model named Temporal Exponential Random Graphical Model(tERGM)

Brief Description of the tERGM Model Methods

This novel Model comes from htERGM Model. However, it has some difference with the htERGM Model in the following aspects:

• The tERGM model considers only the structures and topologies of the temporal networks, while node attributes are ignored.
• the htERGM model learns the network based on node attributes, but it does not make predictions of the future step.
• The application of htERGM is limited to retrieval of networks of up to 10 nodes because the model

requires to learn two sets of latent parameters the evolving structure of a temporal network and the changing attribute values of the nodes are given.

Given the evolving structure of a temporal network and the changing attribute values of the nodes,the tERGM model can facilitate simultaneous prediction of links and nodes attribute in a temporal social network. Instead of training a single joint probability prediction model, they build two conditional exponential random graph models. These two conditional predictors are mutually dependent on each other, and can then be used to predict the links, and the attribute values in an alternative way.

Different models are used to predict nodes and links:

For node prediction, use the following model:

For link prediction, use the following model

The node and link prediction models proposed above are all log-linear.Two sets of parameters, θ and γ need to be learned. This paper use Newton's optimization to learn the two parameters.