2.3 A Mixture of Experts Latent Position Cluster Model for Social Network Data (Claire Gormley)
Description
Social network data represent the interactions between a group of social actors. Interactions between colleagues and friendship networks are typical examples of such data. The latent space model for social network data locates each actor in a network in a latent (social) space and models the probability of an interaction between two actors as a function of their locations. The latent position cluster model extends the latent space model to deal with network data in which clusters of actors exist ? actor locations are drawn from a finite mixture model, each component of which represents a cluster of actors. A mixture of experts model builds on the structure of a mixture model by taking account of both observations and associated covariates when modeling a heterogeneous population. Herein, a mixture of experts extension of the latent position cluster model is developed. The mixture of experts framework allows covariates to enter the latent position cluster model in a number of ways, yielding different model interpretations. Estimates of the model parameters are derived in a Bayesian framework using a Markov Chain Monte Carlo algorithm. The algorithm is generally computationally expensive ? surrogate proposal distributions which shadow the target distributions are derived, reducing the computational burden. The methodology is demonstrated through an illustrative example detailing relations between a group of lawyers in the USA.
Transactional network data arise in many fields. Although social network models have been applied to transactional data, these models typically assume binary relations between pairs of nodes. We develop a latent mixed membership model capable of modelling richer forms of transactional data....
Published 12/04/14
We consider the problem of Gaussian regression (possibly in a high- dimensional setting) when the noise variance is unknown. We propose a procedure which selects within any collection of estimators, an estimator hatf that nearly achieves the best bias/variance trade off. This selection procedure...
Published 12/04/14