Composite likelihood inference for hidden Markov models for dynamic networks

We introduce a hidden Markov model for dynamic network data where directed relations among a set of units are observed at different time occasions. The model can also be used with minor adjustments to deal with undirected networks. In the directional case, dyads referred to each pair of units are explicitly modelled conditional on the latent states of both units. Given the complexity of the model, we propose a composite likelihood method for making inference on its parameters. This method is studied in detail for the directional case by a simulation study in which different scenarios are considered. The proposed approach is illustrated by an example based on the well-known Enron dataset about email exchange.

[1]  Francesco Bartolucci,et al.  Pairwise Likelihood Inference for Nested Hidden Markov Chain Models for Multilevel Longitudinal Data , 2016 .

[2]  Alfred O. Hero,et al.  Dynamic Stochastic Blockmodels for Time-Evolving Social Networks , 2014, IEEE Journal of Selected Topics in Signal Processing.

[3]  T. Snijders,et al.  Estimation and Prediction for Stochastic Blockstructures , 2001 .

[4]  D. Dunson,et al.  Nonparametric Bayes dynamic modelling of relational data , 2013, 1311.4669.

[5]  Purnamrita Sarkar,et al.  A Latent Space Approach to Dynamic Embedding of Co-occurrence Data , 2007, AISTATS.

[6]  E. Xing,et al.  A state-space mixed membership blockmodel for dynamic network tomography , 2008, 0901.0135.

[7]  Kevin S. Xu.  Stochastic Block Transition Models for Dynamic Networks , 2014, AISTATS.

[8]  Harry Joe,et al.  Composite Likelihood Methods , 2012 .

[9]  Antonello Maruotti.  Latent Markov Models for longitudinal data , 2014 .

[10]  Le Song,et al.  Evolving Cluster Mixed-Membership Blockmodel for Time-Evolving Networks , 2011, AISTATS.

[11]  Huan Liu,et al.  Community evolution in dynamic multi-mode networks , 2008, KDD.

[12]  Peter D. Hoff,et al.  Hierarchical multilinear models for multiway data , 2010, Comput. Stat. Data Anal..

[13]  N. H. Lee,et al.  A latent process model for time series of attributed random graphs , 2011 .

[14]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[15]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[16]  V. P. Godambe.  An Optimum Property of Regular Maximum Likelihood Estimation , 1960 .

[17]  C. Varin,et al.  A note on composite likelihood inference and model selection , 2005 .

[18]  Yiming Yang,et al.  The Enron Corpus: A New Dataset for Email Classi(cid:12)cation Research , 2004 .

[19]  Walter Zucchini,et al.  Series of Seminars: Hidden Markov Models for Time Series , 2013 .

[20]  Edoardo M. Airoldi,et al.  A Survey of Statistical Network Models , 2009, Found. Trends Mach. Learn..

[21]  N. Reid,et al.  AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS , 2011 .

[22]  L. Baum,et al.  A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains , 1970 .

[23]  Francesco Bartolucci,et al.  Information matrix for hidden Markov models with covariates , 2015, Stat. Comput..

[24]  P. Song,et al.  Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data , 2010 .

[25]  Yihong Gong,et al.  Detecting communities and their evolutions in dynamic social networks—a Bayesian approach , 2011, Machine Learning.

[26]  P. Holland,et al.  Local Structure in Social Networks , 1976 .

[27]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[28]  P. Pattison,et al.  Random graph models for temporal processes in social networks , 2001 .

[29]  A. Moore,et al.  Dynamic social network analysis using latent space models , 2005, SKDD.

[30]  D. Cox,et al.  A note on pseudolikelihood constructed from marginal densities , 2004 .