Abstract
Dynamic networks models describe a growing number of important
scientific processes, from cell biology and epidemiology to sociology
and finance. There are many aspects of dynamical networks that require
statistical considerations. In this paper we focus on determining
network structure. Estimating dynamic networks is a difficult task since
the number of components involved in the system is very large. As a
result, the number of parameters to be estimated is bigger than the
number of observations. However, a characteristic of many networks is
that they are sparse. For example, the molecular structure of genes make
interactions with other components a highly-structured and therefore
sparse process. Penalized Gaussian graphical models have been used to
estimate sparse networks. However, the literature has focussed on static
networks, which lack specific temporal constraints. We propose a
structured Gaussian dynamical graphical model, where structures can
consist of specific time dynamics, known presence or absence of links
and block equality constraints on the parameters. Thus, the number of
parameters to be estimated is reduced and accuracy of the estimates,
including the identification of the network, can be tuned up. Here, we
show that the constrained optimization problem can be solved by taking
advantage of an efficient solver, logdetPPA, developed in convex
optimization. Moreover, model selection methods for checking the
sensitivity of the inferred networks are described. Finally, synthetic
and real data illustrate the proposed methodologies.
Original language | English |
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Pages (from-to) | 2911 |
Journal | ArXiv |
Volume | 1205 |
Publication status | Published - 1-May-2012 |
Keywords
- Statistics - Methodology
- Mathematics - Statistics Theory
- Statistics - Applications
- Statistics - Computation