2,239 research outputs found
Random graph models for dynamic networks
We propose generalizations of a number of standard network models, including
the classic random graph, the configuration model, and the stochastic block
model, to the case of time-varying networks. We assume that the presence and
absence of edges are governed by continuous-time Markov processes with rate
parameters that can depend on properties of the nodes. In addition to computing
equilibrium properties of these models, we demonstrate their use in data
analysis and statistical inference, giving efficient algorithms for fitting
them to observed network data. This allows us, for instance, to estimate the
time constants of network evolution or infer community structure from temporal
network data using cues embedded both in the probabilities over time that node
pairs are connected by edges and in the characteristic dynamics of edge
appearance and disappearance. We illustrate our methods with a selection of
applications, both to computer-generated test networks and real-world examples.Comment: 15 pages, four figure
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
Detection of Epigenomic Network Community Oncomarkers
In this paper we propose network methodology to infer prognostic cancer
biomarkers based on the epigenetic pattern DNA methylation. Epigenetic
processes such as DNA methylation reflect environmental risk factors, and are
increasingly recognised for their fundamental role in diseases such as cancer.
DNA methylation is a gene-regulatory pattern, and hence provides a means by
which to assess genomic regulatory interactions. Network models are a natural
way to represent and analyse groups of such interactions. The utility of
network models also increases as the quantity of data and number of variables
increase, making them increasingly relevant to large-scale genomic studies. We
propose methodology to infer prognostic genomic networks from a DNA
methylation-based measure of genomic interaction and association. We then show
how to identify prognostic biomarkers from such networks, which we term
`network community oncomarkers'. We illustrate the power of our proposed
methodology in the context of a large publicly available breast cancer dataset
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