24,660 research outputs found
Sparse covariance estimation in heterogeneous samples
Standard Gaussian graphical models (GGMs) implicitly assume that the
conditional independence among variables is common to all observations in the
sample. However, in practice, observations are usually collected form
heterogeneous populations where such assumption is not satisfied, leading in
turn to nonlinear relationships among variables. To tackle these problems we
explore mixtures of GGMs; in particular, we consider both infinite mixture
models of GGMs and infinite hidden Markov models with GGM emission
distributions. Such models allow us to divide a heterogeneous population into
homogenous groups, with each cluster having its own conditional independence
structure. The main advantage of considering infinite mixtures is that they
allow us easily to estimate the number of number of subpopulations in the
sample. As an illustration, we study the trends in exchange rate fluctuations
in the pre-Euro era. This example demonstrates that the models are very
flexible while providing extremely interesting interesting insights into
real-life applications
Discovering Functional Communities in Dynamical Networks
Many networks are important because they are substrates for dynamical
systems, and their pattern of functional connectivity can itself be dynamic --
they can functionally reorganize, even if their underlying anatomical structure
remains fixed. However, the recent rapid progress in discovering the community
structure of networks has overwhelmingly focused on that constant anatomical
connectivity. In this paper, we lay out the problem of discovering_functional
communities_, and describe an approach to doing so. This method combines recent
work on measuring information sharing across stochastic networks with an
existing and successful community-discovery algorithm for weighted networks. We
illustrate it with an application to a large biophysical model of the
transition from beta to gamma rhythms in the hippocampus.Comment: 18 pages, 4 figures, Springer "Lecture Notes in Computer Science"
style. Forthcoming in the proceedings of the workshop "Statistical Network
Analysis: Models, Issues and New Directions", at ICML 2006. Version 2: small
clarifications, typo corrections, added referenc
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