67,422 research outputs found
Factorial graphical lasso for dynamic networks
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.Comment: 30 pp, 5 figure
Bethe Projections for Non-Local Inference
Many inference problems in structured prediction are naturally solved by
augmenting a tractable dependency structure with complex, non-local auxiliary
objectives. This includes the mean field family of variational inference
algorithms, soft- or hard-constrained inference using Lagrangian relaxation or
linear programming, collective graphical models, and forms of semi-supervised
learning such as posterior regularization. We present a method to
discriminatively learn broad families of inference objectives, capturing
powerful non-local statistics of the latent variables, while maintaining
tractable and provably fast inference using non-Euclidean projected gradient
descent with a distance-generating function given by the Bethe entropy. We
demonstrate the performance and flexibility of our method by (1) extracting
structured citations from research papers by learning soft global constraints,
(2) achieving state-of-the-art results on a widely-used handwriting recognition
task using a novel learned non-convex inference procedure, and (3) providing a
fast and highly scalable algorithm for the challenging problem of inference in
a collective graphical model applied to bird migration.Comment: minor bug fix to appendix. appeared in UAI 201
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