31 research outputs found
Estimating time-varying networks
Stochastic networks are a plausible representation of the relational
information among entities in dynamic systems such as living cells or social
communities. While there is a rich literature in estimating a static or
temporally invariant network from observation data, little has been done toward
estimating time-varying networks from time series of entity attributes. In this
paper we present two new machine learning methods for estimating time-varying
networks, which both build on a temporally smoothed -regularized logistic
regression formalism that can be cast as a standard convex-optimization problem
and solved efficiently using generic solvers scalable to large networks. We
report promising results on recovering simulated time-varying networks. For
real data sets, we reverse engineer the latent sequence of temporally rewiring
political networks between Senators from the US Senate voting records and the
latent evolving regulatory networks underlying 588 genes across the life cycle
of Drosophila melanogaster from the microarray time course.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS308 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Estimation of dynamic networks for high-dimensional nonstationary time series
This paper is concerned with the estimation of time-varying networks for
high-dimensional nonstationary time series. Two types of dynamic behaviors are
considered: structural breaks (i.e., abrupt change points) and smooth changes.
To simultaneously handle these two types of time-varying features, a two-step
approach is proposed: multiple change point locations are first identified
based on comparing the difference between the localized averages on sample
covariance matrices, and then graph supports are recovered based on a
kernelized time-varying constrained -minimization for inverse matrix
estimation (CLIME) estimator on each segment. We derive the rates of
convergence for estimating the change points and precision matrices under mild
moment and dependence conditions. In particular, we show that this two-step
approach is consistent in estimating the change points and the piecewise smooth
precision matrix function, under certain high-dimensional scaling limit. The
method is applied to the analysis of network structure of the S\&P 500 index
between 2003 and 2008
Bayesian regularization of non-homogeneous dynamic Bayesian networks by globally coupling interaction parameters
To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori independent. Under weak regularity conditions, the parameters can be integrated out in the likelihood, leading to a closed-form expression of the marginal likelihood. However, the assumption of prior independence is unrealistic in many real-world applications, where the segment-specific regulatory relationships among the interdependent quantities tend to undergo gradual evolutionary adaptations. We therefore propose a Bayesian coupling scheme to introduce systematic information sharing among the segment-specific interaction parameters. We investigate the effect this model improvement has on the network reconstruction accuracy in a reverse engineering context, where the objective is to learn the structure of a gene regulatory network from temporal gene expression profiles
Joint Estimation of Multiple Graphical Models from High Dimensional Time Series
In this manuscript we consider the problem of jointly estimating multiple
graphical models in high dimensions. We assume that the data are collected from
n subjects, each of which consists of T possibly dependent observations. The
graphical models of subjects vary, but are assumed to change smoothly
corresponding to a measure of closeness between subjects. We propose a kernel
based method for jointly estimating all graphical models. Theoretically, under
a double asymptotic framework, where both (T,n) and the dimension d can
increase, we provide the explicit rate of convergence in parameter estimation.
It characterizes the strength one can borrow across different individuals and
impact of data dependence on parameter estimation. Empirically, experiments on
both synthetic and real resting state functional magnetic resonance imaging
(rs-fMRI) data illustrate the effectiveness of the proposed method.Comment: 40 page