Estimating time-varying networks

Abstract

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 $l_1$-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.

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)

References in corpus (10)

• High-dimensional graphs and variable selection with the Lasso
• Pathwise coordinate optimization
• One-step sparse estimates in nonconcave penalized likelihood models
• Sparse permutation invariant covariance estimation
• High-dimensional Ising model selection using ${\ell }_1$-regularized logistic regression
• Network exploration via the adaptive LASSO and SCAD penalties
• Properties and refinements of the fused lasso
• Projected Subgradient Methods for Learning Sparse Gaussians
• Model Selection Through Sparse Maximum Likelihood Estimation
• Sparsistent Estimation of Time-Varying Discrete Markov Random Fields

Cited by in corpus (19)

• Temporal Networks
• A state-space mixed membership blockmodel for dynamic network tomography
• Advances in Distributed Graph Filtering
• Structural and Functional Discovery in Dynamic Networks with Non-negative Matrix Factorization
• Maximin effects in inhomogeneous large-scale data
• Change-Point Estimation in High-Dimensional Markov Random Field Models
• Bootstrap inference for network construction with an application to a breast cancer microarray study
• Network Risk and Forecasting Power in Phase-Flipping Dynamical Networks
• Sparse Nonparametric Graphical Models
• Conditional anomaly detection with soft harmonic functions
• Co-community Structure in Time-varying Networks
• Nonparametric inference for continuous-time event counting and link-based dynamic network models
• Temporal connection signatures of human brain networks after stroke
• Non Parametric Statistics of Dynamic Networks with distinguishable nodes
• Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models
• Estimation of dynamic networks for high-dimensional nonstationary time series
• Efficient Variational Bayes Learning of Graphical Models with Smooth Structural Changes
• Understanding and Predicting Delay in Reciprocal Relations
• Covariate-Assisted Bayesian Graph Learning for Heterogeneous Data