Learning Networks of Stochastic Differential Equations

Abstract

We consider linear models for stochastic dynamics. To any such model can be associated a network (namely a directed graph) describing which degrees of freedom interact under the dynamics. We tackle the problem of learning such a network from observation of the system trajectory over a time interval $T$. We analyze the ${\ell }_1$-regularized least squares algorithm and, in the setting in which the underlying network is sparse, we prove performance guarantees that are \emph{uniform in the sampling rate} as long as this is sufficiently high. This result substantiates the notion of a well defined `time complexity' for the network inference problem.

This publication is to appear in NIPS 2010

Cited by in corpus (12)

• Causal Network Inference via Group Sparse Regularization
• A Direct Estimation of High Dimensional Stationary Vector Autoregressions
• Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning Approach
• Learning the Dependence Graph of Time Series with Latent Factors
• Efficient Reinforcement Learning for High Dimensional Linear Quadratic Systems
• Reconstructing undirected graphs from eigenspaces
• Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach
• On the Sample Complexity of Graphical Model Selection for Non-Stationary Processes
• On the Information-theoretic Limits of Graphical Model Selection for Gaussian Time Series
• Mixing Times and Structural Inference for Bernoulli Autoregressive Processes
• Graphical LASSO Based Model Selection for Time Series
• Learning conditional independence structure for high-dimensional uncorrelated vector processes