41 research outputs found
Reconstruction of Directed Networks from Consensus Dynamics
This paper addresses the problem of identifying the topology of an unknown,
weighted, directed network running a consensus dynamics. We propose a
methodology to reconstruct the network topology from the dynamic response when
the system is stimulated by a wide-sense stationary noise of unknown power
spectral density. The method is based on a node-knockout, or grounding,
procedure wherein the grounded node broadcasts zero without being eliminated
from the network. In this direction, we measure the empirical cross-power
spectral densities of the outputs between every pair of nodes for both grounded
and ungrounded consensus to reconstruct the unknown topology of the network. We
also establish that in the special cases of undirected or purely unidirectional
networks, the reconstruction does not need grounding. Finally, we extend our
results to the case of a directed network assuming a general dynamics, and
prove that the developed method can detect edges and their direction.Comment: 6 page
Bayesian topology identification of linear dynamic networks
In networks of dynamic systems, one challenge is to identify the
interconnection structure on the basis of measured signals. Inspired by a
Bayesian approach in [1], in this paper, we explore a Bayesian model selection
method for identifying the connectivity of networks of transfer functions,
without the need to estimate the dynamics. The algorithm employs a Bayesian
measure and a forward-backward search algorithm. To obtain the Bayesian
measure, the impulse responses of network modules are modeled as Gaussian
processes and the hyperparameters are estimated by marginal likelihood
maximization using the expectation-maximization algorithm. Numerical results
demonstrate the effectiveness of this method
Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes
We investigate approximating joint distributions of random processes with
causal dependence tree distributions. Such distributions are particularly
useful in providing parsimonious representation when there exists causal
dynamics among processes. By extending the results by Chow and Liu on
dependence tree approximations, we show that the best causal dependence tree
approximation is the one which maximizes the sum of directed informations on
its edges, where best is defined in terms of minimizing the KL-divergence
between the original and the approximate distribution. Moreover, we describe a
low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure