Estimation of Node Hidden Processes and Network Topologies by Particle Filtering
August 3, 2018
Light Engineering room 250
Advisor: Prof. Petar M. Djuric
This dissertation addresses the problem of estimation of complex dynamic processes and network topologies from graph signals. We use a state-space representation to describe the nonlinear system and extract information regarding the hidden node states and the interactions between the nodes by using noisy observations. We propose novel methods for inference in networks which are based on sequential Monte Carlo methods and Bayesian statistics. We start by tackling the state estimation problem for high dimensional problems. State space representation allows for the use of particle filters to track the states. However standard particle filters suffer from the curse of dimensionality. We employ a bank of particle filters to track the state of each hidden node separately. For the unknowns of the system, we select Gaussian priors. Then the coefficients describing the interactions between nodes can be marginalized to obtain the posteriors for the states and thereby allowing for improved implementation of the proposed Multiple Particle Filtering approach. Second, we propose an iterative particle-based method for topology estimation. The probabilities of the possible topologies can be computed using only the state estimates which permits the generation of proposals of new topologies in an iterative manner. The resampling step of particle filtering eliminates the topologies with smaller weights and improves the results. Two other topology selection methods are also explored within this setting. The novelty of the mentioned topology estimation methods is that each particle stream has a different topology while the selection is based on the weights of the particles. Finally, we evaluate the proposed methods on gene regulatory networks and compare their performance with that of Lasso-based methods. While for synthetic data sets it is possible to assess the performance of the algorithm using the information of the true network, for real data sets, gold standards are used for comparisons.