| dc.description.abstract | Nonlinear state-space models have long been used in the statistical signal processing community as a powerful tool for modeling and forecasting the behavior of dynamical systems. However, in the case of a large system with many unknown parameters, which is a common scenario in real-world applications, the computational complexity of most methods becomes intractable, especially when the system parameters contain both discrete and continuous components.
This dissertation is focused on efficient state and parameter estimation in nonlinear dynamical
systems with applications in biochemical regulatory networks and epidemic models. First, we
present PALLAS, a practical nonlinear state-space method for gene regulatory network (GRN) and protein-protein interaction network (PPI) inference from real-world time-series data, which employs penalized maximum likelihood and particle swarms for optimization. PALLAS is based on the Partially-Observed Boolean Dynamical System (POBDS) model and thus does not require ad hoc binarization of the data. The penalty in the likelihood is a LASSO regularization term, which encourages the resulting network to be sparse. PALLAS is able to scale to networks of realistic size under no prior knowledge, by virtue of a novel continuous-discrete Fish School Search particle swarm algorithm for efficient simultaneous maximization of the penalized likelihood over the discrete space of networks and the continuous space of observational parameters. The accuracy and efficiency of PALLAS are demonstrated by a comprehensive set of experiments using synthetic data generated from real and artificial networks, as well as real time-series microarray and RNA-seq data, where it is compared to several other well-known methods.
In addition, we developed a similar state-space method to model the outbreak of the COVID 19.
Mathematical models are widely recognized as an important tool to help people better understand the epidemic, predict its future trends, explore intervention scenarios and ultimately control the epidemic, such as lock-down or vaccination. We proposed a sophisticated spatial-temporal nonlinear state-space model based on a discrete-time susceptible - exposed - infected - recovered – deceased (SEIRD) model, which can estimate the hidden states and parameters from a noisy, incomplete, time series of reported epidemiological data, by applying Unscented Kalman Filter (UKF), Maximum Likelihood (ML) adaptive filtering and Broyden–Fletcher–Goldfarb–Shanno (BFGS)/metaheuristic optimization. A comprehensive set of experiments, including simulations with different parameters set on the state model, and estimations by using the synthetic dataset, demonstrate our model can not only effectively simulate the different scenarios of the epidemic, such as spread with complex contagion patterns, lock-down patterns, and vaccination scenario, but also accurately estimate the
unknown states and parameters which can be used for the prediction of the future trend. | |
