Probabilistic models are dominant in many research areas. To learn those models we need to find a way to determine parameters of distributions over variables which are included in the model. The main focus of my research is related to continuous variables. Thus, Gaussian distribution over variables is the most dominant factor in all models used in this document. I have been working on different and important real-life problems such as Uncertainty of Neural Network Based Aerosol Retrieval, Regression Learning with Multiple Noise Oracles and Model Predictive Control (MPC) for Sepsis Treatment, Clustering Causes of Action in Federal Courts. These problems will be discussed in the following chapters. Aerosols, small particles emanating from natural and man-made sources, along with green house gases have been recognized as very important factors in ongoing climate changes. Accurate estimation of aerosol composition and concentration is one of the main challenges in current climate research. Algorithm for prediction of aerosol designed by domain scientists does not provide quantitative information about aerosol estimation uncertainty. We deployed algorithm which uses neural networks to determine both uncertainty and the estimation of the aerosol. The uncertainty estimator has been built under an assumption that uncertainty is a function of variables used for aerosol prediction. Also, the uncertainty of predictions has been computed as the variance of the conditional distribution of targets given the input data. In regression learning, it is often difficult to obtain the true values of the label variables, while multiple sources of noisy estimates of lower quality are readily available. To address this problem, I propose a new Bayesian approach that learns a regression model from a data with noisy labels which are provided by multiple oracles. This method gives closed form solution for model parameters and it is applicable to both linear and nonlinear regression problems. Sepsis is a medical condition characterized as a systemic inflammatory response to an infection. High mortality rate (30-35%) of septic patients is usually caused by inadequate treatment. Thus, development of tools that can aid clinicians in designing optimal strategies for inflammation treatments is of utmost importance. Towards this objective I developed a data driven approach for therapy optimization where a predictive model for patients' behavior is learned directly from historical data. As such, the predictive model is incorporated into a model predictive control optimization algorithm to find optimal therapy, which will lead the patient to a healthy state. A more careful targeting of specific therapeutic strategies to more biologically homogeneous groups of patients is essential to developing effective sepsis treatment. We propose a kernel-based approach to characterize dynamics of inflammatory response in a heterogeneous population of septic patients. The method utilizes Linear State Space Control (LSSC) models to take into account dynamics of inflammatory response over time as well as the effect of therapy applied to the patient. We use a similarity measure defined on kernels of LSSC models to find homogeneous groups of patients. In addition to clustering of dynamics of inflammatory response we also explored a clustering of civil litigation from its inception by examining the content of civil complaints. We utilize spectral cluster analysis on a newly compiled federal district court dataset of causes of action in complaints to illustrate the relationship of legal claims to one another, the broader composition of lawsuits in trial courts, and the breadth of pleading in individual complaints. Our results shed light not only on the networks of legal theories in civil litigation but also on how lawsuits are classified and the strategies that plaintiffs and their attorneys employ when commencing litigation. / Computer and Information Science

Harmonic domain models have been developed for Thyristor Controller Reactors (TCR) and other power electronic devices. Recently, these models have been extended to describe not just the steady-state harmonic interactions but harmonic transients as well. However, these dynamic models consistently do not incorporate models for controls. On the other hand, for the TCR as a FACTS Controller, dynamic models are available in which only the fundamental frequency component of the Controller is included; excluding harmonic interactions presumes that these do not affect the dynamics of the Controller. This thesis describes the development of a Harmonic State Space (HSS) model of a three phase TCR. As an extended state space description, this model describes the dynamics of the Controller while capturing harmonic interactions. It also includes the effect of switching instant variation which significantly improves the effectiveness of the model and allows the controller feedback characteristics to be included. The result of this model was validated with a purely time-domain simulation in PSCAD/EMTDC. Using the HSS to model a power system with TCR, it is illustrated that harmonic interactions play a significant role in the dynamics of the system. It is observed that for the specific system analysed, the least-damped pole-pair which dominates the dynamics of the system is associated with the 5th harmonic. Failure to include interactions with this specific harmonic produces an inaccurate dynamic description. Preliminary to the development of HSS model, a linearised harmonic domain model of a TCR which establishes the harmonic interactions across the device is also developed. Results of this model are validated with a time-domain simulation. This characterisation paves the way for a reduced harmonic state space model that is used in the HSS model. The principles and procedures established in this thesis can be applied to the development of models for other FACTS Controllers or HVDC links.

A common interest of scientists in many fields is to understand the relationship between the dynamics of a physical system and the occurrences of discrete events within such physical system. Seismologists study the connection between mechanical vibrations of the Earth and the occurrences of earthquakes so that future earthquakes can be better predicted. Astrophysicists study the association between the oscillating energy of celestial regions and the emission of photons to learn the Universe's various objects and their interactions. Neuroscientists study the link between behavior and the millisecond-timescale spike patterns of neurons to understand higher brain functions. Such relationships can often be formulated within the framework of state-space models with point process observations. The basic idea is that the dynamics of the physical systems are driven by the dynamics of some stochastic state variables and the discrete events we observe in an interval are noisy observations with distributions determined by the state variables. This thesis proposes several new methodological developments that advance the framework of state-space models with point process observations at the intersection of statistics and neuroscience. In particular, we develop new methods 1) to characterize the rhythmic spiking activity using history-dependent structure, 2) to model population spike activity using marked point process models, 3) to allow for real-time decision making, and 4) to take into account the need for dimensionality reduction for high-dimensional state and observation processes. We applied these methods to a novel problem of tracking rhythmic dynamics in the spiking of neurons in the subthalamic nucleus of Parkinson's patients with the goal of optimizing placement of deep brain stimulation electrodes. We developed a decoding algorithm that can make decision in real-time (for example, to stimulate the neurons or not) based on various sources of information present in population spiking data. Lastly, we proposed a general three-step paradigm that allows us to relate behavioral outcomes of various tasks to simultaneously recorded neural activity across multiple brain areas, which is a step towards closed-loop therapies for psychological diseases using real-time neural stimulation. These methods are suitable for real-time implementation for content-based feedback experiments.

In this thesis, we consider the clustering of time series data; specifically, time series that can be modeled in the state space framework. Of primary focus is the pairwise discrepancy between two state space time series. The state space model can be formulated in terms of two equations: the state equation, based on a latent process, and the observation equation. Because the unobserved state process is often of interest, we develop discrepancy measures based on the estimated version of the state process. We compare these measures to discrepancies based on the observed data. In all, seven novel discrepancies are formulated. First, discrepancies derived from Kullback-Leibler (KL) information and Mahalanobis distance (MD) measures are proposed based on the observed data. Next, KL information and MD discrepancies are formulated based on the composite marginal contributions of the smoothed estimates of the unobserved state process. Furthermore, an MD is created based on the joint contributions of the collection of smoothed estimates of the unobserved state process. The cross trajectory distance, a discrepancy heavily influenced by both observed and smoothed data, is proposed as well as a Euclidean distance based on the smoothed state estimates. The performance of these seven novel discrepancies is compared to the often used Euclidean distance based on the observed data, as well as a KL information discrepancy based on the joint contributions of the collection of smoothed state estimates (Bengtsson and Cavanaugh, 2008). We find that those discrepancy measures based on the smoothed estimates of the unobserved state process outperform those discrepancy measures based on the observed data. The best performance was achieved by the discrepancies founded upon the joint contributions of the collection of unobserved states, followed by the discrepancies derived from the marginal contributions. We observed a non-trivial degradation in clustering performance when estimating the parameters of the state space model. To improve estimation, we propose an iterative estimation and clustering routine based on the notion of finding a series' most similar counterparts, pooling them, and estimating a new set of parameters. Under ideal circumstances, we show that the iterative estimation and clustering algorithm can potentially achieve results that approach those obtained in settings where parameters are known. In practice, the algorithm often improves the performance of the model-based clustering measures. We apply our methods to two examples. The first application pertains to the clustering of time course genetic data. We use data from Cho et al. (1998) where a time course experiment of yeast gene expression was performed in order to study the yeast mitotic cell cycle. We attempt to discover the phase to which 219 genes belong. The second application seeks to answer whether or not influenza and pneumonia mortality can be explained geographically. Data from a collection of cities across the U.S. are acquired from the Morbidity and Mortality Weekly Report (MMWR). We cluster the MMWR data without geographic constraints, and compare the results to clusters defined by MMWR geographic regions. We find that influenza and pneumonia mortality cannot be explained by geography.

A numerical scheme to simulate time-domain motion responses of multibody floating systems has been successfully proposed. This scheme is integrated into a time-domain simulation tool, with fully coupled hydrodynamic coefficients obtained from the hydrodynamic software - WAMIT which solves the Boundary Value Problem (BVP). The equations of motion are transformed into standard state-space format, using the constant coefficient approximation and the impulse response function method. Thus the Ordinary Differential Equation (ODE) solvers in MATLAB can be directly employed. The time-domain responses of a single spar at sea are initially obtained. The optimal Linear Quadratic Regulator (LQR) controller is further applied to this single spar, by assuming that the Dynamic Positioning (DP) system can provide the optimized thruster forces. Various factors that affect the controlling efficiency, e.g., the time steps ∆τ and ∆t, the weighting factors(Q,R), are further investigated in detail. Next, a two-body floating system is studied. The response amplitude operators (RAOs) of each body are calculated and compared with the single body case. Then the effects of the body-to-body interaction coefficients on the time-domain responses are further investigated. Moreover, the mean drift force is incorporated in the DP system to further mitigate the motion responses of each body. Finally, this tool is extended to a three-body floating system, with the relative motions between them derived.

In recent years, reliability evaluation of substation automation systems has received a significant attention from the research community. With the advent of the concept of smart grid, there is a growing trend to integrate more computation and communication technology into power systems. This thesis focuses on the reliability evaluation of modern substation automation systems. Such systems include both physical devices (current carrying) such as lines, circuit breakers, and transformers, as well as cyber devices (Ethernet switches, intelligent electronic devices, and cables) and belong to a broader class of cyber-physical systems. We assume that the substation utilizes IEC 61850 standard, which is a dominant standard for substation automation. Focusing on IEC 61850 standard, we discuss the failure modes and analyze their effects on the system. We utilize reliability block diagrams for analyzing the reliability of substation components (bay units) and then use the state space approach to study the effects at the substation level. Case study is based on an actual IEC 61850 substation automation system, with different network topologies consideration concluded. Our analysis provides a starting point for evaluating the reliability of the substation and the effects of substation failures to the rest of the power system. By using the state space methods, the steady state probability of each failure effects were calculated in different bay units. These probabilities can be further used in the modeling of the composite power system to analyze the loss of load probabilities.

The artificial neural network (ANN) approach has been recognized as a capable technique to model the highly complex and nonlinear problem of travel time prediction. In addition to the nonlinearity, a traffic system is also temporally and spatially dynamic. Addressing the temporal-spatial relationships of a traffic system in the context of neural networks, however, has not received much attention. Furthermore, many of the past studies have not fully explored the inclusion of incident information into the ANN model development, despite that incident might be a major source of prediction degradations. Additionally, directly deriving corridor travel times in a one-step manner raises some intractable problems, such as pairing input-target data, which have not yet been adequately discussed. In this study, the corridor travel time prediction problem has been divided into two stages with the first stage on prediction of the segment travel time and the second stage on corridor travel time aggregation methodologies of the predicted segmental results. To address the dynamic nature of traffic system that are often under the influence of incidents, time delay neural network (TDNN), state-space neural network (SSNN), and an extended state-space neural network (ExtSSNN) that incorporates incident inputs are evaluated for travel time prediction along with a traditional back propagation neural network (BP) and compared with baseline methods based on historical data. In the first stage, the empirical results show that the SSNN and ExtSSNN, which are both trained with Bayesian regulated Levenberg Marquardt algorithm, outperform other models. It is also concluded that the incident information is redundant to the travel time prediction problem with speed and volume data as inputs. In the second stage, the evaluations on the applications of the SSNN model to predict snapshot travel times and experienced travel times are made. The outcomes of these evaluations are satisfactory and the method is found to be practically significant in that it (1) explicitly reconstructs the temporalspatial traffic dynamics in the model, (2) is extendable to arbitrary O-D pairs without complete retraining of the model, and (3) can be used to predict both traveler experiences and system overall conditions.

In power system reliability analysis, state space pruning has been investigated to improve the efficiency of the conventional Monte Carlo Simulation (MCS). New algorithms have been proposed to prune the state space so as to make the Monte Carlo Simulation sample a residual state space with a higher density of failure states. This thesis presents a modified Genetic Algorithm (GA) as the state space pruning tool, with higher efficiency and a controllable stopping criterion as well as better parameter selection. This method is tested using the IEEE Reliability Test System (RTS 79 and MRTS), and is compared with the original GA-MCS method. The modified GA shows better efficiency than the previous methods, and it is easier to have its parameters selected. This thesis also presents a Dynamic Programming (DP) algorithm as an alternative state space pruning tool. This method is also tested with the IEEE Reliability Test System and it shows much better efficiency than using Monte Carlo Simulation alone.

Thesis (M.Sc.)--Memorial University of Newfoundland, 2000. / Bibliography: p. 79-84.

Thesis (Ph. D.)--University of California, Riverside, 2008. / Includes abstract. Title from first page of PDF file (viewed March 10, 2010). Available via ProQuest Digital Dissertations. Includes bibliographical references (p. 166-170). Also issued in print.