One of the hardest challenges in building a realistic Bayesian network (BN) model is to construct the node probability tables (NPTs). Even with a fixed predefined model structure and very large amounts of relevant data, machine learning methods do not consistently achieve great accuracy compared to the ground truth when learning the NPT entries (parameters). Hence, it is widely believed that incorporating expert judgment or related domain knowledge can improve the parameter learning accuracy. This is especially true in the sparse data situation. Expert judgments come in many forms. In this thesis we focus on expert judgment that specifies inequality or equality relationships among variables. Related domain knowledge is data that comes from a different but related problem. By exploiting expert judgment and related knowledge, this thesis makes novel contributions to improve the BN parameter learning performance, including: • The multinomial parameter learning model with interior constraints (MPL-C) and exterior constraints (MPL-EC). This model itself is an auxiliary BN, which encodes the multinomial parameter learning process and constraints elicited from the expert judgments. • The BN parameter transfer learning (BNPTL) algorithm. Given some potentially related (source) BNs, this algorithm automatically explores the most relevant source BN and BN fragments, and fuses the selected source and target parameters in a robust way. • A generic BN parameter learning framework. This framework uses both expert judgments and transferred knowledge to improve the learning accuracy. This framework transfers the mined data statistics from the source network as the parameter priors of the target network. Experiments based on the BNs from a well-known repository as well as two realworld case studies using different data sample sizes demonstrate that the proposed new approaches can achieve much greater learning accuracy compared to other state-of-theart methods with relatively sparse data.

Inertial navigation is a relative navigation technique commonly used by autonomous vehicles to determine their linear velocity, position and orientation in three-dimensional space. The basic premise of inertial navigation is that measurements of acceleration and angular velocity from an inertial measurement unit (IMU) are integrated over time to produce estimates of linear velocity, position and orientation. However, this process is a particularly involved one. The raw inertial data must first be properly analyzed and modeled in order to ensure that any inertial navigation system (INS) that uses the inertial data will produce accurate results. This thesis describes the process of analyzing and modeling raw IMU data, as well as how to use the results of that analysis to design an INS. Two separate INS units are designed using two different micro-electro-mechanical system (MEMS) IMUs. To test the effectiveness of each INS, each IMU is rigidly mounted to an unmanned ground vehicle (UGV) and the vehicle is driven through a known test course. The linear velocity, position and orientation estimates produced by each INS are then compared to the true linear velocity, position and orientation of the UGV over time. Final results from these experiments include quantifications of how well each INS was able to estimate the true linear velocity, position and orientation of the UGV in several different navigation scenarios as well as a direct comparison of the performances of the two separate INS units.

An innovative artificial immune system (AIS) is proposed herein for structural health monitoring (SHM) to ensure the structural integrity and functionality. While satisfactory results were obtained by previous AIS schemes, their performance is strongly structural-parameter-value (SPV) dependent and deviations of SPVs in testing from training due to modeling errors and measurement noises significantly deteriorates the AIS' performance. This thesis presents a less SPV-dependent AIS with a three-phase architecture, including damage-existence-detection, damage-location-determination, and damage-severity-estimation, using specially designed feature vectors (FVs) based on structural modal parameters. The maximum-relative-modal-parameter-change is used to detect the damage's existence and estimate its severity, and the pattern in normalized-modal-parameter-change is used to determinate the damage's location. Comparisons between the proposed FVs and their existing counterparts were conducted for 2/3/4-degree-of-freedom structures to illustrate the superior performance and less SPV-dependence of the proposed method, particularly in determining damage location. The proposed AIS was tested on a 4-degree-of-freedom model using 440 randomly generated damage conditions with a different SPV set per condition. A success rate of 95.23% in the determination of damage's existence and its location was obtained. The trained AIS for the 4-degree-of-freedom model was further evaluated by a four-story and two-bay by two-bay prototype structure used in the benchmark problem proposed by the IASC-ASCE Structural Health Monitoring Task Group. Results have shown great potentials of the proposed approach in its real-world applications.

Non-convex optimization of deep neural networks is a well-researched problem. We present a novel application of continuation methods for deep learning optimization that can potentially arrive at a better solution. In our method, we first decompose the original optimization problem into a sequence of problems using a homotopy method. To achieve this in neural networks, we derive the Continuation(C)- Activation function. First, C-Activation is a homotopic formulation of existing activation functions such as Sigmoid, ReLU or Tanh. Second, we apply a method which is standard in the parameter continuation domain, but to the best of our knowledge, novel to the deep learning domain. In particular, we use Natural Parameter Continuation with Secant approximation(NPCS), an effective training strategy that may find a superior local minimum for a non-convex optimization problem. Additionally, we extend our work on Step-up GANs, a data continuation approach, by deriving a method called Continuous(C)-SMOTE which is an extension of standard oversampling algorithms. We demonstrate the improvements made by our methods and establish a categorization of recent work done on continuation methods in the context of deep learning.

The widely collected and analyzed genetic data help in understanding the underlying mechanisms of heterogeneous diseases. Cellular components interact in a network fashion where genes are nodes and edges are the interactions. The failure in individual genes lead to dys-regulation of sub-groups of genes which causes a disease phenotype, and this dys-functional region is called a disease module. Disease module identification in complex diseases such as asthma and cancer is a huge challenge. Despite the development of numerous sophisticated methods there is a still no gold standard. In this study we apply different parameter settings to test the performance of a widely used method for disease module detection in multi-omics data called Weighted Gene Co-expression Network Analysis (WGCNA). A systematic approach is used to identify disease modules in asthma and arthritis diseases. The accuracy of obtained modules is validated by a pathway scoring algorithm (PASCAL) and GWAS SNP enrichment. Our results differ between the tested data sets and therefore we cannot conclude with recommendations for an optimal setting that could perform best for multiple data sets using this method.

We provide an L² theory for the local double Hilbert transform along an analytic surface (s, t ,φ(s, t )) in the Heisenberg group H¹, that is operator f ↦ Hφ f (x) := p.v.∫∣s∣,∣t∣≤1 f (x ∙ (s, t ,φ(s, t ))-¹) ds/s dt/t, where ∙ denotes the group operation in H1. This operator combines several features: it is amulti-parameter singular integral, its kernel is supported along a submanifold, and convolution is with respect to a homogeneous group structure. We reprove Hφ is always L²(H¹)→L²(H¹) bounded (a result first obtained in [Str12]) to illustrate the method and then refine it to characterize the largest class of polynomials P of degree less than d such that the operator HP is uniformly bounded when P ranges in the class. Finally, we provide examples of surfaces that can be treated by our method but not by the theory of [Str12].

We address questions related to the parameterization of two distinct types of seismic sources: earthquakes and underground nuclear explosions. For earthquakes, we focus on the improvement of location parameters, latitude and longitude, using relative measurements of spatial cluster of events. For underground nuclear explosions, we focus on the seismic source model, especially with regard to the generation of surface waves. We develop a procedure to improve relative earthquake location estimates by fitting predicted differential travel times to those measured by cross-correlating Rayleigh- and Love-wave arrivals for multiple earthquakes recorded at common stations. Our procedure can be applied to populations of earthquakes with arbitrary source mechanisms because we mitigate the phase delay that results from surface-wave radiation patterns by making source corrections calculated from the source mechanism solutions published in the Global CMT Catalog. We demonstrate the effectiveness of this relocation procedure by first applying it to two suites of synthetic earthquakes. We then relocate real earthquakes in three separate regions: two ridge-transform systems and one subduction zone. In each scenario, relocated epicenters show a reduction in location uncertainty compared to initial single-event location estimates. We apply the relocation procedure on a larger scale to the seismicity of the Eltanin Fault System which is comprised of three large transform faults: the Heezen transform, the Tharp transform, and the Hollister transform. We examine the localization of seismicity in each transform, the locations of earthquakes with atypical source mechanisms, and the spatial extent of seismic rupture and repeating earthquakes in each transform. We show that improved relative location estimates, aligned with bathymetry, greatly reduces the localization of seismicity on each of the three transforms. We also show how improved location estimates enhance the ability to use earthquake locations to address geophysical questions such as the presence of atypical earthquakes and the nature of seismic rupture along an oceanic transform fault. We investigate the physical basis for the mb-MS discriminant, which relies on differences between amplitudes of body waves and surface waves. We analyze observations for 71 well-recorded underground nuclear tests that were conducted between 1977-1989 at the Balapan test site near Semipalatinsk, Kazakhstan in the former Soviet Union. We combine revised mb values and earlier long-period surface-wave results with a new source model, which allows the vertical and horizontal forces of the explosive source to be different. We introduce a scaling factor between vertical and horizontal forces in the explosion model, to reconcile differences between body wave and surface wave observations. We find that this parameter is well correlated with the scaled depth of burial for UNEs at this test site. We use the modified source model to estimate the scaled depth of burial for the 71 UNEs considered in this study.

This thesis considers the problem of feature selection when the number of predictors is larger than the number of samples. The performance of supersaturated design (SSD) working with least absolute shrinkage and selection operator (LASSO) is studied in this setting. In order to achieve higher feature selection correctness, self-voting LASSO is implemented to select the tuning parameter while approximately optimize the probability of achieving Sign Correctness. Furthermore, we derive the probability of achieving Direction Correctness, and extend the self-voting LASSO to multi-task self-voting LASSO, which has a group screening effect for multiple tasks.

In this dissertation I suggest a new (regularized) weighted quantile regression estimation approach for nonlinear regression models and double threshold ARCH (DTARCH) models. I allow the number of parameters in the nonlinear regression models to be fixed or diverge. The proposed estimation method is robust and efficient and is applicable to other models. I use the adaptive-LASSO and SCAD regularization to select parameters in the nonlinear regression models. I simultaneously estimate the AR and ARCH parameters in the DTARCH model using the proposed weighted quantile regression. The values of the proposed methodology are revealed. / Keywords: Weighted quantile regression, Adaptive-LASSO, High dimensionality, Model selection, Oracle property, SCAD, DTARCH models. / Under regularity conditions, I establish asymptotic distributions of the proposed estimators, which show that the model selection methods perform as well as if the correct submodels are known in advance. I also suggest an algorithm for fast implementation of the proposed methodology. Simulations are conducted to compare different estimators, and a real example is used to illustrate their performance. / Jiang, Xuejun. / Adviser: Xinyuan Song. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 86-92). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.

Sunnyson Y.F. Seid. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 65-66). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Applications in parameter identifications --- p.1 / Chapter 1.2 --- Inverse problems --- p.6 / Chapter 1.3 --- Difficulties arising in inverse problems --- p.7 / Chapter 2 --- Methods in Parameter Identifications --- p.9 / Chapter 2.1 --- Output Least Squares Method --- p.9 / Chapter 2.2 --- Equation Error Method --- p.11 / Chapter 2.3 --- Augmented Lagrangian Techniques --- p.12 / Chapter 2.4 --- Variational Techniques --- p.14 / Chapter 2.5 --- Adaptive Control Methods --- p.15 / Chapter 2.6 --- Method of Characteristics --- p.16 / Chapter 2.7 --- Our Proposed Method --- p.17 / Chapter 3 --- Parameter Identifications in Elliptic Systems --- p.19 / Chapter 3.1 --- Introduction --- p.19 / Chapter 3.2 --- Finite element approach and its convergence --- p.21 / Chapter 3.3 --- Unconstrained minimization problems --- p.28 / Chapter 3.4 --- Armijo algorithm --- p.31 / Chapter 3.5 --- Numerical experiments --- p.34 / Chapter 3.6 --- Multi-level coarse grid techniques --- p.55 / Bibliography --- p.65