As of the writing of this thesis, machine learning has become one of the most active research fields. The interest comes from a variety of disciplines which include computer science, statistics, engineering, and medicine. The main idea behind learning from data is that, when an analytical model explaining the observations is hard to find ---often in contrast to the models in physics such as Newton's laws--- a statistical approach can be taken where one or more candidate models are tuned using data. Since the early 2000's this challenge has grown in two ways: (i) The amount of collected data has seen a massive growth due to the proliferation of digital media, and (ii) the data has become more complex. One example for the latter is the high dimensional datasets, which can for example correspond to dyadic interactions between two large groups (such as customer and product information a retailer collects), or to high resolution image/video recordings. Another important issue is the study of dynamic data, which exhibits dependence on time. Virtually all datasets fall into this category as all data collection is performed over time, however I use the term dynamic to hint at a system with an explicit temporal dependence. A traditional example is target tracking from signal processing literature. Here the position of a target is modeled using Newton's laws of motion, which relates it to time via the target's velocity and acceleration. Dynamic data, as I defined above, poses two important challenges. Firstly, the learning setup is different from the standard theoretical learning setup, also known as Probably Approximately Correct (PAC) learning. To derive PAC learning bounds one assumes a collection of data points sampled independently and identically from a distribution which generates the data. On the other hand, dynamic systems produce correlated outputs. The learning systems we use should accordingly take this difference into consideration. Secondly, as the system is dynamic, it might be necessary to perform the learning online. In this case the learning has to be done in a single pass. Typical applications include target tracking and electricity usage forecasting. In this thesis I investigate several important dynamic and online learning problems, where I develop novel tools to address the shortcomings of the previous solutions in the literature. The work is divided into three parts for convenience. The first part is about matrix factorization for time series analysis which is further divided into two chapters. In the first chapter, matrix factorization is used within a Bayesian framework to model time-varying dyadic interactions, with examples in predicting user-movie ratings and stock prices. In the next chapter, a matrix factorization which uses autoregressive models to forecast future values of multivariate time series is proposed, with applications in predicting electricity usage and traffic conditions. Inspired by the machinery we use in the first part, the second part is about nonlinear Kalman filtering, where a hidden state is estimated over time given observations. The nonlinearity of the system generating the observations is the main challenge here, where a divergence minimization approach is used to unify the seemingly unrelated methods in the literature, and propose new ones. This has applications in target tracking and options pricing. The third and last part is about cost sensitive learning, where a novel method for maximizing area under receiver operating characteristics curve is proposed. Our method has theoretical guarantees and favorable sample complexity. The method is tested on a variety of benchmark datasets, and also has applications in online advertising.

The first part of this thesis considers the residual empirical process of a nearly unstable long-memory time series. Chan and Ling [8] showed that the usual limit distribution of the Kolmogorov-Smirnov test statistics does not hold when the characteristic polynomial of the unstable autoregressive model has a unit root. A key question of interest is what happens when this model has a near unit root, that is, when it is nearly non-stationary. In this thesis, it is established that the statistics proposed by Chan and Ling can be extended. The limit distribution is expressed as a functional of an Orenstein-Uhlenbeck process that is driven by a fractional Brownian motion. This result extends and generalizes Chan and Ling's results to a nearly non-stationary long-memory time series. / The second part of the thesis investigates the weak convergence of weighted sums of random variables that are functionals of moving aver- age processes. A non-central limit theorem is established in which the Wiener integrals with respect to the Hermite processes appear as the limit. As an application of the non-central limit theorem, we examine the asymptotic theory of least squares estimators (LSE) for a nearly unstable AR(1) model when the innovation sequences are functionals of moving average processes. It is shown that the limit distribution of the LSE appears as functionals of the Ornstein-Uhlenbeck processes driven by Hermite processes. / Liu, Weiwei. / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 60-67). / 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. / Abstract also in Chinese.

Xu, Yang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 99-104). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Sensors and Sensor Networks --- p.2 / Chapter 1.2 --- Introduction to Coverage Problems --- p.6 / Chapter 1.3 --- Literature Review --- p.8 / Chapter 1.3.1 --- Deterministic Deployment Methods --- p.9 / Chapter 1.3.2 --- Dynamic Deployment Methods --- p.10 / Chapter 1.4 --- A Brief Introduction to Least Squares Analysis --- p.13 / Chapter 1.5 --- Thesis Outline --- p.15 / Chapter 2 --- Mobile Sensor Network Deployment Problem --- p.18 / Chapter 2.1 --- Sensor Coverage Models --- p.18 / Chapter 2.1.1 --- Binary Sensor Models --- p.19 / Chapter 2.1.2 --- Attenuated and Truncated Attenuated Disk Models --- p.20 / Chapter 2.2 --- Problem Statement --- p.23 / Chapter 3 --- Coverage Optimization as Nonlinear Least Squares Problems --- p.26 / Chapter 3.1 --- Introduction --- p.26 / Chapter 3.2 --- Network Deployment as Least Squares Problems --- p.28 / Chapter 3.2.1 --- Assignment of Sample Points --- p.28 / Chapter 3.2.2 --- Least Squares Function --- p.30 / Chapter 3.2.3 --- Gauss-Newton Method --- p.33 / Chapter 3.2.4 --- Solutions --- p.36 / Chapter 3.3 --- Extension to Binary Sensor Models --- p.39 / Chapter 3.3.1 --- Restrictions of Subgradient Methods --- p.40 / Chapter 3.3.2 --- Sigmoid Functions --- p.42 / Chapter 3.4 --- Convergence and Multiple Minima Issues --- p.44 / Chapter 3.4.1 --- Convergence --- p.44 / Chapter 3.4.2 --- Multiple Minima --- p.48 / Chapter 3.5 --- Stopping Criteria --- p.52 / Chapter 3.6 --- Summary --- p.53 / Chapter 4 --- Experimental Results --- p.55 / Chapter 4.1 --- Introduction --- p.55 / Chapter 4.2 --- Numerical Examples --- p.56 / Chapter 4.2.1 --- Examples of Attenuated Disk Models --- p.57 / Chapter 4.2.2 --- Examples of Binary Sensor Models --- p.63 / Chapter 4.3 --- Performance Metrics of Mobile Sensor Deployment Schemes --- p.68 / Chapter 4.4 --- Comparison to Existing Methods --- p.74 / Chapter 4.5 --- Summary --- p.81 / Chapter 5 --- Conclusions --- p.83 / Chapter 5.1 --- Conclusions --- p.83 / Chapter 5.2 --- Future Research Directions --- p.85 / Appendices --- p.87 / Chapter A --- An Overview of Existing Deployment Methods --- p.88 / Chapter A.1 --- Potential Fields and Virtual Forces --- p.88 / Chapter A.2 --- Distributed Self-Spreading Algorithm --- p.92 / Chapter A.3 --- VD-Based Deployment Algorithm --- p.96 / Bibliography --- p.99

Fung, Chun Yip. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 53-54). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Exchange Algorithm Framework --- p.4 / Chapter 2.1 --- Ordinary Least Squares Linear Regression --- p.5 / Chapter 2.2 --- The Exchange Algorithm --- p.6 / Chapter 3 --- Methodology --- p.12 / Chapter 3.1 --- Least Median Squares Linear Regression --- p.12 / Chapter 3.2 --- Least Median Squares Algorithm for Clusterwise Linear Re- gression --- p.16 / Chapter 3.3 --- Measures of Performance --- p.20 / Chapter 3.4 --- An Illustrative Example --- p.24 / Chapter 4 --- Monte Carlo Simulation Study --- p.34 / Chapter 4.1 --- Simulation Plan --- p.34 / Chapter 4.2 --- Simulation Results --- p.41 / Chapter 4.2.1 --- Effects of the Six factors --- p.41 / Chapter 4.2.2 --- Comparisons between LMSA and the Exchange Algorithm --- p.47 / Chapter 4.2.3 --- Evaluation of the Improvement of Regression Parame- ters by Performing Stage 3 in LMSA --- p.50 / Chapter 5 --- Concluding Remarks --- p.51 / Bibliography --- p.52

Hops are one of the four main ingredients used to produce beer. Many studies have been done to analyze the science behind growing and harvesting hops, creating hop hybrids, and how to brew beer with hops. However, there has been little research done revolving around the economic demand and supply model of the hop market. The objectives of this study are to create an econometric model of supply and demand of hops in the United States from 1981 to 2012, and to identify important exogenous variables that explain the supply and demand of hops using the two-stage least squares (2SLS) method of analysis. Using the 2SLS method, the demand model yielded that the US beer production variable is significant at the 10 percent level. For every 1 percent change in US beer production, there will be a 6.25 percent change in quantity of hops demanded in the same direction. The supply model showed that US acreage is significant at the 1 percent level. For every 1 percent change in US acreage, there will be a 0.889 percent change in quantity of hops supplied in the same direction. The implications of this study are viewed in relation to both producers and consumers.

Adaptive filters have found applications in many signal processing problems. In some situations, linear constraints are imposed on the filter weights such that the filter is forced to exhibit a certain desired response. Several algorithms for linearly constrained least-squares adaptive filtering have been developed in the literature. When implemented with finite precision arithmetic, these algorithms are inevitably subjected to rounding errors. It is essential to understand how these algorithms react to rounding errors.In this thesis, the numerical properties of three linearly constrained least-squares adaptive filtering algorithms, namely, the linearly constrained fast least algorithm, the linear systolic array for MVDR beamforming and the linearly constrained QRD-RLS algorithm, are studied. It is shown that all these algorithms can be separated into a constrained part and an unconstrained part. The numerical properties of unconstrained least-squares algorithms (i.e., the unconstrained part of the linearly constrained algorithms under study) are reviewed from the perspectives of error propagation, error accumulation and numerical persistency. It is shown that persistent excitation and sufficient numerical resolution are needed to ensure the stability of the CRLS algorithm, while the QRD-RLS algorithm is unconditionally stable. The numerical properties of the constrained algorithms are then examined. Based on the technique of how the constraints are applied, these algorithms can be grouped into two categories. The first two algorithms admit a similar structure in that the unconstrained parts preceed the constrained parts. Error propagation analysis shows that this structure gives rise to unstable error propagation in the constrained part. In contrast, the constrained part of the third algorithm preceeds the unconstrained part. It is shown that this algorithm gives an ++ / exact solution to a linearly constrained least-squares adaptive filtering problem with perturbed constraints and perturbed input data. A minor modification to the constrained part of the linearly constrained QRD-RLS algorithm is proposed to avoid a potential numerical difficulty due to the Gaussian elimination operation employed in the algorithm.

Doctor of Philosophy (PhD) / This thesis considers transmission techniques for current and future wireless and mobile communications systems. Many of the results are quite general, however there is a particular focus on code-division multiple-access (CDMA) and multi-input multi-output (MIMO) systems. The thesis provides analytical techniques and results for finding key performance metrics such as signal-to-interference and noise power ratios (SINR) and capacity. This thesis considers a large-system analysis of a general linear matrix-vector communications channel, in order to determine the asymptotic performance of linear fixed and adaptive receivers. Unlike many previous large-system analyses, these results cannot be derived directly from results in the literature. This thesis considers a first-principles analytical approach. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. The approach is also used to derive the distribution of sums and products of free random matrices. Expressions for the asymptotic SINR of the MMSE receiver are derived, along with the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.

<p>Shooter localization systems are used to detect and locate the origin of gunfire. A wireless sensor network is one possible implementation of such a system. A wireless sensor network is sensitive to synchronization errors. Localization techniques that rely on the timing will give less accurate or even useless results if the synchronization errors are too large.</p><p>This thesis focuses on the influence of synchronization errors on the abilityto localize a shooter using a wireless sensor network. A localization algorithm</p><p>is developed and implemented and the effect of synchronization errors is studied. The localization algorithm is evaluated using numerical experiments, simulations, and data from real gunshots collected at field trials.</p><p>The results indicate that the developed localization algorithm is able to localizea shooter with quite good accuracy. However, the localization performance is to a high degree influenced by the geographical configuration of the network as well as the synchronization error.</p> / <p><p>Skottlokaliseringssystem används för att upptäcka och lokalisera ursprunget för avlossade skott. Ett trådlöst sensornätverk är ett sätt att utforma ett sådant system.Trådlösa sensornätverk är känsliga för synkroniseringsfel. Lokaliseringsmetoder som bygger på tidsobservationer kommer med för stora synkroniseringsfel ge dåliga eller helt felaktiga resultat.</p><p>Detta examensarbete fokuserar på vilken inverkan synkroniseringsfel har på möjligheterna att lokalisera en skytt i ett trådlöst sensornätverk. En lokaliseringsalgoritm utvecklas och förmågan att korrekt lokalisera en skytt vid olika synkroniseringsfel undersöks. Lokaliseringsalgoritmen prövas med numeriska experiment, simuleringar och även för data från riktiga skottljud, insamlade vid fältförsök.</p><p>Resultaten visar att lokaliseringsalgoritmen fungerar tillfredställande, men att lokaliseringsförmågan till stor del påverkas av synkroniseringsfel men även av sensornätverkets geografiska utseende.</p></p>

The incidence of infectious diseases in livestock is a major concern for animal breeders as well as for consumers. As a alternative approach to the use of prophylactic measures or therapeutic agents, infectious diseases can be contended by increasing the disease resistance of animals by genetic improvement. Animals can be selected either on a measure of their resistance (indicator trait) or on the presence or absence of some specific resistance genes in their genotype. A prerequisite to the latter approach is the identification of the genes, or QTL for quantitative trait loci, underlying the trait of interest. By means of sophisticated statistical tools, the QTL mapping strategy combines the information from genetic markers and phenotypic values to dissect quantitative traits into their individual genetic components. Some of the methodological aspects of this strategy are studied in the present thesis in the context of disease resistance in livestock. Indicator traits of the resistance (such as bacteria or parasites counts) are not always satisfying the normality assumption underlying most of the QTL mapping methods. In this context, the ability of statistical tests to identify the underlying genes (i.e. the statistical power) can be considerably reduced. We show that compared to the use of a non-parametric method, the use of the least-squares-based parametric method on mathematically transformed phenotypes gives always the best results. In the context of high number of ties (equal values) as observed when measuring resistance to bacterial or parasitic diseases, the non-parametric test is a good alternative to this approach, as far as midranks are used for ties instead of random ranks. The efficiency of QTL mapping methods can also be increased by use of simple combinations of repeated measurements of the same trait. As a result of analyses performed on real data sets in chicken and sheep, we show that much attention should be paid to obtaining good quality measurements, reflecting at best differences in terms of resistance between animals, before performing a QTL search. The appropriate choice of resistance traits as well as of the time of their measurement are, beside the choice of the method and the quality of marker information, among the most preponderant factors to guarantee satisfying results.

This study considers whether or not optimizing process metrics and settings across a supply chain gives significantly different outcomes than consideration at a firm level. While, the importance of supply chain integration has been shown in areas such as inventory management, this study appears to be the first empirical test for optimizing process settings. A Partial Least Squares (PLS) procedure is used to determine the crucial components and indicators that make up each component in a supply chain system. PLS allows supply chain members to have a greater understanding of critical coordination components in a given supply chain. Results and implications give an indication of what performance is possible with supply chain optimization versus local optimization on simulated and manufacturing data. It was found that pursuing an integrated approach over a traditional independent approach provides an improvement of 2% to 49% in predictive power for the supply chain under study.