Advances in technology have provided industry with an array of devices for collecting data. The frequency and scale of data collection means that there are now many large datasets being generated. To find patterns in these datasets it would be useful to be able to apply modern methods of classification such as support vector machines. Unfortunately these methods are computationally expensive, quadratic in the number of data points in fact, so cannot be applied directly. This thesis proposes a framework whereby a variety of clustering methods can be used to summarise datasets, that is, reduce them to a smaller but still representative dataset so that these advanced methods can be applied. It compares the results of using this framework against using random selection on a large number of classification and regression problems. Results show that the clustered datasets are on average fifty percent smaller than the original datasets without loss of classification accuracy which is significantly better than random selection. They also show that there is no free lunch, for each dataset it is important to choose a clustering method carefully.

This dissertation focuses on the novel learning strategy based on geometric support vector machines to address the difficulties of processing immense data set. Support vector machines find the hyper-plane that maximizes the margin between two classes, and the decision boundary is represented with a few training samples it becomes a favorable choice for incremental learning. The dissertation presents a novel method Geometric Incremental Support Vector Machines (GISVMs) to address both efficiency and accuracy issues in handling massive data sets. In GISVM, skin of convex hulls is defined and an efficient method is designed to find the best skin approximation given available examples. The set of extreme points are found by recursively searching along the direction defined by a pair of known extreme points. By identifying the skin of the convex hulls, the incremental learning will only employ a much smaller number of samples with comparable or even better accuracy. When additional samples are provided, they will be used together with the skin of the convex hull constructed from previous dataset. This results in a small number of instances used in incremental steps of the training process. Based on the experimental results with synthetic data sets, public benchmark data sets from UCI and endoscopy videos, it is evident that the GISVM achieved satisfactory classifiers that closely model the underlying data distribution. GISVM improves the performance in sensitivity in the incremental steps, significantly reduced the demand for memory space, and demonstrates the ability of recovery from temporary performance degradation.

Large datasets require efficient processing, storage and management to efficiently extract useful information for innovation and decision-making. This dissertation demonstrates novel approaches and algorithms using virtual memory approach, parallel computing and cyberinfrastructure. First, we introduce a tailored user-level virtual memory system for parallel algorithms that can process large raster data files in a desktop computer environment with limited memory. The application area for this portion of the study is to develop parallel terrain analysis algorithms that use multi-threading to take advantage of common multi-core processors for greater efficiency. Second, we present two novel parallel WaveCluster algorithms that perform cluster analysis by taking advantage of discrete wavelet transform to reduce large data to coarser representations so data is smaller and more easily managed than the original data in size and complexity. Finally, this dissertation demonstrates an HPC gateway service that abstracts away many details and complexities involved in the use of HPC systems including authentication, authorization, and data and job management.

Technological advances have allowed to collect and store large volumes of data over the years. Besides, it is significant that today's applications have high performance and can analyze these large datasets effectively. Today, it remains a challenge for data mining to make its algorithms and applications equally efficient in the need of increasing data size and dimensionality [1]. To achieve this goal, many applications rely on parallelism, because it is an area that allows the reduction of cost depending on the execution time of the algorithms because it takes advantage of the characteristics of current computer architectures to run several processes concurrently [2]. This paper proposes a parallel version of the FuzzyPred algorithm based on the amount of data that can be processed within each of the processing threads, synchronously and independently.

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The dissertation introduces Sphere Support Vector Machines (SphereSVM) and Minimal Norm Support Vector Machines (MNSVM) as the new fast classification algorithms that use geometrical properties of the underlying classification problems to efficiently obtain models describing training data. SphereSVM is based on combining minimal enclosing ball approach, state of the art nearest point problem solvers and probabilistic techniques. The blending of the three speeds up the training phase of SVMs significantly and reaches similar (i.e., practically the same) accuracy as the other classification models over several big and large real data sets within the strict validation frame of a double (nested) cross-validation (CV). MNSVM is further simplification of SphereSVM algorithm. Here, relatively complex classification task was converted into one of the simplest geometrical problems -- minimal norm problem. This resulted in additional speedup compared to SphereSVM. The results shown are promoting both SphereSVM and MNSVM as outstanding alternatives for handling large and ultra-large datasets in a reasonable time without switching to various parallelization schemes for SVMs algorithms proposed recently. The variants of both algorithms, which work without explicit bias term, are also presented. In addition, other techniques aiming to improve the time efficiency are discussed (such as over-relaxation and improved support vector selection scheme). Finally, the accuracy and performance of all these modifications are carefully analyzed and results based on nested cross-validation procedure are shown.

A modality device can today capture high resolution volumetric data sets and as the data resolutions increase so does the challenges of processing volumetric data through a visualization pipeline. Standard volume rendering pipelines often use a graphic processing unit (GPU) to accelerate rendering performance by taking beneficial use of the parallel architecture on such devices. Unfortunately, graphics cards have limited amounts of video memory (VRAM), causing a bottleneck in a standard pipeline. Multi-resolution techniques can be used to efficiently modify the rendering pipeline, allowing a sub-domain within the volume to be represented at different resolutions. The active resolution distribution is temporarily stored on the VRAM for rendering and the inactive parts are stored on secondary memory layers such as the system RAM or on disk. The active resolution set can be optimized to produce high quality renders while minimizing the amount of storage required. This is done by using a dynamic compression scheme which optimize the visual quality by evaluating user-input data. The optimized resolution of each sub-domain is then, on demand, streamed to the VRAM from secondary memory layers. Rendering a multi-resolution data set requires some extra care between boundaries of sub-domains. To avoid artifacts, an intrablock interpolation (II) sampling scheme capable of creating smooth transitions between sub-domains at arbitrary resolutions can be used. The result is a highly optimized rendering pipeline complemented with a preprocessing pipeline together capable of rendering large volumetric data sets in real-time.

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<p dir="ltr">In this thesis, we delve into the exploration of several nonparametric and semiparametric econometric models within the Bayesian framework, highlighting their applicability across a broad spectrum of microeconomic and macroeconomic issues. Positioned in the big data era, where data collection and storage expand at an unprecedented rate, the complexity of economic questions we aim to address is similarly escalating. This dual challenge ne- cessitates leveraging increasingly large datasets, thereby underscoring the critical need for designing flexible Bayesian priors and developing scalable, efficient algorithms tailored for high-dimensional datasets.</p><p dir="ltr">The initial two chapters, Chapter 2 and 3, are dedicated to crafting Bayesian priors suited for environments laden with a vast array of variables. These priors, alongside their corresponding algorithms, are optimized for computational efficiency, scalability to extensive datasets, and, ideally, distributability. We aim for these priors to accommodate varying levels of dataset sparsity. Chapter 2 assesses nonparametric additive models, employing a smoothing prior alongside a band matrix for each additive component. Utilizing the Bayesian backfitting algorithm significantly alleviates the computational load. In Chapter 3, we address multiple linear regression settings by adopting a flexible scale mixture of normal priors for coefficient parameters, thus allowing data-driven determination of the necessary amount of shrinkage. The use of a conjugate prior enables a closed-form solution for the posterior, markedly enhancing computational speed.</p><p dir="ltr">The subsequent chapters, Chapter 4 and 5, pivot towards time series dataset model- ing and Bayesian algorithms. A semiparametric modeling approach dissects the stochastic volatility in macro time series into persistent and transitory components, the latter addi- tional component addressing outliers. Utilizing a Dirichlet process mixture prior for the transitory part and a collapsed Gibbs sampling algorithm, we devise a method capable of efficiently processing over 10,000 observations and 200 variables. Chapter 4 introduces a simple univariate model, while Chapter 5 presents comprehensive Bayesian VARs. Our al- gorithms, more efficient and effective in managing outliers than existing ones, are adept at handling extensive macro datasets with hundreds of variables.</p>

This thesis explores Chance-Constrained Programming (CCP) in the context of learning. It is shown that chance-constraint approaches lead to improved algorithms for three important learning problems — classification with specified error rates, large dataset classification and Ordinal Regression (OR). Using moments of training data, the CCPs are posed as Second Order Cone Programs (SOCPs). Novel iterative algorithms for solving the resulting SOCPs are also derived. Borrowing ideas from robust optimization theory, the proposed formulations are made robust to moment estimation errors. A maximum margin classifier with specified false positive and false negative rates is derived. The key idea is to employ chance-constraints for each class which imply that the actual misclassification rates do not exceed the specified. The formulation is applied to the case of biased classification. The problems of large dataset classification and ordinal regression are addressed by deriving formulations which employ chance-constraints for clusters in training data rather than constraints for each data point. Since the number of clusters can be substantially smaller than the number of data points, the resulting formulation size and number of inequalities are very small. Hence the formulations scale well to large datasets. The scalable classification and OR formulations are extended to feature spaces and the kernelized duals turn out to be instances of SOCPs with a single cone constraint. Exploiting this speciality, fast iterative solvers which outperform generic SOCP solvers, are proposed. Compared to state-of-the-art learners, the proposed algorithms achieve a speed up as high as 10000 times, when the specialized SOCP solvers are employed. The proposed formulations involve second order moments of data and hence are susceptible to moment estimation errors. A generic way of making the formulations robust to such estimation errors is illustrated. Two novel confidence sets for moments are derived and it is shown that when either of the confidence sets are employed, the robust formulations also yield SOCPs.