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When forecasting time series variables, it is usual to use only the information provided by past observations to foresee potential future developments. However, if available, additional information should be taken into account to get the forecast. For example, let us consider a case where the Government announces an economic target for next year. Since the Government has the empowerment to implement the economic or social policies to approach the target, an analyst that does not consider this information to get the forecast and makes use only of the historical record of the variables, will not anticipate the change on the economic system. In fact, if predictions based on historical data would be invalid when a policy change affects the economy, the economic agents are forward rather than backward-looking and adapt their expectations and behavior to the new policy stance. Thus, given some targets for the variables under study it is important to know the simultaneous future path that will lead to achieving those targets. Here it is considered the case in which a system of variables are to be forecasted with the aid of a VAR model with a cointegration relationship. The paths projected forward into the future as a combination of the model-based forecasts and the additional information provides what is known as a restricted forecast.This work is an attempt to contribute to the literature on Restricted Forecasting Theory for Multiple Time Series within the VAR framework. Specifically, Chapter 2 decomposes the JCT into single tests by a variance-covariance matrix associated with the restrictions and derives the formulas of a feasible JCT that accounts for estimated parameters. Chapter 3 develops, by Lagrangian optimization, the restricted forecasts of the multiple time series process with structural change, as well as its mean squared error. In addition, the univariate time series types of changes are considered here in a multivariate setting. Finally, Chapter 4 derives a methodology for forecasting multivariate time series that satisfy a contemporaneous binding constraint for which there exists a future target. A Monte Carlo study of a VEC model with one unit root shows that, for a forecast horizon large enough, the forecasts obtained with the proposed methodology are more efficient. A more detailed account of these contributions is provided below.

A significant problem in many machine learning tasks is that it is time consuming and costly to gather the necessary labeled data for training the learning algorithm to a reasonable level of performance. In reality, it is often the case that a small amount of labeled data is available and that more unlabeled data could be labeled on demand at a cost. If the labeled data is obtained by a process outside of the control of the learner, then the learner is passive. If the learner picks the data to be labeled, then this becomes active learning. This has the advantage that the learner can pick data to gain specific information that will speed up the learning process. Support Vector Machines (SVMs) have many properties that make them attractive to use as a learning algorithm for many real world applications including classification tasks. Some researchers have proposed algorithms for active learning with SVMs, i.e. algorithms for choosing the next unlabeled instance to get label for. Their approach is supervised in nature since they do not consider all unlabeled instances while looking for the next instance. In this thesis, we propose three new algorithms for applying active learning for SVMs in a semi-supervised setting which takes advantage of the presence of all unlabeled points. The suggested approaches might, by reducing the number of experiments needed, yield considerable savings in costly classification problems in the cases when finding the training data for a classifier is expensive.

Support vector machines (SVMs) have been a dominant machine learning technique for more than a decade. The intuitive principle behind SVM training is to find the maximum margin separating hyperplane for a given set of binary labeled training data. Previously, SVMs have been primarily applied to supervised learning problems, where target class labels are provided with the data. Developing unsupervised extensions to SVMs, where no class labels are given, turns out to be a challenging problem. In this dissertation, I propose a principled approach for unsupervised and semi-supervised SVM training by formulating convex relaxations of the natural training criterion: find a (constrained) labeling that would yield an optimal SVM classifier on the resulting labeled training data. This relaxation yields a semidefinite program (SDP) that can be solved in polynomial time. The resulting training procedures can be applied to two-class and multi-class problems, and ultimately to the multivariate case, achieving high quality results in each case. In addition to unsupervised training, I also consider the problem of reducing the outlier sensitivity of standard supervised SVM training. Here I show that a similar convex relaxation can be applied to improve the robustness of SVMs by explicitly suppressing outliers in the training process. The proposed approach can achieve superior results to standard SVMs in the presence of outliers.

Kernel methods have recently become popular in bioinformatics machine learning. Kernel methods allow linear algorithms to be applied to non-linear learning situations. By using kernels, non-linear learning problems can benefit from the statistical and runtime stability traditionally enjoyed by linear learning problems. However, traditional kernel learning frameworks use implicit feature spaces whose mathematical properties were hard to characterize. In order to address this problem, recent research has proposed a vector learning framework that uses landmark vectors which are unlabeled vectors belonging to the same distribution and the same input space as the training vectors. This thesis introduces an extension to the landmark vector learning framework that allows it to utilize two new classes of landmark vectors in the input space. This augmented learning framework is named the power landmark vector learning framework. A theoretical description of the power landmark vector learning framework is given along with proofs of new theoretical results. Experimental results show that the performance of the power landmark vector learning framework is comparable to traditional kernel learning frameworks.

Algorithms are presented that enable the use of vector graphics representations of images in texture maps for 3D real time rendering. Vector graphics images are resolution independent and can be zoomed arbitrarily without losing detail or crispness. Many important types of images, including text and other symbolic information, are best represented in vector form. Vector graphics textures can also be used as transparency mattes to augment geometric detail in models via trim curves. Spline curves are used to represent boundaries around regions in standard vector graphics representations, such as PDF and SVG. Antialiased rendering of such content can be obtained by thresholding implicit representations of these curves. The distance function is an especially useful implicit representation. Accurate distance function computations would also allow the implementation of special effects such as embossing. Unfortunately, computing the true distance to higher order spline curves is too expensive for real time rendering. Therefore, normally either the distance is approximated by normalizing some other implicit representation or the spline curves are approximated with simpler primitives. In this thesis, three methods for rendering vector graphics textures in real time are introduced, based on various approximations of the distance computation. The first and simplest approach to the distance computation approximates curves with line segments. Unfortunately, approximation with line segments gives only C0 continuity. In order to improve smoothness, spline curves can also be approximated with circular arcs. This approximation has C1 continuity and computing the distance to a circular arc is only slightly more expensive than computing the distance to a line segment. Finally an iterative algorithm is discussed that has good performance in practice and can compute the distance to any parametrically differentiable curve (including polynomial splines of any order) robustly. This algorithm is demonstrated in the context of a system capable of real-time rendering of SVG content in a texture map on a GPU. Data structures and acceleration algorithms in the context of massively parallel GPU architectures are also discussed. These data structures and acceleration structures allow arbitrary vector content (with space-variant complexity, and overlapping regions) to be represented in a random-access texture.

The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge instantons on Minkowski space. Since these discoveries, a generalised theory of instantons has been emerging for manifolds with special holonomy. Beginning with connections and curvature on complex vector bundles, this thesis provides some of the essential background for studying moduli spaces of instantons. Manifolds with exceptional holonomy are special types of seven and eight dimensional manifolds whose holonomy group is contained in G2 and Spin(7), respectively. Focusing on the G2 case, instantons on G2 manifolds are defined to be solutions to an analogue of the four dimensional anti-self-dual equations. These connections are known as Donaldson-Thomas connections and a couple of examples are noted.

Given the recent abundance of brand choice data from scanner panels market researchers have neglected the measurement and analysis of perceptions. Heterogeneity of perceptions is still a largely unexplored issue in market structure and segmentation studies. Over the last decade various parametric approaches toward modelling segmented perception-preference structures such as combined MDS and Latent Class procedures have been introduced. These methods, however, are not taylored for qualitative data describing consumers' redundant and fuzzy perceptions of brand images. A completely different method is based on topology-sensitive vector quantization (VQ) for consumers-by-brands-by-attributes data. It maps the segment-specific perceptual structures into bubble-pie-bar charts with multiple brand positions demonstrating perceptual distinctiveness or similarity. Though the analysis proceeds without any distributional assumptions it allows for significance testing. The application of exploratory and inferential data processing steps to the same data base is statistically sound and particularly attractive for market structure analysts. A brief outline of the VQ method is followed by a sample study with travel market data which proved to be particularly troublesome for conventional processing tools. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

This thesis paper is meant to serve as a supporting document for a thesis exhibition that was held the University of Waterloo Art Gallery. The show consisted of paintings on Plexiglas and sculptural installations with fluorescent lights. <br /><br /> The aesthetic style of my paintings makes a strong reference to the visual vocabulary of computer software. More specifically, it mimics architectural computer vector graphics from the 1980s. There is a visual metaphor created in my paintings where it blueprint drawing has 'evolved' into computer vector graphics, ultimately though, nothing has changed. The images are still hand drafted with pencils and then hand painted. The lexicon of digital software is appropriated, but by transferring the images from the virtual space of the screen to a literal three-dimensional space, the meaning is discarded. They become generalized abstract signs that retain their connotations, but not their meaning and function. The work thus makes a simple point in its refusal to 'get digital. ' There is a fetishization of technology, yet simultaneously a refusal of it. <br /><br /> Other concerns that I deal with in my work and thesis paper, include notions of good and bad taste, kitsch and the Camp aesthetic, science-fiction, nostalgia, representations of the 'future,' Suprematist painting, Minimalism, Design, and the utopian ideals of Modernism.

A significant problem in many machine learning tasks is that it is time consuming and costly to gather the necessary labeled data for training the learning algorithm to a reasonable level of performance. In reality, it is often the case that a small amount of labeled data is available and that more unlabeled data could be labeled on demand at a cost. If the labeled data is obtained by a process outside of the control of the learner, then the learner is passive. If the learner picks the data to be labeled, then this becomes active learning. This has the advantage that the learner can pick data to gain specific information that will speed up the learning process. Support Vector Machines (SVMs) have many properties that make them attractive to use as a learning algorithm for many real world applications including classification tasks. Some researchers have proposed algorithms for active learning with SVMs, i.e. algorithms for choosing the next unlabeled instance to get label for. Their approach is supervised in nature since they do not consider all unlabeled instances while looking for the next instance. In this thesis, we propose three new algorithms for applying active learning for SVMs in a semi-supervised setting which takes advantage of the presence of all unlabeled points. The suggested approaches might, by reducing the number of experiments needed, yield considerable savings in costly classification problems in the cases when finding the training data for a classifier is expensive.