Aspects of Credit Risk Modeling

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Deep Learning in Medical Image Analysis

The accelerating power of deep learning in diagnosing diseases will empower physicians and speed up decision making in clinical environments. Applications of modern medical instruments and digitalization of medical care have generated enormous amounts of medical images in recent years. In this big data arena, new deep learning methods and computational models for efficient data processing, analysis, and modeling of the generated data are crucially important for clinical applications and understanding the underlying biological process. This book presents and highlights novel algorithms, architectures, techniques, and applications of deep learning for medical image analysis

Doctor of Philosophy

dissertationThe contributions in the area of kernelized learning techniques have expanded beyond a few basic kernel functions to general kernel functions that could be learned along with the rest of a statistical learning model. This dissertation aims to explore various directions in \emph{kernel learning}, a setting where we can learn not only a model, but also glean information about the geometry of the data from which we learn, by learning a positive definite (p.d.) kernel. Throughout, we can exploit several properties of kernels that relate to their \emph{geometry} -- a facet that is often overlooked. We revisit some of the necessary mathematical background required to understand kernel learning in context, such as reproducing kernel Hilbert spaces (RKHSs), the reproducing property, the representer theorem, etc. We then cover kernelized learning with support vector machines (SVMs), multiple kernel learning (MKL), and localized kernel learning (LKL). We move on to Bochner's theorem, a tool vital to one of the kernel learning areas we explore. The main portion of the thesis is divided into two parts: (1) kernel learning with SVMs, a.k.a. MKL, and (2) learning based on Bochner's theorem. In the first part, we present efficient, accurate, and scalable algorithms based on the SVM, one that exploits multiplicative weight updates (MWU), and another that exploits local geometry. In the second part, we use Bochner's theorem to incorporate a kernel into a neural network and discover that kernel learning in this fashion, continuous kernel learning (CKL), is superior even to MKL

Constrained support vector machines theory and applications to health science

En los últimos años, la ciencia de los datos se ha convertido en una herramienta muy importante para tratar datos, así como para descubrir patrones y generar información útil en la toma de decisiones. Una de las tareas más importantes de la ciencia de los datos es la clasificación supervisada, la cual se ha aplicado de forma exitosa en muchas áreas, tales como la biología o la medicina. En este trabajo nos centramos en los Support Vector Machines, introducidos por Vapnik a principios de los 90 y que hoy en día son de los más usados en clasificación supervisada. En primer lugar, se hace un breve repaso de la teoría general acerca de los SVM, centrándonos en el caso binario, y dando un breve repaso al caso multiclase. Tras ello, presentamos una nueva formulación de los mismos, en las que se añaden nuevas restricciones para intentar asegurar un mínimo en los valores de ciertas medidas de rendimiento como las probabilidades de clasificación correcta. Además se realizan experimentos usando el software estadístico R, así como AMPL.Universidad de Sevilla. Máster Universitario en Matemática

Least square multi-class kernel machines with prior knowledge and applications.

In this study, the problem of discriminating between objects of two or more classes with (or without) prior knowledge is investigated. We present how a two-class discrimination model with or without prior knowledge can be extended to the case of multi-categorical discrimination with or without prior knowledge. The prior knowledge of interest is in the form of multiple polyhedral sets belonging to one or more categories, classes, or labels, and it is introduced as additional constraints into a classification model formulation. The solution of the knowledge-based support vector machine (KBSVM) model for two-class discrimination is characterized by a linear programming (LP) problem, and this is due to the specific norm (L1 or Linfinity) that is used to compute the distance between the two classes. We propose solutions to classification problems expressed as a single unconstrained optimization problem with (or without) prior knowledge via a regularized least square cost function in order to obtain a linear system of equations in input space and/or dual space induced by a kernel function that can be solved using matrix methods or iterative methods. Advantages of this formulation include the explicit expressions for the classification weights of the classifier(s); its ability to incorporate and handle prior knowledge directly to the classifiers; its ability to incorporate several classes in a single formulation and provide fast solutions to the optimal classification weights for multicategorical separation.Comparisons with other learning techniques such as the least square SVM & MSVM developed by Suykens & Vandewalle (1999b & 1999c), and the knowledge-based SVM developed by Fung et al. (2002) indicate that the regularized least square methods are more efficient in terms of misclassification testing error and computational time

Bundle methods for regularized risk minimization with applications to robust learning

Supervised learning in general and regularized risk minimization in particular is about solving optimization problem which is jointly defined by a performance measure and a set of labeled training examples. The outcome of learning, a model, is then used mainly for predicting the labels for unlabeled examples in the testing environment. In real-world scenarios: a typical learning process often involves solving a sequence of similar problems with different parameters before a final model is identified. For learning to be successful, the final model must be produced timely, and the model should be robust to (mild) irregularities in the testing environment. The purpose of this thesis is to investigate ways to speed up the learning process and improve the robustness of the learned model. We first develop a batch convex optimization solver specialized to the regularized risk minimization based on standard bundle methods. The solver inherits two main properties of the standard bundle methods. Firstly, it is capable of solving both differentiable and non-differentiable problems, hence its implementation can be reused for different tasks with minimal modification. Secondly, the optimization is easily amenable to parallel and distributed computation settings; this makes the solver highly scalable in the number of training examples. However, unlike the standard bundle methods, the solver does not have extra parameters which need careful tuning. Furthermore, we prove that the solver has faster convergence rate. In addition to that, the solver is very efficient in computing approximate regularization path and model selection. We also present a convex risk formulation for incorporating invariances and prior knowledge into the learning problem. This formulation generalizes many existing approaches for robust learning in the setting of insufficient or noisy training examples and covariate shift. Lastly, we extend a non-convex risk formulation for binary classification to structured prediction. Empirical results show that the model obtained with this risk formulation is robust to outliers in the training examples

Unlabeled pattern management through Semi-Supervised classification techniques

l'obbiettivo di questo progetto consiste nell'analizzare le performance di alcuni algoritmi di semi-supervised learning proposti negli ultimi anni. In particolare si è usato un algoritmo di feature selection basato su Self-training per determinare l'insieme ottimo di features per ogni dataset. Poi sono stati applicati alcuni algoritmi di semi-supervised learning per classificare i dati. Questi algoritmi sono stati testati usando rispettivamente come classificatore di base SVM e SMC