Time series classification methodology using reproducing kernel Hilbert spaces embedding

La clasificación de series de tiempo es una tarea fundamental en las áreas de aprendizaje de máquina y reconocimiento de patrones, debido a las múltiples aplicaciones que existen en el estado del arte, tales como análisis en mercados bursátiles, medicina, redes de sensores, experimentos científicos de objetos en movimiento, biología y clasificación de formas. La mayoría de modelos basados en datos suponen que las observaciones son independientes e idénticamente distribuidas. Sin embargo, al suponer lo anterior ciertos factores discriminantes pueden ser pasados por alto

Hypothesis testing and causal inference with heterogeneous medical data

Learning from data which associations hold and are likely to hold in the future is a fundamental part of scientific discovery. With increasingly heterogeneous data collection practices, exemplified by passively collected electronic health records or high-dimensional genetic data with only few observed samples, biases and spurious correlations are prevalent. These are called spurious because they do not contribute to the effect being studied. In this context, the modelling assumptions of existing statistical tests and causal inference methods are often found inadequate and their practical utility diminished even though these models are increasingly used as decision-support tools in practice. This thesis investigates how modern computational techniques may broaden the fields of hypothesis testing and causal inference to handle the subtleties of large heterogeneous data sets, as well as simultaneously improve the robustness and theoretical understanding of machine learning algorithms using insights from causality and statistics. The first part of this thesis is concerned with hypothesis testing. We develop a framework for hypothesis testing on set-valued data, a representation that faithfully describes many real-world phenomena including patient biomarker trajectories in the hospital. Using similar techniques, we develop next a two-sample test for making inference on selection-biased data, in the sense that not all individuals are equally likely to be included in the study, a fact that biases tests if not accounted for and if the desideratum is to obtain conclusions that are generally applicable. We conclude this section with an investigation of conditional independence in high-dimensional data, such as found in gene expression data, and propose a test using generative adversarial networks. The second part of this thesis is concerned with causal inference and discovery, with a special focus on the influence of unobserved confounders that distort the observed associations between variables and yet may not be ruled out or adjusted for using data alone. We start by demonstrating that unobserved confounders may bias substantially the generalization performance of machine learning algorithms trained with conventional learning paradigms such as empirical risk minimization. Acknowledging this spurious effect, we develop a new learning principle inspired by causal insights that provably generalizes to test data sampled from a larger set of distributions different from the training distribution. In the last chapter we consider the influence of unobserved confounders for causal discovery. We show that with some assumptions on the type and influence on the nature of unobserved confounding one may develop provably consistent causal discovery algorithms, formulated as a solution to a continuous optimization program

Generative Adversarial Networks (GANs): Challenges, Solutions, and Future Directions

Generative Adversarial Networks (GANs) is a novel class of deep generative models which has recently gained significant attention. GANs learns complex and high-dimensional distributions implicitly over images, audio, and data. However, there exists major challenges in training of GANs, i.e., mode collapse, non-convergence and instability, due to inappropriate design of network architecture, use of objective function and selection of optimization algorithm. Recently, to address these challenges, several solutions for better design and optimization of GANs have been investigated based on techniques of re-engineered network architectures, new objective functions and alternative optimization algorithms. To the best of our knowledge, there is no existing survey that has particularly focused on broad and systematic developments of these solutions. In this study, we perform a comprehensive survey of the advancements in GANs design and optimization solutions proposed to handle GANs challenges. We first identify key research issues within each design and optimization technique and then propose a new taxonomy to structure solutions by key research issues. In accordance with the taxonomy, we provide a detailed discussion on different GANs variants proposed within each solution and their relationships. Finally, based on the insights gained, we present the promising research directions in this rapidly growing field.Comment: 42 pages, Figure 13, Table

On Novel Approaches to Model-Based Structural Health Monitoring

Structural health monitoring (SHM) strategies have classically fallen into two main categories of approach: model-driven and data-driven methods. The former utilises physics-based models and inverse techniques as a method for inferring the health state of a structure from changes to updated parameters; hence defined as inverse model-driven approaches. The other frames SHM within a statistical pattern recognition paradigm. These methods require no physical modelling, instead inferring relationships between data and health states directly. Although successes with both approaches have been made, they both suffer from significant drawbacks, namely parameter estimation and interpretation difficulties within the inverse model-driven framework, and a lack of available full-system damage state data for data-driven techniques. Consequently, this thesis seeks to outline and develop a framework for an alternative category of approach; forward model-driven SHM. This class of strategies utilise calibrated physics-based models, in a forward manner, to generate health state data (i.e. the undamaged condition and damage states of interest) for training machine learning or pattern recognition technologies. As a result the framework seeks to provide potential solutions to these issues by removing the need for making health decisions from updated parameters and providing a mechanism for obtaining health state data. In light of this objective, a framework for forward model-driven SHM is established, highlighting key challenges and technologies that are required for realising this category of approach. The framework is constructed from two main components: generating physics-based models that accurately predict outputs under various damage scenarios, and machine learning methods used to infer decision bounds. This thesis deals with the former, developing technologies and strategies for producing statistically representative predictions from physics-based models. Specifically this work seeks to define validation within this context and propose a validation strategy, develop technologies that infer uncertainties from various sources, including model discrepancy, and offer a solution to the issue of validating full-system predictions when data is not available at this level. The first section defines validation within a forward model-driven context, offering a strategy of hypothesis testing, statistical distance metrics, visualisation tools, such as the witness function, and deterministic metrics. The statistical distances field is shown to provide a wealth of potential validation metrics that consider whole probability distributions. Additionally, existing validation metrics can be categorised within this fields terminology, providing greater insight. In the second part of this study emulator technologies, specifically Gaussian Process (GP) methods, are discussed. Practical implementation considerations are examined, including the establishment of validation and diagnostic techniques. Various GP extensions are outlined, with particular focus on technologies for dealing with large data sets and their applicability as emulators. Utilising these technologies two techniques for calibrating models, whilst accounting for and inferring model discrepancies, are demonstrated: Bayesian Calibration and Bias Correction (BCBC) and Bayesian History Matching (BHM). Both methods were applied to representative building structures in order to demonstrate their effectiveness within a forward model-driven SHM strategy. Sequential design heuristics were developed for BHM along with an importance sampling based technique for inferring the functional model discrepancy uncertainties. The third body of work proposes a multi-level uncertainty integration strategy by developing a subfunction discrepancy approach. This technique seeks to construct a methodology for producing valid full-system predictions through a combination of validated sub-system models where uncertainties and model discrepancy have been quantified. This procedure is demonstrated on a numerical shear structure where it is shown to be effective. Finally, conclusions about the aforementioned technologies are provided. In addition, a review of the future directions for forward model-driven SHM are outlined with the hope that this category receives wider investigation within the SHM community

Time-Varying Correlation Networks for Interpretable Change Point Detection

Change point detection (CPD) methods aim to detect abrupt changes in time-series data. Recent CPD methods have demonstrated their potential in identifying changes in underlying statistical distributions but often fail to capture complex changes in the correlation structure in time-series data. These methods also fail to generalize effectively, as even within the same time-series, different kinds of change points (CPs) may arise that are best characterized by different types of time-series perturbations. To address this issue, we propose TiVaCPD, a CPD methodology that uses a time-varying graphical lasso based method to identify changes in correlation patterns between features over time, and combines that with an aggregate Kernel Maximum Mean Discrepancy (MMD) test to identify subtle changes in the underlying statistical distributions of dynamically established time windows. We evaluate the performance of TiVaCPD in identifying and characterizing various types of CPs in time-series and show that our method outperforms current state-of-the-art CPD methods for all categories of CPs