Browsing by Author "Mak, Simon"

With remarkable advances in sensing and experimental technologies, scientists and engineers now have access to massive datasets with complex forms for decision-making, and the ability to efficiently process and analyze high-dimensional datasets in real time is more critical than ever. Anomaly detection and change point detection are pivotal in various applications, from video surveillance to solar activity monitoring, enabling timely responses to dynamic changes and aberrant behaviors within the data.

This dissertation offers three main contributions to the field. In Chapter 1, we introduce a novel persistence diagram-based method for change point detection, and the key component is to leverage the embedded topological structured from topological data analysis. In Chapter 2, we extend the Robust Principal Component Analysis to accommodate Exponential Family distributions. This extension enables the decomposition of data into low-rank and sparse matrices, where the sparse matrix effectively captures anomalies essential for process monitoring and diagnosis. In Chapter 3, we propose a Bayesian change-point detection framework, which incorporates image and spatial features learned from Gaussian Markov random fields. We investigate the effectiveness of our proposed methods through extensive numerical experiments, and demonstrate their applicability in diverse fields such as engineering, physics, and computer vision.

With breakthroughs in virtual experimentation, computer simulation has been replacing physical experiments that are prohibitively expensive or infeasible to perform in a large scale. However, as the system becomes more complex and realistic, such simulations can be extremely time-consuming and simulating the entire parameter space becomes impractical. One solution is computer emulation, which builds a predictive model based on a handful of simulation data. Gaussian process is a popular emulator used in many physics and engineering applications for this purpose. In particular, for complicated scientific phenomena like the Quark-Gluon Plasma, employing a multi-fidelity emulator to pool information from multi-fidelity simulation data may enhance predictive performance while simultaneously reducing simulation costs. In this dissertation, we explore two novel approaches for multi-fidelity Gaussian process modeling. The first model is the Graphical Multi-fidelity Gaussian Process (GMGP) model, which embeds scientific dependencies among multi-fidelity data in a directed acyclic graph (DAG). The second model we present is the Conglomerate Multi-fidelity Gaussian Process (CONFIG) model, applicable to scenarios where the accuracy of a simulator is controlled by multiple continuous fidelity parameters.

Software engineering is another domain relying heavily on virtual experimentation. In order to ensure the robustness of a new software application, it is required to go through extensive testing and validation before production. Such testing is typically carried out through virtual experimentation and can require substantial computing resources, particularly as the system complexity grows. Fault localization is a key step in software testing as it pinpoints root causes of failures based on executed test case outcomes. However, existing fault localization techniques are mostly deterministic and provides limited insight into assessing the probabilistic risk of failure-inducing combinations. To address this limitation, we present a novel Bayesian Fault Localization (BayesFLo) framework for software testing, yielding a principled and probabilistic ranking of suspicious inputs for identifying the root causes of software failures.