DOI: 10.25549/usctheses-c3-205925
title: Advanced learning systems for highly uncertain environments

description: Data quality, which broadly refers to both data frequency and accuracy, has been the key factor that determines the performances of most of today's machine learning systems. However, making frequent and accurate measurements for certain applications can be extremely costly, or simply impossible in some cases. ❧ Given a seriously limited number of measurements that are subject to heavy noises, the efforts to ensure the reliability of the outcomes can usually be spent on both the data side and the system side. More specifically, one can try to interpolate the measurements that one fails to collect, and, at the same time, find ways to suppress noises in the actual measurements; on the other hand, one can also design the system in such a way that it becomes more robust even under a great amount of uncertainties. ❧ To this end, the work presented in this dissertation is aimed at addressing this issue from both of these two perspectives, separately. Using the subsurface flow trend detection problem, an increasingly popular topic in the domain of petroleum engineering in recent years, as our background application, the first part of the dissertation introduces a novel iterated state-estimation-based interpolation approach that fills in virtual measurements for an extremely sparsely sampled dataset, and demonstrates that, with the help of these interpolated measurements, the original extended Kalman filter technique, that was developed for this estimation problem, could obtain significantly improved results, almost as if the full set of measurements were given. ❧ Then, from a system design point of view, the second part of this dissertation introduces a paradigm for building certain types of advanced fuzzy logic systems, e.g., non-singleton interval type-2 fuzzy logic systems that operate in extremely uncertain environments. Such systems have not been widely studied before due to their very complex analytical forms that make conventional gradient-based learning processes impractical; however, with the introduction and advancement of population-based random optimization techniques, such as the one this dissertation mainly focuses on, quantum-based particle swarm, the learning process of these systems can be significantly simplified and made more efficient. This dissertation uses a universal image noise removal problem and a forest-fire-size prediction problem as examples to demonstrate general design frameworks. Under such frameworks, these systems can be easily modified and applied to other applications. ❧ The third and final part of this dissertation presents theoretical studies that were performed for the most advanced fuzzy logic sets that are currently under research ― general type-2 fuzzy sets. Our results include 1) a unified theorem that demonstrates how previously uncomputable uncertainty measures for such type-2 fuzzy sets, centroid, cardinality, fuzziness, variance, and skewness, can be obtained through a novel α-plane representation theorem; and, 2) a fast centroid-flow algorithm for computing the centroid of a general type-2 fuzzy set.