This PhD thesis investigates the application of normalising flows, a powerful generative modelling technique, to advance statistical learning, particularly in modelling complex data distributions across both low- and high-dimensional datasets. The study begins with a comprehensive exploration of the theoretical foundations, types, and mechanisms of normalising flows, tracing their development and historical context. The thesis then delves into various applications, utilising synthetic datasets to demonstrate the capabilities of these models in density estimation, clustering, and classification tasks. The experimental analysis reveals that simpler flow models, such as Sylvester, planar, and radial flows, excel in specific tasks due to their computational efficiency, while more complex models like Glow, Non-linear independent component estimation (NICE), and Real-valued non-volume preserving (Real NVP) are better suited for applications requiring high-dimensional data representation, such as image and audio processing. However, these advanced models often struggle to generalise across different types of datasets, indicating the necessity of aligning model complexity with data characteristics. Additionally, this work introduces a novel modification of radial flows, termed shifted radial flows, which offers improved performance in certain scenarios. The thesis also explores the integration of normalising flows with clustering and classification techniques, showing that while these flows can enhance performance, their effectiveness is highly dependent on the datasets structure and the chosen method. The research concludes with an assessment of the limitations of normalising flows, particularly in handling highly unbalanced data, and suggests future research directions, including the development of adaptive flow architectures and their application to more complex, unstructured real-world data. This thesis contributes to the growing field of normalising flows by providing a detailed understanding of their applications and offering new perspectives on their potential for advancing statistical learning.
- unbalanced data
- classification
- complex data distributions
- clustering
- low-dimensional data
- density estimation
- statistical learning
- probabilistic modeling
- normalising flows
- high-dimensional data
Investigation of Statistical Learning using Normalising Flows
Nikolopoulou, I. (Author). 27 Nov 2024
Student thesis: Phd