Krein Space Methods for Structured DataTools Redshaw, Joseph (2024) Krein Space Methods for Structured Data. PhD thesis, University of Nottingham.
AbstractLearning from structured data, including sequences and graphs, is a significant and central challenge in machine learning that has far-reaching applications across numerous disciplines, including chemistry and biochemistry. Kernel methods are undoubtedly an essential tool in this challenge. Their use of a similarity function, known as a kernel function, facilitates learning complex relationships from data of arbitrary structure. However, many expressive notions of similarity are not valid kernel functions, meaning they are not applicable to standard kernel methods. Krein space methods are a potential solution to this problem, as they generalise kernel methods to a much larger class of similarity functions. In this thesis, we explore the application of Krein space methods to structured data. Focusing on problems in chemistry and biochemistry, in which structured data and domain-specific similarity measures are commonplace, we investigate to what extent Krein space methods can be utilised to develop supervised learning models for structured data. In particular, we develop models to identify translation initiation sites in nucleic acid sequences, predict the yield of a carbon-nitrogen cross coupling reaction and identify peptides exhibiting antimicrobial properties. We find that the resulting performance of the models is highly dependent on the choice of similarity function and that Krein space methods outperform standard kernel methods in some, but not all, of the domains considered.
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