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Bayesian Topological Machine Learning, Christopher A. Oballe
Bayesian Topological Machine Learning, Christopher A. Oballe
Doctoral Dissertations
Topological data analysis encompasses a broad set of ideas and techniques that address 1) how to rigorously define and summarize the shape of data, and 2) use these constructs for inference. This dissertation addresses the second problem by developing new inferential tools for topological data analysis and applying them to solve real-world data problems. First, a Bayesian framework to approximate probability distributions of persistence diagrams is established. The key insight underpinning this framework is that persistence diagrams may be viewed as Poisson point processes with prior intensities. With this assumption in hand, one may compute posterior intensities by adopting techniques …
Neuroscience-Inspired Dynamic Architectures, Catherine Dorothy Schuman
Neuroscience-Inspired Dynamic Architectures, Catherine Dorothy Schuman
Doctoral Dissertations
Biological brains are some of the most powerful computational devices on Earth. Computer scientists have long drawn inspiration from neuroscience to produce computational tools. This work introduces neuroscience-inspired dynamic architectures (NIDA), spiking neural networks embedded in a geometric space that exhibit dynamic behavior. A neuromorphic hardware implementation based on NIDA networks, Dynamic Adaptive Neural Network Array (DANNA), is discussed. Neuromorphic implementations are one alternative/complement to traditional von Neumann computation. A method for designing/training NIDA networks, based on evolutionary optimization, is introduced. We demonstrate the utility of NIDA networks on classification tasks, a control task, and an anomaly detection task. There …