Graph-Based Learning and Data Analysis
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Graph-Based Learning and Data Analysis


We present several results on the subject of graph-based semi-supervised learning and a novel application of network analysis to analyzing complex spatiotemporal data. The first piece of work showcases a specific graph-based semi-supervised learning algorithm in the application to ego-activity classification in body-worn video. The classification method is inspired by three interrelated processes: the Allen-Cahn equation, the Merriman-Bence-Osher scheme, and mean curvature flow. We present results on real-world body-worn videos and demonstrate our method's comparable performance to supervised methods. The second piece of work presents semi-supervised learning problem in the framework of Bayesian inverse problems; we prove posterior consistency and elucidate how hyperparameter choices in the Bayesian model combine to affect the contraction rates of the posterior. The third piece of work presents a method of uncertainty quantification in the aforementioned framework; we also develop the foundations for a system with a human in the loop who serves to provide additional class labels based on the uncertainty quantification. The fourth piece of work further extends the Bayesian inverse problem framework to the active learning problem. We introduce an adaptation of non-Gaussian Bayesian models to allow efficient calculations previously done only on Gaussian models and a novel way of choosing new training data. The last piece of work presents a multivariate point-process model that infers latent relationships from complex spatiotemporal data.

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