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My thesis was on semi-supervised learning on graphs. In semi-supervised learning on graphs, features observed at one node are used to estimate missing values at other nodes. Many prediction methods have been proposed in the machine learning community over the past few years. In this thesis we show that several such proposals are equivalent to kriging predictors based on a fixed covariance matrix driven by the link structure of the graph. We then propose a data-driven estimator of the correlation
structure that exploits patterns among the observed response values. We also show how we can scale some of the algorithms to large graphs. Finally, we investigate the fundamental smoothness assumption underlying many prediction methods by exploring some normality properties arising from empirical data analysis.
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