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Universal consistency of the $k$-NN rule in metric spaces and Nagata dimension. II
Thanks to the results of C\'erou and Guyader (2006) and Preiss (1983), this rule is known to be universally consistent in every such metric space that is sigma-finite dimensional in the sense of Nagata.
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Universal consistency of the $k$-NN rule in metric spaces and Nagata dimension
The generalization is non-trivial because of the distance ties being more prevalent in the non-euclidean setting, and on the way we investigate the relevant geometric properties of the metrics and the limitations of the Stone argument, by constructing various examples.
Topics in Random Matrices and Statistical Machine Learning
The main results of this thesis are as follows: a necessary and sufficient condition for the inverse moments of $(m, n,\beta)$-Laguerre matrices and compound Wishart matrices to be finite; the universal weak consistency and the strong consistency of the $k$-nearest neighbor rule in metrically sigma-finite dimensional spaces and metrically finite dimensional spaces respectively.
