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Elementos da teoria de aprendizagem de máquina supervisionada
The topics include: the geometry of the Hamming cube, concentration of measure, shattering and VC dimension, Glivenko-Cantelli classes, PAC learnability, universal consistency and the k-NN classifier in metric spaces, dimensionality reduction, universal approximation, sample compression.
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.
A learning problem whose consistency is equivalent to the non-existence of real-valued measurable cardinals
We show that the $k$-nearest neighbour learning rule is universally consistent in a metric space $X$ if and only if it is universally consistent in every separable subspace of $X$ and the density of $X$ is less than every real-measurable cardinal.
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.
