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Abstract: One qualifying aspect of the more general term ?Big Data? is given by the data analysis problems that involve the curse of dimensionality. This means that in the context of the multitude of attributes related to a given phenomenon, the number of available observations is apparently insufficient for reliably determining a law that governs the quantitative processes involved. In recent years progress for addressing this problem has been developed from different mathematical perspectives. In this talk we present a brief history of this progress along with some new developments motivated by regression problems.

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