Wiener's conjecture about transformation groups helps predict which fuzzy techniques work better

Zapata, Francisco; Kosheleva, Olga; Kreinovich, Vladik

doi:10.1109/norbert.2014.6893886

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Dimensionality Of Temporal Origin1

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2021

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“…and the corresponding proof can be shortened to a few pages; see, e.g., [43,44]. So, we arrive at the following conclusion.…”

supporting

confidence: 51%

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Limit Theorems as Blessing of Dimensionality: Neural-Oriented Overview

Kreinovich

Kosheleva

2021

Entropy

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As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system’s complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution gets close to an easy-to-analyze normal one—and indeed, normal distributions are ubiquitous. We show that such limit theorems often make analysis of complex systems easier—i.e., lead to blessing of dimensionality phenomenon—for all the aspects of these systems: the corresponding transformation, the system’s uncertainty, and the desired result of the system’s analysis.

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“…and the corresponding proof can be shortened to a few pages; see, e.g., [43,44]. So, we arrive at the following conclusion.…”

supporting

confidence: 51%

“…However, good news is that at present, we are only interested in the transformations of 1D signals. In this case, projective transformations are nothing else but fractional-linear ones

and the corresponding proof can be shortened to a few pages; see, e.g., [ 43 , 44 ].…”

Section: Dimensionality Of Temporal Originmentioning

confidence: 99%