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2min chapter
061: Interpolation, Extrapolation and Linearisation (Prof. Yann LeCun, Dr. Randall Balestriero)
Machine Learning Street Talk (MLST)
The Curse of Dimensionality
i think it's possible to build understanding of the curse of dimensionality through visual analogy to familiar lower dimensional shapes such as circles, squares, balls and cubes. Imagine perfectly sampling an entire space with a regular grid this would partition space into squares or cubes or hypercubes. Now imagine around each sample a disk or ball or hyper ball representing that point's region of nearness or influence. And let's ask, how much of the total volume of that point's grid cell is actually near the sample? The answer is a fraction, which diminishes faster than expedentially with increasing dimension.
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