3 ms·
It fails in multiple ways. For example the volume (hypervolume) gets concentrated close to the surface of the sphere when dimension grows. For example, if you
by nabla9 5y ago
It fails in multiple ways.
For example the volume (hypervolume) gets concentrated close to the surface of the sphere when dimension grows. For example, if you have symmetric multidimensional probability distributions around the zero it becomes weird.
- kgwgk 5y agoWhat does become weird?
- nabla9 5y agoConsider normal distribution. n-dimensional vectors with independent N(0,1) with expectation 0. When n increases the mass of the probabilities are around a sphere of radius n^0.5, nowhere near the origin.
- kgwgk 5y agoTrue, a huge volume with low density will contain more mass than a small volume with large density. But we can say that it gets “concentrated” far from the origin only in the same sense that Japan’s population is “concentrated” outside of Tokio…