Timeline for Probability of two Points being divided by an high-Dimensional Hyperplane
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2019 at 15:17 | vote | accept | Alfred | ||
| Feb 21, 2019 at 13:00 | comment | added | Iosif Pinelis | I don't see an intuition (or an argument) that the probability should decrease (or increase) with the dimension $n$. The best and shortest explanation that I have at the moment of why the probability does not depend on $n$ is in the first half of this answer: that the joint distribution of the signs of $x\cdot v$ and $y\cdot v$ does not depend on $n$ (whereas the joint distribution of $x\cdot v$ and $y\cdot v$ themselves likely does depend on $n$). So, the problem is essentially two dimensional, and the answer depends only on the distance between the points $x,y$ on the unit sphere. | |
| Feb 21, 2019 at 9:03 | comment | added | Alfred | Thank you very much! Just one more question: why does it not depend on the dimension $n$? Intuitively, the bigger the dimension is, the smaller the probability should be, or am I wrong? | |
| Feb 21, 2019 at 4:22 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 21, 2019 at 4:14 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 21, 2019 at 4:05 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 21, 2019 at 3:58 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Feb 21, 2019 at 3:46 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |