Timeline for Why does the von Mises-Fisher distribution need two parameters?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2022 at 10:19 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
added 6579 characters in body
|
| Feb 8, 2022 at 10:13 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
added 6579 characters in body
|
| Feb 8, 2022 at 4:41 | comment | added | Rylan Schaeffer | I might also suggest that $\kappa \mu $ has a physically intuitive meaning, perhaps one that's even more clear. Imagine you wrap a sphere in cloth (the density) and then pull the cloth away from the sphere at a particular point. How hard you pull dictates how sharp the peak will be. | |
| Feb 8, 2022 at 1:03 | comment | added | Rylan Schaeffer | To explain why one might want to use 1 parameter, I have three answers: (1) notational succinctness, (2) avoiding confusion (e.g. my own) and (3) reducing computation when performing variational inference. (3) was what motivated this question. In my particular problem (mixture of von Mises-Fisher distributions), my update equations relate $\kappa_{nk} \mu_{nk} = \kappa_{n-1,k} \mu_{n-1,k} + \pi_{nk} o_n$, and so thinking in terms of 2 parameters requires at every step I decompose $\kappa_{nk} \mu_{nk}$ into 2 components, only to compose them at the next step. | |
| Feb 7, 2022 at 16:31 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
added 427 characters in body
|
| Feb 7, 2022 at 16:08 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
added 5 characters in body
|
| Feb 7, 2022 at 16:02 | history | answered | Sextus Empiricus | CC BY-SA 4.0 |