Timeline for Metropolis-Hastings sampling as a group action
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2021 at 3:39 | comment | added | Juan Sebastian Lozano | @NWMT I'm not, but that definitely sounds related! I'll check it out thanks | |
| Apr 7, 2021 at 11:11 | comment | added | NWMT | The process $x_i \to x_{i+1}$ you describe could be achieved by sampling some element $g_i$ from a symmetry group of $\Omega$ from a probability distribution $p_i$ and then $x_{i+i}=g_i\cdot x_i$. | |
| Apr 7, 2021 at 11:01 | comment | added | NWMT | Are you aware of random walks on groups? mathoverflow.net/questions/158210/… googling also found me these notes: math.u-bordeaux.fr/~jquint/publications/CoursChili.pdf | |
| Apr 6, 2021 at 16:24 | comment | added | Steve Huntsman | Also maybe relevant: mathoverflow.net/a/36037/1847 | |
| Apr 6, 2021 at 16:20 | comment | added | Steve Huntsman | Not sure--maybe? I don't really think of it that way. I think of it as there is a Lie group that encodes the residual freedom of any MCMC acceptance criterion. Practical acceptance criteria correspond to "tractable" elements of the Lie group. Two threads I did not really pull on are what happens if you allow negative entries and/or trying to do something a bit more elaborate along the lines at the end of section 4. Re: the latter, a decent computer algebra system will highlight some alternative if lengthy expressions that might be salient/useful. | |
| Apr 6, 2021 at 15:39 | comment | added | Juan Sebastian Lozano | Wow that's amazing, so instead if thinking about it as an optimization problem where the lie group is encoding the distribution you think about it as a lie group encoding certain information about the invariance of the distribution, and then sampling is about moving along a vector field on that lie group? | |
| Apr 6, 2021 at 14:22 | comment | added | Steve Huntsman | Let's think about the simpler situation $\Omega = \{1,\dots,n\} =: [n]$. For some proposal $j \in [n]$, Metropolis-Hastings corresponds to a particular simple (I hesitate to say "natural") choice of sparse matrix in the Lie algebra of the Lie group preserving the target distribution, as arxiv.org/abs/1901.08606 points out. As to the decomposition you suggest, nothing immediately comes to mind, but this is probably just a deficit of my own imagination at the moment. | |
| Apr 6, 2021 at 5:57 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Apr 6, 2021 at 4:11 | history | asked | Juan Sebastian Lozano | CC BY-SA 4.0 |