Timeline for concentration of functions of Gaussian processes
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 20, 2016 at 10:24 | comment | added | Joe Neeman | The countable assumption isn't very important, since unless $f$ is extremely pathological you can just replace $\mathcal{C}$ by a countable, dense subset and the supremum will be the same. In general, the countable assumption is just there to ensure that the supremum is measurable. | |
| Jun 19, 2016 at 1:11 | comment | added | mohi | Another question: Do you know what is the most general class of functions for which a Gordon type result holds (I actually realized this is easy when the function is Lipschitz by just applying symmetrization+comparison inequality) | |
| Jun 19, 2016 at 1:07 | comment | added | mohi | Thanks your comment was very useful. I some how did not think in terms of Talagrand's concentration result. I have a few followup questions. I'm looking at his result through Massart's paper Theorem 4 "About the Constants in Talagrand's Concentration Inequalities for Empirical Processes". Do you by any chance know how crucial is the countable assumption? This theorem is useful for the bounded version case but I can't apply it to the above because of the countable $\mathcal{F}$ assumption. | |
| Jun 17, 2016 at 19:34 | comment | added | Joe Neeman | You can certainly get bounds on the quantity you're interested in (in the bounded case, see Talagrand's concentration inequality for empirical processes). But $\omega^2(\mathcal{C})$ is not the right bound for the sample size. For example, in Gordon's lemma there is a homogeneity that is not present when you have an arbitrary function. | |
| Jun 4, 2016 at 0:14 | history | edited | mohi | CC BY-SA 3.0 |
added 24 characters in body
|
| Jun 3, 2016 at 23:34 | history | edited | mohi | CC BY-SA 3.0 |
edited body
|
| Jun 3, 2016 at 23:27 | history | asked | mohi | CC BY-SA 3.0 |