×
Well done. You've clicked the tower. This would actually achieve something if you had logged in first. Use the key for that. The name takes you home. This is where all the applicables sit. And you can't apply any changes to my site unless you are logged in.

Our policy is best summarized as "we don't care about _you_, we care about _them_", no emails, so no forgetting your password. You have no rights. It's like you don't even exist. If you publish material, I reserve the right to remove it, or use it myself.

Don't impersonate. Don't name someone involuntarily. You can lose everything if you cross the line, and no, I won't cancel your automatic payments first, so you'll have to do it the hard way. See how serious this sounds? That's how serious you're meant to take these.

×
Register


Required. 150 characters or fewer. Letters, digits and @/./+/-/_ only.
  • Your password can’t be too similar to your other personal information.
  • Your password must contain at least 8 characters.
  • Your password can’t be a commonly used password.
  • Your password can’t be entirely numeric.
Enter the same password as before, for verification.
Login

Grow A Dic
Define A Word
Make Space
Set Task
Mark Post
Apply Votestyle
Create Votes
(From: saved spaces)
Exclude Votes
Apply Dic
Exclude Dic

Hoeffding's inequality for continuous-time Markov chains

Click here to flash read.

arXiv:2404.14888v1 Announce Type: new
Abstract: Hoeffding's inequality is a fundamental tool widely applied in probability theory, statistics, and machine learning. In this paper, we establish Hoeffding's inequalities specifically tailored for an irreducible and positive recurrent continuous-time Markov chain (CTMC) on a countable state space with the invariant probability distribution ${\pi}$ and an $\mathcal{L}^{2}(\pi)$-spectral gap ${\lambda}(Q)$. More precisely, for a function $g:E\to [a,b]$ with a mean $\pi(g)$, and given $t,\varepsilon>0$, we derive the inequality \[ \mathbb{P}_{\pi}\left(\frac{1}{t} \int_{0}^{t} g\left(X_{s}\right)\mathrm{d}s-\pi (g) \geq \varepsilon \right) \leq \exp\left\{-\frac{{\lambda}(Q)t\varepsilon^2}{(b-a)^2} \right\}, \] which can be viewed as a generalization of Hoeffding's inequality for discrete-time Markov chains (DTMCs) presented in [J. Fan et al., J. Mach. Learn. Res., 22(2022), pp. 6185-6219] to the realm of CTMCs. The key analysis enabling the attainment of this inequality lies in the utilization of the techniques of skeleton chains and augmented truncation approximations. Furthermore, we also discuss Hoeffding's inequality for a jump process on a general state space.

Click here to read this post out
ID: 820811; Unique Viewers: 0
Unique Voters: 0
Total Votes: 0
Votes:
Latest Change: April 24, 2024, 7:32 a.m. Changes:
/u/anonymous
Dictionaries:
Words:
Spaces:
Views: 9
CC:
No creative common's license
Comments: