The Generalized Chernoff-Stein Lemma, Applications and Examples
Jihad Fahs, Ibrahim Abou Faycal, and Ibrahim Issa

TL;DR
This paper extends Stein's lemma to continuous and correlated scenarios by introducing $\
Contribution
It introduces $\\delta$-typicality and extends Stein's lemma to continuous and correlated data, broadening its applicability.
Findings
Extended Stein's lemma to continuous quantities.
Defined $\\delta$-typicality for entropy and relative entropy.
Applied results to Gaussian hypothesis testing with correlations.
Abstract
In this manuscript we define the notion of "-typicality" for both entropy and relative entropy, as well as a notion of -goodness and provide an extension to Stein's lemma for continuous quantities as well as correlated setups. We apply the derived results on the Gaussian hypothesis testing problem where the observations are possibly correlated.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsadvanced mathematical theories · Mathematical Analysis and Transform Methods · Advanced Algebra and Geometry
