Papers › MMSE Bounds Under Kullback-Leibler Divergence Constraints on the Joint Input-Output...
MMSE Bounds Under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution
Michael Fauß, Alex Dysto, H. Vincent Poor
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This paper proposes a new family of lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in a Kullback-Leibler divergence ball centered at some Gaussian reference distribution. Both bounds are tight and are attained by Gaussian distributions whose mean is identical to that of the reference distribution and whose covariance matrix is determined by a scalar parameter that can be obtained by finding the root of a monotonic function. The upper bound corresponds to a minimax optimal estimator and provides performance guarantees under distributional uncertainty. The lower bound provides an alternative to well-known inequalities in estimation theory, such as the Cram\'er-Rao bound, that is potentially tighter and defined for a larger class of distributions. Examples of applications in signal processing and information theory illustrate the usefulness of the proposed bounds in practice.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections