
TL;DR
This paper presents improved Renyi entropy power inequalities (R-EPIs) for sums of independent random vectors, tightening existing bounds and employing convex optimization and matrix analysis techniques.
Contribution
The paper introduces tighter R-EPI bounds for all 1, improving upon recent inequalities by leveraging convex optimization and matrix rank-one modification methods.
Findings
Tighter lower bounds on Renyi entropy power for sums of independent vectors.
Extension of existing R-EPI results with improved constants.
Application of convex optimization and matrix analysis to entropy inequalities.
Abstract
This paper gives improved R\'{e}nyi entropy power inequalities (R-EPIs). Consider a sum of independent continuous random vectors taking values on , and let . An R-EPI provides a lower bound on the order- R\'enyi entropy power of that, up to a multiplicative constant (which may depend in general on ), is equal to the sum of the order- R\'enyi entropy powers of the random vectors . For , the R-EPI coincides with the well-known entropy power inequality by Shannon. The first improved R-EPI is obtained by tightening the recent R-EPI by Bobkov and Chistyakov which relies on the sharpened Young's inequality. A further improvement of the R-EPI also relies on convex optimization and results on rank-one modification of a real-valued diagonal matrix.
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.
