Majorization Techniques for Entropy Bounds
Event details
| Date | 15.06.2023 |
| Hour | 15:00 › 17:00 |
| Speaker | Anuj Kumar Yadav |
| Location | |
| Category | Conferences - Seminars |
EDIC candidacy exam
Exam president: Prof. Emre Telatar
Thesis advisor: Prof. Michael Gastpar
Thesis co-advisor: Prof. Yanina Shkel
Co-examiner: Prof. Negar Kiyavash
Abstract
Majorization is a well-established mathematical concept
that allows us to compare the relative magnitudes of two
probability mass functions (PMFs). It serves as an ordering
relation, that enables us to determine the dominance relationship
between the PMFs. In this report, we will show that the
majorization partial order forms a lattice, indeed it is a complete
lattice. Moreover, we will delve into the fascinating properties of
entropy on the majorization lattice. Additionally, we will explore
how these properties find applications
Background papers
1. F. Cicalese and U. Vaccaro, "Supermodularity and subadditivity properties of the entropy on the majorization lattice," in IEEE Transactions on Information Theory, vol. 48, no. 4, pp. 933-938, April 2002, DOI: 10.1109/18.992785. [ Link: https://ieeexplore.ieee.org/document/992785 ]
2. I. Sason, "Tight Bounds on the Rényi Entropy via Majorization with Applications to Guessing and Compression”. Entropy 2018, 20, 896. DOI: 10.3390/e20120896 . [Link: https://www.mdpi.com/1099-4300/20/12/896]
3. F. Cicalese, L. Gargano and U. Vaccaro, "An Information Theoretic Approach to Probability Mass Function Truncation," 2019 IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019, pp. 702-706, DOI: 10.1109/ISIT.2019.8849355. [ Link: https://ieeexplore.ieee.org/document/8849355]
Exam president: Prof. Emre Telatar
Thesis advisor: Prof. Michael Gastpar
Thesis co-advisor: Prof. Yanina Shkel
Co-examiner: Prof. Negar Kiyavash
Abstract
Majorization is a well-established mathematical concept
that allows us to compare the relative magnitudes of two
probability mass functions (PMFs). It serves as an ordering
relation, that enables us to determine the dominance relationship
between the PMFs. In this report, we will show that the
majorization partial order forms a lattice, indeed it is a complete
lattice. Moreover, we will delve into the fascinating properties of
entropy on the majorization lattice. Additionally, we will explore
how these properties find applications
Background papers
1. F. Cicalese and U. Vaccaro, "Supermodularity and subadditivity properties of the entropy on the majorization lattice," in IEEE Transactions on Information Theory, vol. 48, no. 4, pp. 933-938, April 2002, DOI: 10.1109/18.992785. [ Link: https://ieeexplore.ieee.org/document/992785 ]
2. I. Sason, "Tight Bounds on the Rényi Entropy via Majorization with Applications to Guessing and Compression”. Entropy 2018, 20, 896. DOI: 10.3390/e20120896 . [Link: https://www.mdpi.com/1099-4300/20/12/896]
3. F. Cicalese, L. Gargano and U. Vaccaro, "An Information Theoretic Approach to Probability Mass Function Truncation," 2019 IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019, pp. 702-706, DOI: 10.1109/ISIT.2019.8849355. [ Link: https://ieeexplore.ieee.org/document/8849355]
Practical information
- General public
- Free