Information Geometric Approach on Most Informative Boolean Function Conjecture
- Authors
- No, Albert
- Issue Date
- Sep-2018
- Publisher
- MDPI
- Keywords
- Boolean function; Bregman divergence; clustering; geometric mean; Jensen-Shannon divergence
- Citation
- ENTROPY, v.20, no.9
- Journal Title
- ENTROPY
- Volume
- 20
- Number
- 9
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/3270
- DOI
- 10.3390/e20090688
- ISSN
- 1099-4300
- Abstract
- Let be a memoryless uniform Bernoulli source and be the output of it through a binary symmetric channel. Courtade and Kumar conjectured that the Boolean function that maximizes the mutual information is a dictator function, i.e., for some i. We propose a clustering problem, which is equivalent to the above problem where we emphasize an information geometry aspect of the equivalent problem. Moreover, we define a normalized geometric mean of measures and interesting properties of it. We also show that the conjecture is true when the arithmetic and geometric mean coincide in a specific set of measures.
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Collections - College of Engineering > School of Electronic & Electrical Engineering > 1. Journal Articles
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