Information Geometric Approach on Most Informative Boolean Function Conjecture
Department of Electronical and Electrical Engineering, Hongik University, Seoul 04066, Korea
Received: 26 July 2018 / Revised: 6 September 2018 / Accepted: 8 September 2018 / Published: 10 September 2018
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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No, A. Information Geometric Approach on Most Informative Boolean Function Conjecture. Entropy 2018, 20, 688.
No A. Information Geometric Approach on Most Informative Boolean Function Conjecture. Entropy. 2018; 20(9):688.
No, Albert. 2018. "Information Geometric Approach on Most Informative Boolean Function Conjecture." Entropy 20, no. 9: 688.
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