A geometric perspective on guesswork
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Medard_A geometric.pdf
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Author(s)
Beirami, Ahmad
Calderbank, Robert
Christiansen, Mark
Duffy, Ken
Makhdoumi Kakhaki, Ali
Medard, Muriel
Date Issued
April 2016
Journal
2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Beirami, Ahmad, et al. "A Geometric Perspective on Guesswork." 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 29 September- 2 October, 2015, Monticello, Illinois, IEEE, 2015, pp. 941–48.
Version
Author's final manuscript
Abstract
Guesswork is the position at which a random string drawn from a given probability distribution appears in the list of strings ordered from the most likely to the least likely. We define the tilt operation on probability distributions and show that it parametrizes an exponential family of distributions, which we refer to as the tilted family of the source. We prove that two sources result in the same guesswork, i.e., the same ordering from most likely to least likely on all strings, if and only if they belong to the same tilted family. We also prove that the strings whose guesswork is smaller than a given string are concentrated on the tilted family. Applying Laplace's method, we derive precise approximations on the distribution of guesswork on i.i.d. sources. The simulations show a good match between the approximations and the actual guesswork for i.i.d. sources.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/ALLERTON.2015.7447109
