2026-09-19T05:52:45Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1541582024-04-17T03:46:50Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Médard, Muriel
Mariona, Alexander
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2024-04-16T19:04:26Z
2024-04-16T19:04:26Z
2024-02
2024-04-08T16:52:51.034Z
https://hdl.handle.net/1721.1/154158
We study two different ways of measuring the similarity between distributions over a finite alphabet. The first is an invariance principle which gives a quantitative bound on the expected difference between general functions of two finite sequences of random variables. This result is one way to generalize the foundational basic invariance principle to a particular multivariate setting. The second framework is based on guesswork, which is one way to measure the randomness of a distribution, similar to but notably distinct from the Shannon entropy. Given a bound on the total variation distance between two finite distributions, we give a bound on the difference in guesswork between those distributions and study the geometrical properties of the problem in the non-asymptotic setting.
S.M.
Massachusetts Institute of Technology
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Comparing Distributions: Invariance Principles & Mismatched Guesswork
Thesis
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Master
Master of Science in Electrical Engineering and Computer Science
Publication
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<Abstract>We study two different ways of measuring the similarity between distributions over a finite alphabet. The first is an invariance principle which gives a quantitative bound on the expected difference between general functions of two finite sequences of random variables. This result is one way to generalize the foundational basic invariance principle to a particular multivariate setting. The second framework is based on guesswork, which is one way to measure the randomness of a distribution, similar to but notably distinct from the Shannon entropy. Given a bound on the total variation distance between two finite distributions, we give a bound on the difference in guesswork between those distributions and study the geometrical properties of the problem in the non-asymptotic setting.</Abstract>
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