Comparing Distributions: Invariance Principles & Mismatched Guesswork
| Autor: | Mariona, Alexander |
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| Rok vydání: | 2024 |
| Druh dokumentu: | Diplomová práce |
| Popis: | 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. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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