{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/154158"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/154158","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Comparing Distributions: Invariance Principles & Mismatched Guesswork","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_html":"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_has_math":false,"creators":["Mariona, Alexander"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Comparing Distributions: Invariance Principles & Mismatched Guesswork"]}]}],"canonical_facts":{"dc:contributor.advisor":["Médard, Muriel"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Mariona, Alexander"],"dc:date.accessioned":["2024-04-16T19:04:26Z"],"dc:date.available":["2024-04-16T19:04:26Z"],"dc:date.issued":["2024-02"],"dc:description.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."],"dc:description.degree":["S.M."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/154158"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Comparing Distributions: Invariance Principles & Mismatched Guesswork"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Science in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:21:17Z"}