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TEST OF EXCHANGEABILITY UNDER BINARY EXPANSION
Tian, Yu
Tian, Yu
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Thesis/Dissertation
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2025-08
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Statistics
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https://doi.org/10.34944/rq07-nn10
Abstract
Exchangeability serves as a foundational concept in statistical modeling, especially within Bayesian inference and machine learning frameworks. While extensively studied in the bivariate setting, exchangeability remains challenging to assess in high-dimensional and structured data contexts. This dissertation aims to address the above gap by developing a novel nonparametric test for exchangeability under the binary expansion framework. The proposed method, termed BREVITY (Binary REpresentation of Variables with ExchangeabilITY), introduces a binary expansion framework that transforms the problem of an arbitrary and unknown joint distribution into an approximate multinomial modeling problem. By decomposing continuous random variables into binary representations, the joint distribution can be characterized through binary interaction terms, which serve to capture the dependency structure among variables. In general, BREVITY reformulates the exchangeability testing problem in terms of binary interactions in a nonparametric and data-adaptive manner.
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