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- W3106234071 abstract "Total correlation (`TC') and dual total correlation (`DTC') are two classical ways to quantify the correlation among an $n$-tuple of random variables. They both reduce to mutual information when $n=2$. The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part considers the structural implications when a joint distribution $mu$ has small TC or DTC. If $mathrm{TC}(mu) = o(n)$, then $mu$ is close to a product measure according to a suitable transportation metric: this follows directly from Marton's classical transportation-entropy inequality. If $mathrm{DTC}(mu) = o(n)$, then the structural consequence is more complicated: $mu$ is a mixture of a controlled number of terms, most of them close to product measures in the transportation metric. This is the main new result of the paper." @default.
- W3106234071 created "2020-11-23" @default.
- W3106234071 creator A5069962326 @default.
- W3106234071 date "2020-07-23" @default.
- W3106234071 modified "2023-09-25" @default.
- W3106234071 title "Multi-variate correlation and mixtures of product measures" @default.
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- W3106234071 doi "https://doi.org/10.14736/kyb-2020-3-0459" @default.
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