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- W4380551405 abstract "This paper studies distribution-free inference in settings where the data set has a hierarchical structure -- for example, groups of observations, or repeated measurements. In such settings, standard notions of exchangeability may not hold. To address this challenge, a hierarchical form of exchangeability is derived, facilitating extensions of distribution-free methods, including conformal prediction and jackknife+. While the standard theoretical guarantee obtained by the conformal prediction framework is a marginal predictive coverage guarantee, in the special case of independent repeated measurements, it is possible to achieve a stronger form of coverage -- the second-moment coverage property -- to provide better control of conditional miscoverage rates, and distribution-free prediction sets that achieve this property are constructed. Simulations illustrate that this guarantee indeed leads to uniformly small conditional miscoverage rates. Empirically, this stronger guarantee comes at the cost of a larger width of the prediction set in scenarios where the fitted model is poorly calibrated, but this cost is very mild in cases where the fitted model is accurate." @default.
- W4380551405 created "2023-06-14" @default.
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- W4380551405 date "2023-06-10" @default.
- W4380551405 modified "2023-10-16" @default.
- W4380551405 title "Distribution-free inference with hierarchical data" @default.
- W4380551405 doi "https://doi.org/10.48550/arxiv.2306.06342" @default.
- W4380551405 hasPublicationYear "2023" @default.
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