Generalized Data Thinning Using Sufficient Statistics Article Swipe

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Ameer Dharamshi , Anna Neufeld , Keshav Motwani , Lucy L. Gao , Daniela Witten , Jacob Bien ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2303.12931

Our goal is to develop a general strategy to decompose a random variable $X$ into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural exponential families, $X$ can be "thinned" into independent random variables $X^{(1)}, \ldots, X^{(K)}$, such that $X = \sum_{k=1}^K X^{(k)}$. These independent random variables can then be used for various model validation and inference tasks, including in contexts where traditional sample splitting fails. In this paper, we generalize their procedure by relaxing this summation requirement and simply asking that some known function of the independent random variables exactly reconstruct $X$. This generalization of the procedure serves two purposes. First, it greatly expands the families of distributions for which thinning can be performed. Second, it unifies sample splitting and data thinning, which on the surface seem to be very different, as applications of the same principle. This shared principle is sufficiency. We use this insight to perform generalized thinning operations for a diverse set of families.

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Generalization Random variable Thinning Mathematics Inference Exponential function Sample (material) Variables Set (abstract data type) Function (biology) Variable (mathematics) Sum of normally distributed random variables Applied mathematics Statistics Computer science Marginal distribution Artificial intelligence Mathematical analysis Ecology Biology Evolutionary biology Chemistry Programming language Chromatography

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2303.12931
PDF: https://arxiv.org/pdf/2303.12931
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Cited By: 2
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2303.12931

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Title: Generalized Data Thinning Using Sufficient Statistics

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Language: en

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Publication year: 2023

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Publication date: 2023-03-22

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Authors: Ameer Dharamshi, Anna Neufeld, Keshav Motwani, Lucy L. Gao, Daniela Witten, Jacob Bien

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Landing page: https://arxiv.org/abs/2303.12931

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Concepts: Generalization, Random variable, Thinning, Mathematics, Inference, Exponential function, Sample (material), Variables, Set (abstract data type), Function (biology), Variable (mathematics), Sum of normally distributed random variables, Applied mathematics, Statistics, Computer science, Marginal distribution, Artificial intelligence, Mathematical analysis, Ecology, Biology, Evolutionary biology, Chemistry, Programming language, Chromatography

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Cited by: 2

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abstract_inverted_index.unifies	128
abstract_inverted_index.unknown	24
abstract_inverted_index.various	63
abstract_inverted_index.without	19
abstract_inverted_index.contexts	71
abstract_inverted_index.families	117
abstract_inverted_index.function	95
abstract_inverted_index.multiple	15
abstract_inverted_index.relaxing	85
abstract_inverted_index.strategy	7
abstract_inverted_index.thinning	122, 161
abstract_inverted_index.variable	12
abstract_inverted_index."thinned"	40
abstract_inverted_index.$X^{(1)},	45
abstract_inverted_index.X^{(K)}$,	47
abstract_inverted_index.X^{(k)}$.	53
abstract_inverted_index.decompose	9
abstract_inverted_index.families,	36
abstract_inverted_index.families.	168
abstract_inverted_index.including	69
abstract_inverted_index.inference	67
abstract_inverted_index.principle	151
abstract_inverted_index.procedure	83, 108
abstract_inverted_index.purposes.	111
abstract_inverted_index.splitting	75, 130
abstract_inverted_index.summation	87
abstract_inverted_index.thinning,	133
abstract_inverted_index.variables	44, 57, 100
abstract_inverted_index.different,	142
abstract_inverted_index.generalize	81
abstract_inverted_index.operations	162
abstract_inverted_index.performed.	125
abstract_inverted_index.principle.	148
abstract_inverted_index.validation	65
abstract_inverted_index.variables,	18
abstract_inverted_index.well-known	33
abstract_inverted_index.exponential	35
abstract_inverted_index.generalized	160
abstract_inverted_index.independent	16, 42, 55, 98
abstract_inverted_index.information	22
abstract_inverted_index.parameters.	25
abstract_inverted_index.reconstruct	102
abstract_inverted_index.requirement	88
abstract_inverted_index.sacrificing	20
abstract_inverted_index.traditional	73
abstract_inverted_index.\sum_{k=1}^K	52
abstract_inverted_index.applications	144
abstract_inverted_index.sufficiency.	153
abstract_inverted_index.distributions	119
abstract_inverted_index.generalization	105
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	6
citation_normalized_percentile