The Cut Metric For Probability Distributions
SIAM JOURNAL ON DISCRETE MATHEMATICS(2021)
摘要
Guided by the theory of graph limits, we investigate a variant of the cut metric for limit objects of sequences of discrete probability distributions. Apart from establishing basic results, we introduce a natural operation called pinning on the space of limit objects and show how this operation yields a canonical cut metric approximation to a given probability distribution akin to the weak regularity lemma for graphons. We also establish the cut metric continuity of basic operations such as taking product measures.
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关键词
cut metric, probability distribution, pinning, regularity lemma
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