An Information-Theoretic View of Stochastic Localization

Ahmed El Alaoui; Andrea Montanari

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An Information-Theoretic View of Stochastic Localization

机译：An Information-Theoretic View of Stochastic Localization

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摘要

Given a probability measure $mu $ over $mathbb {R}^{n}$ , it is often useful to approximate it by the convex combination of a small number of probability measures, such that each component is close to a product measure. Recently, Ronen Eldan used a stochastic localization argument to prove a general decomposition result of this type. In Eldan’s theorem, the ‘number of components’ is characterized by the entropy of the mixture, and ‘closeness to product’ is characterized by the covariance matrix of each component. We present an elementary proof of Eldan’s theorem which makes use of an information theory (or estimation theory) interpretation. The proof is analogous to the one of an earlier decomposition result known as the ‘pinning lemma.’

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来源
《IEEE Transactions on Information Theory》 |2022年第11期|7423-7426|共4页
作者
Ahmed El Alaoui; Andrea Montanari;
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作者单位

Department of Statistics and Data Science, Cornell University, Ithaca, NY, USA;

Department of Electrical Engineering and the Department of Statistics, Stanford University, Stanford, CA, USA;

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正文语种英语
中图分类通信;
关键词
Entropy; Location awareness; Noise measurement; Mutual information; Gaussian channels; Writing; Standards;

An Information-Theoretic View of Stochastic Localization

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