An Information-Theoretic View of Stochastic Localization
An Information-Theoretic View of Stochastic Localization
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DOI：
10.1109/tit.2022.3180298
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发表时间：
2021-09
影响因子：
2.5
通讯作者：
Ahmed El Alaoui;A. Montanari
中科院分区：
文献类型：
--
作者：
Ahmed El Alaoui;A. Montanari
给定概率度量$ \ mu $ $ \ mathbb {r}^{n} $，通常可以通过少量概率度量的凸组合来近似它很有用，因此每个组件都接近产品测量值最近，罗恩·埃尔丹（Ronen Eldan）使用随机定位参数证明了这种类型的一般分解结果。以每个组件的协方差矩阵为特征，我们提出了Eldan理论的基本证明，该证明使用了信息理论（或估计理论）的解释。 '
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.’