High-dimensional structure estimation in Ising models: Local separation criterion

We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the presence of sparse local separators between node pairs in the underlying graph. For such graphs, the proposed algorithm has a sample complexity of $n=\Omega(J_{\min}^{-2}\log p)$ , where $p$ is the number of variables, and $J_{\min}$ is the minimum (absolute) edge potential in the model. We also establish nonasymptotic necessary and sufficient conditions for structure estimation.We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the presence of sparse local separators between node pairs in the underlying graph. For such graphs, the proposed algorithm has a sample complexity of $n=\Omega(J_{\min}^{-2}\log p)$, where $p$ is the number of variables, and $J_{\min}$ is the minimum (absolute) edge potential in the model. We also establish nonasymptotic necessary and sufficient conditions for structure estimation.

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笔记与分组

分类依据与纠错

High-dimensional structure estimation in Ising models: Local separation criterion

代码、数据与补充材料

高维 Ising 模型结构估计：局部分离准则

原文摘要

同方向的基础文献

同方向的基础文献