High-dimensional Ising model selection using ℓ1-regularized logistic regression
利用 ℓ1 正则化逻辑回归选择高维 Ising 模型AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究二元图模型的结构恢复，未涉及所列网络与干扰方向中的经济网络或干扰效应。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
利用 ℓ1 正则化逻辑回归选择高维 Ising 模型
- 研究问题
- 当节点数与最大邻域规模随样本量增长时，如何从二元 Ising 模型的观测中恢复图结构，并同时正确选择所有节点的邻域？
- 方法与思路
- 作者对每个节点实施带 ℓ1 约束的逻辑回归，并在总体或样本 Fisher 信息矩阵满足相应条件时分析高维邻域选择。
- 材料陈述的贡献
- 摘要称给出了同时一致恢复各节点邻域的充分条件与指数衰减的错误界，并区分总体矩阵条件和样本矩阵条件下的样本需求。
- 阅读关注点
- 应核对信息矩阵条件、最小信号要求及两类样本规模界的准确表达，并检查节点邻域估计如何组合为最终图结构。
- 阅读边界
- 依据版本未注明的 OpenAlex 摘要；条件细节与证明未提供，样本规模表达的幂次应查原文，离散模型推广仅被概述。
原文摘要
We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on ℓ1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main results provide sufficient conditions on the triple (n, p, d) and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes n=Ω(d3log p) with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of n=Ω(d2log p) suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.