Open Access
 Issue JNWPU Volume 37, Number 6, December 2019 1320 - 1325 https://doi.org/10.1051/jnwpu/20193761320 11 February 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1 基于Elastic net的邻域选择模型

### 1.1 邻域选择方法(neighborhood selection)

X=(X1, …, Xp)~Npμ, Σ, 则由多元正态分布的性质得给定除Xi以外的变量X-i, Xi的条件分布为

## 2 实验

### 2.1 模拟实验

 图1带Hub点的网络3组模拟结果
 图2无标度网络的3组模拟结果

### 2.3 调控参数实验

Elastic net的罚函数为岭回归罚函数和Lasso罚函数的凸线性组合, 即α|β|1+(1-α)|β|2, 0≤α≤1。α=0时, Elastic net即为岭回归; 当α=1时, Elastic net即为Lasso回归。α表示的是L1范数惩罚项所占比例, 实验中通过改变α的值控制调控参数, 模拟实验中α的取值为0.001。为了说明调控参数对模型的影响, 改变模拟实验中α的值, 生成n=200, p=100, Hub点的个数为3的带Hub点的网络, α分别取0.1, 0.01和0.000 5。结果如图 3所示。可以看出α=0.1时, 模型的效果差异并不很明显, α=0.01时, 只有估计Hub的边数这一组的效果有明显差异, α=0.000 5时, 模型的效果有明显差异, Elastic net正则化模型对Hub点的估计效果比其他模型都好。

 图3调控参数对模型的影响模拟结果

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## All Figures

 图1带Hub点的网络3组模拟结果 In the text
 图2无标度网络的3组模拟结果 In the text
 图3调控参数对模型的影响模拟结果 In the text

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