论文网址：[1611.07308] Variational Graph Auto-Encoders (arxiv.org)

英文是纯手打的！论文原文的summarizing and paraphrasing。可能会出现难以避免的拼写错误和语法错误，若有发现欢迎评论指正！文章偏向于笔记，谨慎食用

目录

1. 省流版

1.1. 心得

1.2. 论文总结图

2. 论文逐段精读

2.1. A latent variable model for graph-structured data

2.2. Experiments on link prediction

3. Reference

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1. 省流版

1.1. 心得

（1）好短的文章捏，只有两页

1.2. 论文总结图

2. 论文逐段精读

2.1. A latent variable model for graph-structured data

        ①Task: unsupervised learning

        ②Latent space of unsupervised VGAE in Cora, a citation network dataset:

        ③Definitions: for undirected and unweighted graph , the number of nodes , the adjacency matrix with self-loop and the diagnal elements all set to 1defined as , the degree matrix is , the stochastic latent variables is , , node feature matrix （但是没说这个节点特征是啥，估计自己随便定义吧）

        ④Inference model:

with 

where  is the matrix of mean vectors ;

（为啥左边要有个log啊）

        ⑤A 2 layer GCN:

where  denotes weight matrix, 

        ⑥ 和 共享的参数？？？什么玩意儿？？为啥有俩，是引用了之前的什么高斯吗？

        ⑦Generative model:

with 

where  represents the logistic sigmoid function

        ⑧Loss function:

where Gaussian prior 

        ⑨作者觉得对于非常稀疏的邻接矩阵，在损失函数中重新加权a) 的项，或b) 的子样本项可能是有益的。然后它们选择了a) 方法。

        ⑩If there is no node features, replace  by indentity matrix

        ⑪Reconstruct adjacency matrix by non-probabilistic graph auto-encoder (GAE) model:

2.2. Experiments on link prediction

        ①Prediction task: randomly delete some edges and keep all the node features

        ②Validation/Test set: deleted edges and unconnected node pairs with the same number

        ③Connection contained: 5% for val set and 10% for test set

        ④Epoch: 200

        ⑤Optimizer: Adam

        ⑥Learning rate: 0.01

        ⑦Hidden dim: 32

        ⑧Latent variable dim: 16

        ⑨Embedding dim: 128

        ⑩Performance comparison table with mean results and std error for 10 runs:

where * means w/o node features

3. Reference

Kipf, T. N. & Welling, M. (2016) 'Variational Graph Auto-Encoders', NIPS. doi: https://doi.org/10.48550/arXiv.1611.07308