Flashcards on Advanced Deep Learning Techniques
Advanced Deep Learning Techniques: VGAE & GAE Explained
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Variational Graph Autoencoder (VGAE)
14 cards
Card 1
Question: What is a Variational Graph Auto-Encoder (VGAE)?
Answer: A framework for unsupervised learning on graph-structured data based on the variational auto-encoder (VAE), using latent variables to learn interpreta
Card 2
Question: Which encoder architecture is used in the VGAE described here?
Answer: A graph convolutional network (GCN) encoder parameterizing the variational posterior.
Card 3
Question: How are the latent variables represented in VGAE?
Answer: As stochastic node-level latent variables z_i, summarized in an N×F matrix Z.
Card 4
Question: What node and graph inputs does the VGAE use?
Answer: An adjacency matrix A (with diagonal elements set to 1), degree matrix D, and node feature matrix X (N×D).
Card 5
Question: How is the variational posterior q(Z|X,A) factorized in VGAE?
Answer: q(Z|X,A)=∏_{i=1}^N q(z_i|X,A), with each q(z_i|X,A)=N(z_i|μ_i, diag(σ_i^2)).
Card 6
Question: How are the mean μ and log-standard-deviation log σ computed in the VGAE inference model?
Answer: μ = GCN_μ(X,A) and log σ = GCN_σ(X,A); both are outputs of two-layer GCNs sharing the first-layer weights W0.
Card 7
Question: Write the two-layer GCN layer definition used in VGAE.
Answer: GCN(X,A) = ˜A ReLU(˜A X W0) W1, where ˜A = D^{-1/2} A D^{-1/2}, ReLU(x)=max(0,x), and W0,W1 are weight matrices.
Card 8
Question: What generative model p(A|Z) does the VGAE use?
Answer: An inner product decoder: p(A|Z)=∏_{i,j} p(A_ij|z_i,z_j) with p(A_ij=1|z_i,z_j)=σ(z_i^T z_j) where σ is the logistic sigmoid.
Card 9
Question: How is the adjacency matrix A treated in VGAE for self-connections?
Answer: Diagonal elements of A are set to 1, i.e., every node is connected to itself.
Card 10
Question: What objective is optimized to learn the VGAE parameters?
Answer: The variational lower bound L = E_{q(Z|X,A)}[log p(A|Z)] − KL[q(Z|X,A)||p(Z)], optimized w.r.t. the variational parameters (GCN weights).