Test on Advanced Deep Learning Techniques

Question 1: The VGAE's generative model determines the probability of an edge (A_ij = 1) between two nodes by taking the logistic sigmoid of an inner product between their latent variables (z_i, z_j).

A. Yes

B. No

Explanation: The study materials state: "Our generative model is given by an inner product between latent variables: p ( A | Z ) = ∏ N i =1 ∏ N j =1 p ( A ij | z i , z j ) , with p ( A ij = 1 | z i , z j ) = σ ( z > i z j ) , (2) where A ij are the elements of A and σ ( · ) is the logistic sigmoid function." This confirms that the probability of an edge (A_ij = 1) is found using the logistic sigmoid of an inner product of latent variables.

Question 2: According to the study materials, what is the primary purpose of the Variational Graph Auto-Encoder (VGAE) framework?

A. Supervised classification of graph nodes.

B. Unsupervised learning on graph-structured data.

C. Predicting future node features in dynamic graphs.

D. Learning to classify directed graphs exclusively.

Explanation: The study materials explicitly state, 'We introduce the variational graph auto-encoder (VGAE), a framework for unsupervised learning on graph-structured data based on the variational auto-encoder (VAE)'. This indicates its primary purpose.

Question 3: Spectral Clustering (SC) and DeepWalk (DW) models are capable of utilizing input features during their operation, as described in the study materials.

A. Yes

B. No

Explanation: The study materials explicitly state: "Both SC and DW do not support input features."

Question 4: In the non-probabilistic graph auto-encoder (GAE) model, the reconstructed adjacency matrix \u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0A is directly calculated by applying GCN(X, A).

A. Yes

B. No

Explanation: The study materials state that for the GAE model, Z = GCN(X, A), and then the reconstructed adjacency matrix \u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0A is calculated as \u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0A = \u00cf\u0083(ZZ>). Therefore, \u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0\u00c2\u00a0A is derived from Z, which is calculated by GCN(X,A), but it is not directly calculated by GCN(X,A).

Question 5: According to the study materials, what characterizes the Gaussian prior p(Z) used in the Variational Graph Autoencoder (VGAE), and what potential issue is identified regarding its combination with an inner product decoder?

A. The Gaussian prior is a uniform distribution over the latent variables, and it is a good choice for all decoders.

B. The Gaussian prior is a product of independent normal distributions N(zi | 0, I), but it is potentially a poor choice with an inner product decoder because the decoder pushes embeddings towards the zero-center.

C. The Gaussian prior is a product of independent normal distributions N(zi | 0, I), and it is considered a potentially poor choice with an inner product decoder because the decoder tries to push embeddings away from the zero-center.

D. The Gaussian prior is a product of independent normal distributions N(zi | 1, I), and it significantly improves performance with an inner product decoder.

Explanation: The study materials state that 'We further take a Gaussian prior p ( Z ) = ∏ i p ( z i ) = ∏ i N ( z i | 0 , I )'. It also mentions that 'A Gaussian prior is potentially a poor choice in combination with an inner product decoder, as the latter tries to push embeddings away from the zero-center'. Option 2 accurately reflects both these points from the text.