Contributions:

• They construct a probabilistic model for graph generation. They called it as gated graph neural networks Q: what is gated graph neural network
• Provide a method of how to incorporate hard domain-specific constraints into model as a CGVAE
• Allowing optimization in latent space for molecular generation

Challenge

1. Since the size of the graph is large enough, it is really hard for one to iterate through all possibility. The possibility means the relationship between node and node. The relationship is not only just connecting or not, sometime it also related to the label of the edge. And sometime, we need to also find the correlation between two edges
2. To solve this problem, authors claimed that we can ignore the correlation and directly predict the label or existence.
3. Another approach is to factor the distribution into a sequence of discrete decisions in a graph construction trace Q: What is Graph Construction trace
4. They apply two things on their model, one for hard constrain mask, one for soft correlation learning

Related Work

There are several different task in this field. They are all related to generation problem.

1. The uncorrelated generation is the easiest one. In principle, we just need to random generate the edges on the adjacent matrix. Or simply given a graph, and then add some variation on the graph.
2. Sequential Generation: This part can be regarded as an image inpainting problem. For example, we have an incomplete graph, we need to generate the missing part. Furthermore, we can also add so called “auxiliary stream” (which is additional information). We can use this auxiliary stream to further guide the generation of the graph. (My thought, denoising problem can be regard as an auto-regression problem or a inpainting problem)

Method