여러가지 graph generative models (autoregressive / sequential decision ) : computation 많고 permutation invariant 지켜지지 않을때가 많다. one shot generative models : modeling structural information 실패 (tractable 하지 않은 likelihood computation)
Score-based model인 EDP-GNN는 discrete-step perturbation of heuristically chosen noise scales 사용해서 flexibility와 efficiency에 문제 있음. 그리고, unable to fully capture the node-edge dependency since it only generates adjacency matrices.
autoregressive graph generative models : GAN, RNN, VAE, flow models. : computational expensive and permutation invariant X
one-shot-graph generative model : dist of all the component of a graph. (consider permutational invariance): GAN, VAE, normalizing flow → restrictive architecture
EBM → intractable
기존의 score based : Langevin dynamics → large scale graph 힘듦. + adjacency withdout the generation of node feature.
graph $G$ with N node defined by its node features $X \in \mathbb{R}^{N \times F}$ and the weighted adjacency matrix $A \in \mathbb{R}^{N \times N}$ as $G= (X, A)\in \mathcal{G}$. Diffusion process can be represented as $G_t = (X_t, A_t)$ with cont variable $t \in [0, T]$.
$f_t(\cdot)$ : linear drift coef, $g_t : \mathcal{G} \to \mathcal{G} \times \mathcal{G}$, $w$ is standard wiener process. The coefficient f and g are designed to guarnatee $G_t \sim p_T$.
problem) to expensive to calculate $\nabla_{G_t} \log p_t(G_t)$.
The key property of GDSS is that the SDEs in the system are dependent on each other, related by the gradients of the joint log-density which we refer to as the partial score functions. Due to the partial scores, GDSS is able to model the dependency between the components through time.