*3.6. Optimization Objective*

Based on the above content, the final objective function of our framework is given as

$$\min\_{\mathcal{O}, \Theta, \Psi} \mathcal{L}\_{nc} + \lambda \cdot \mathcal{L}\_{node} + \mu \cdot \mathcal{L}\_{edge} \tag{19}$$

where Θ, Φ, and Ψ are the sets of parameters for the synthetic node generator (Section 3.3), edge generator (Section 3.4), and node classifier (Section 3.5), respectively. *λ* and *μ* in Equation (19) are weight parameters. The best training strategy in our experiments is to first pre-train the node generator and the edge generator and then minimize Equation (19) to train the node classifier and fine-tune the node generator and edge generator at the same time. Our entire framework is easy to implement, general, and flexible. Different structural choices can be adopted for each component, and different regularization terms can be enforced to provide prior knowledge.
