graph-level problem

In graph-level problems, there are multiple graphs. Each graph $G$ represents a predictor associated with an observation $y\in Y$. We assume that $G,y\sim p(G,y)$ and want to regress $y$ on $G$.

Here, our hypothesis class is $\mathcal{F}\mathcal{=}$$\{f(S)=\sum _{k=1}^{K-1}{h}_k{S}^k\mathbb{1}|h_k\in \mathbb{R}\}$

And our minimization problem is given by $$\min_{h_{k}} \frac{1}{m} \sum_{i=1}^M \ell\left( \sum_{k=0}^{K-1} h_{k} S^k \mathbb{1}, y \right)$$