How the practical objectives match the theoretical ones? about dir-gnn HOT 4 CLOSED

Hi,

Intuitively, Eq 11 optimizes both the shortcut classifier and the DIR objective. For the optimization of the shortcut classifier, the reason that we isolated it is because we don't want the shortcut prediction to affect the graph encoder. And the DIR objective directly corresponds to the target we want.

One way to view Figure 3 vs. Figure 2 is that, instead of doing intervention in the graph level (actually concatenate two graphs or remove edges), we do intervention in the representation level in Figure 3.

In this case, \hat{y} is the model prediction with both S and C. And Eq. 9 computes the risk in each environment (each row in Figure 2). Since our principle is that whatever S is, the risk should be both small and invariant. Thus we have (informally) R_{DIR} = E[Eq. 9] + Var(Eq. 9).

from dir-gnn.

Thany your very much for your reply. After your explanation, my major question becomes why you say "And Eq. 9 computes the risk in each environment (each row in Figure 2). ". Are there any formal analysis or references about Eq .8?

from dir-gnn.

Hi, do you mean Eq .8 or Eq. 9? For Eq. 8 we provide the reference in the Appendix. And for Eq.9 it's just iterating over different interventions and taking the expectation.

from dir-gnn.

Thank you very much. Now I think I somewhat get it!

from dir-gnn.