Datasets:

zai-org
/

RPC-Bench

@@ -240,7 +240,7 @@ $$
 199 $X _ { i }$ in the causal graph. To fulfill this property, the GNN of the decoder should satisfy the following:
 200 Proposition 1. (Causal factorization). VCAUSE satisfies causal factorization, $p _ { \theta } ( \mathbf { X } \mid \mathbf { Z } , \mathbf { A } ) =$
 201 $\prod _ { i } { \bar { p } } _ { \theta _ { i } } ( X _ { i } \mid \mathbf { Z } _ { a n ^ { * } ( i ) } )$ , if and only if the number of hidden layers in the decoder is greater or equal
-202 than $\delta - 1$ , with  being the longest shortest directed path between any two endogenous nodes.
 203 The above proposition (proved in Appendix $\boxed { \mathbf { B } }$ is based on the fact that, in a GNN with $N _ { h }$ hidden
 204 layers (and $N _ { h } + 1$ layers in total), the output for the $i$ -th node depends on its neighbors of up
 205 to $N _ { h } + 1$ hops. As an example, consider the following chain causal graph: $X _ { 1 }  X _ { 2 }  X _ { 3 }$ ,

 199 $X _ { i }$ in the causal graph. To fulfill this property, the GNN of the decoder should satisfy the following:
 200 Proposition 1. (Causal factorization). VCAUSE satisfies causal factorization, $p _ { \theta } ( \mathbf { X } \mid \mathbf { Z } , \mathbf { A } ) =$
 201 $\prod _ { i } { \bar { p } } _ { \theta _ { i } } ( X _ { i } \mid \mathbf { Z } _ { a n ^ { * } ( i ) } )$ , if and only if the number of hidden layers in the decoder is greater or equal
+202 than $\delta - 1$ , with  being the longest shortest directed path between any two endogenous nodes.
 203 The above proposition (proved in Appendix $\boxed { \mathbf { B } }$ is based on the fact that, in a GNN with $N _ { h }$ hidden
 204 layers (and $N _ { h } + 1$ layers in total), the output for the $i$ -th node depends on its neighbors of up
 205 to $N _ { h } + 1$ hops. As an example, consider the following chain causal graph: $X _ { 1 }  X _ { 2 }  X _ { 3 }$ ,