Because this sparsity is partially driven by directionality, we implemented a bidirectional embedding model (cEm-bedBi) that (a) trains a second embedding model by reversing the input (effects as targets, causes as contexts), and (b) ranks pairs by the average of the scores returned by these two unidirectional causal embedding models.
the final bidirectional score of the pair, (e 1 , e 2 ), where e 1 is the can-didate cause and e 2 is the candidate effect, is: s bi (e 1 , e 2 ) = 1 2 (s c→e (e 1 , e 2 ) + s e→c (e 2 , e 1 )) (2) where s c→e is the score given by the original causal embeddings, i.e., from cause to effect, and s e→c is the score given by the reversed-input causal embeddings, i.e., from effect to cause.