How to actually do link prediction

[sinaziaee]

Hello everyone and thanks a lot for both the creation of pyg and the great documentation.
I've been following the examples on the examples directory and I came a cross link prediction at this link. It was a great scenario for understanding this concept but I was actually wondering where the real prediction based on the available data is happening. We split the data into train val and test to compute the loss and accuracy of val and test but where does it actually predict new edges based on the available data. The part that negative sampling is happening is where we want to predict does neg_edges based on our pos_edges but what about when we want to use all the edges as pos_edge and predict new edges. Sorry if it is a simple question but I'm a rookie at gnn and pyg and I would really appreciate all your help and if it was possible to attach a sample code or suggest a link for this purpose that would be really helpful. Thanks guys.

[rusty1s]

The prediction of new edges happens inside the decoder part of the model. That is, we use the existing edges in the graph to encode node embeddings using a GNN (encoder part), and then use these node embeddings to find new links (decoder part). You can best see this here, where decode_all produces a new adjacency matrix. Let me know if this clarifies your issues.

[sinaziaee]

Also one another problem. why prob_adj is not sth between 0 and 1 ? isn't this a probability ?

[rusty1s]

It is not guaranteed that all existing edges are also part of the predicted ones. If you want to guarantee that, you would have to merge them, e.g.:

edge_index = torch.cat([orig_edge_index, pred_edge_index], dim=1)
edge_index, _ = coalesce(edge_index)  # Remove duplicates

Increasing the threshold on prob_adj definitely helps to maintain only the edges that should be connected with higher probability.

Edit: Note that the decoder part of the network is untrained/heavily regularized, so it is expected that not all training edges can be recovered.

[sinaziaee]

Oh that's right. Thank you very much Matthias.
Do you have any example on how to have a trained decoder for link prediction ?
Just like the encoding part that we can train in the training loop.

[rusty1s]

The most simple way to achieve this is to utilize an MLP, e.g., based on the Hadamard product of edge-level source and destination node features:

z = x[edge_index[0]] * x[edge_index[1]]
out = MLP(z)

The Hadamard product achieves that link predictions are undirected/symmetric. You can also use concatenation to make your decoder directional.

[sinaziaee]

Thank you Matthias. You're always very helpful.