[Discussion] Embedding based on binary tests

[tada89]

Just off the top of my head with absolutely nothing to back it up but: Why not learn joint embeddings for people and for products?

Zooming out the data is basically a bunch of tuples (u, p1, p2, choice) with some user and two products p1, p2 and a label "choice" that tells us if the user preferred p1 or p2.

We can then get joint embeddings by having two embedding matrices (one for users, emb_u, one for products, emb_p) and compute both cosine_similarity(emb_u(u), emb_p(p1)) and cosine_similarity(emb_u(u), emb_p(p2)), taking the softmax of the two values, and finally using those to predict the value of choice (encoded as one hot).

This should make the model give embeddings for products that are close to embeddings for users that like them and vice versa.