I have a dataset where I have a sparse utility matrix (user-product) with binary input: 1 if the user $i$ bought the product $j$, and 0 if it hasn't.
However it has a different meaning on the test set, 0 means that we don't know if the user bought this product, and 1 means that we're sure that the user bought that given product.
I need to get for each user in each product the probability that a user $i$ bought a product $j$ in the test set. For this I wish to use different matrix factorization techniques like FunkSVD, NMF or SVD++ , but I'm quite confused:
These techniques would only allow me to get the label (1 or 0) on test set, but I need to compute a probability of getting 1 and not the label in it self.
How can I approach this problem ? Or do I treat it as a classification problem and then use all common classification techniques ?