# Use Matrix Factorization to predict probability of a recommendation system?

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 ?