my problem is the following: I have purchase probabilitiy estimations of some products. The model behind don't take care of any inter-correlations through these products. So my task is to re-calibrate the probabilities and take inter-correlations into account:

Example of problem discription, there are for exmple two products recommanded for the same user:

Product 1: purchase prob. for user 1 is 50%

Product 2: purchase prob. for user 1 is 30%

PROBABLY: for user 1 product 2 is better to advertise him because of the underlying inter-corrleations AND NOT product 1 as it is recommanded through the model because of the higher probability.

My raw data consists of:

-> 1. matrix of useritems: consists of purchase probabilities

-> 2. matrix of useritems: consists of real pruchases (binary, but really sparse)

-> 3. matrix of user*items: consists of real click data (counts how often a user clicked on the product-page; also very sparse)

My question is now:

how to combine the data and is there any similar approch maybe you have seen in some papers? Until now my research was very unlucky. There are some ideas about scoring rules or hybrid recommander systems? But until know, I had not seen any similar task...

Kind regards

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