In **Recommender Systems** design we are faced with the following problem: given incomplete information about users preference, content information, user-items rating and contextual information, learn the user preference and suggest new items for users based on features as:

- previous pattern of items preference of the user;
- preference of users with similar rating pattern;
- contextual information: location, time (of the day, week, month, year), social network.

This is usually formulated as a matrix completion problem using **Matrix Factorization **techniques to offer a optimal solution. Is this case latent features for users and item are inferred from the observed/rated items for each user, and from this latent features the missing entries are estimated. One major modelling tool for this problem is probabilistic modelling, and there are many proposals in the literature of different **Probabillistic Matrix Factorization** approaches. We will briefly discuss some of this models, starting with the seminal paper: **Probabilistic Matrix Factorization (PMF) – [Salakhutdinov and Mnih, 2008, NIPS]**. Continue reading “Probabilistic models for Recommender systems (part I): Probabilistic Matrix Factorization”