The role of bias terms in binary recommender systems

Question

I realize that a recommender system applied to, for example, the Movielens dataset needs to account for bias. That is, one needs to adjust for the varying popularity of movies, and that users have different baselines for their ratings. If one users tends to rates movies high and another users rates movies low, a rating of 4 out of 5 implies different level of appreciation.

However, I struggle to understand the meaning of bias terms in a recommenders systems that uses binary data as its input. For example, when we instead of movie ratings have yes/no information on if a user purchased or viewed an item in an online store.

This implementation introduces scalar bias terms for both products and users. The method is a hybrid in the sense that it takes into account both user behaviour and metadata. The paper also describes how it is used on binary data in an online store. How should the bias terms be interpreted in this case?

Answer 1

Even if the system uses binary data as input (0/1), it can still have some "bias" (average, offset) of these zeros and ones. You can look at matrix factorization implementation here (for netflix competition data, which is very similar to movielens dataset): https://github.com/pepe78/netflix_matrix_factorization

Answer 2

Look once more at the model definition, in the simplest case, it predicts the rating for $u$-th user and $i$-th item $\hat r_{ui}$ using

$$ \hat r_{ui} = f(\boldsymbol{q}_u \cdot \boldsymbol{p}_i + b_u + b_i) $$

where $\boldsymbol{q}_u$ and $\boldsymbol{p}_i$ are latent representations per user and item, while $b_u$ and $b_i$ are bias terms. Bias term for user $b_u$ is the "default" or "average" rating the user gives, bias term for the item is the "default" rating for the item. Notice that the part $\boldsymbol{q}_u \cdot \boldsymbol{p}_i$ depends on the interaction of a particular user with a particular item, it tells you how well does the item matches the person. On another hand, $b_u$ is the base rating by the user regardless of everything else, and $b_i$ is the base rating for the item regardless of everything else. If the latent representations for user and item are orthogonal, $\boldsymbol{q}_u \cdot \boldsymbol{p}_i$ would be equal to zero, so the rating would reduce to $f(b_u + b_i)$.

To give an example, say that you are Netflix and your user Bob likes watching sci-fi movies, so a romantic comedy probably would not be a great fit for him. On another hand, if it is a multi-category Oscar winner, so it may make sense to "bump" the predicted rating by the fact that the movie has a very high average rating $b_i$. Another user, Anna is very critical and rarely gives thumbs-up to the movies, so $b_u$ would be negative for her, always decreasing the predicted ratings by a constant.

Additionally, same as in linear regression, intercepts improve the numerical stability of the algorithm and are beneficial when training the model.

Including additional features, such as metadata, does not change the interpretation.