Matrix Factorization

Give every user and every item a short vector, and predict an interaction by their dot product. Fit the vectors so the products match what was observed. It won the Netflix Prize, it is still a strong baseline, and it is the same low-rank idea that appears everywhere else in this graph — here applied to a matrix of behaviour rather than of weights.

The bias terms do more work than the factors on real data: a per-user and per-item offset captures that some people rate generously and some items are broadly liked, and fitting factors without them makes the factors absorb that instead. A careful implementation with bias terms and regularisation beats many neural replacements, which a well-known reproducibility study found repeatedly.

Predict r̂ sub _ui  = μ + b sub _u  + b sub _i  + p sub _u ·q sub _i  and minimise squared error over observed entries plus λ(‖p sub _u ‖² + ‖q sub _i ‖²), which is the same objective as a regularised truncated SVD restricted to what was observed. Regularisation is not optional here — with most entries missing, the unregularised optimum fits the observed few exactly and generalises to nothing.