Recommenders and Ranking

Bayesian Personalised Ranking maximises the probability that a user's observed item scores above an un-observed one. Per triplet it maximises the log of a sigmoid of the two scores' difference, plus regularisation, so only differences matter.

The weighted normal equations split into a term shared by all users plus a small correction from that user's own interactions. The shared item Gram matrix is built once per sweep, so cost tracks observed interactions, not the full grid.

Never materialise the full matrix: two million items give roughly two trillion pairs. Compute only pairs sharing a rater by walking each user's rated list, cap oversized profiles, keep a few hundred neighbours per item, and rebuild on a schedule.

Sampling 100 negatives replaces the real task, ranking against a whole catalog, with a much easier one. It compresses the tail toward the top, unequally across models, so the sampled winner need not be the full-catalog winner.

Ship logging before ranking, launch a non-personalised baseline from catalogue metadata and business rules, add content-based personalisation once users have any history, and define in advance the data density that justifies a collaborative model.

Do not blend the two into one score. Make relevance a guardrail with an explicit tolerance, make catalog coverage the metric you move, and set that tolerance with a long-horizon experiment.

Measure first: compare the model against a non-personalised most-popular ranker. Popularity is partly real taste, so correct it only where the head demonstrably crowds out items a user would prefer, or where tail supply matters commercially.

Only when the log recorded the probability with which each item was shown, the candidate ranker mostly promotes items the old ranker did sometimes show, and enough logged sessions survive importance weighting to give a usable interval.