Global Mean (RecSys)
Before a recommender knows anything about a particular person or a particular item, it still has to put a number on an unseen rating. The most defensible guess is the average of every rating in the dataset, and that single number — the global mean — does more work than its simplicity suggests.
The anchor everything else hangs off
In a factorization model with bias terms, a prediction is assembled as the global mean plus a user bias, plus an item bias, plus the interaction between the user and item factors. The mean carries the overall level of the scale — around 3.5 on a five-star MovieLens dataset — which frees every other term to express a deviation: this person rates half a star below average, this film half a star above. Remove the mean and the biases have to absorb the level themselves, while regularisation keeps pulling them toward zero, which now means a rating of nothing at all.
The baseline you have to beat
Predicting the global mean for every unknown cell is the crudest model available, and its error is the yardstick the rest are judged against. On five-star data its RMSE sits near a full star, and a factorization model that fails to beat mean-plus-biases by a clear margin has not learned preference — it has learned the scale.
Where it shows up in serving
It is also the honest answer when signal is absent: a newly added item with no interactions scores the mean adjusted by whatever user bias is already known, so a cold-start row produces a sane number instead of a zero that would bury it beneath the entire catalogue.
The global mean is the average of all observed ratings in a dataset, used as the starting point of a prediction before any personalisation is added. In a biased factorization model the score is the mean plus a user bias, an item bias and the factor interaction, so every learned term expresses a deviation from it rather than an absolute level. It is also the trivial baseline whose error any real model must beat.
Imagine a shop that has to guess how much you will like a product it knows nothing about, for a customer it has never served. The sanest answer is the average score everything in the shop gets.
That average is the global mean, and recommenders start from it. Everything personal is then a nudge away from that number: this customer is harsher than most, this product better liked than most. Starting from the average gives the system something honest to say about a brand-new product, and it sets the bar — if the clever machinery cannot beat the plain average, it has learned nothing about taste.