Why does multinomial likelihood work better for click prediction?

The choice of likelihood function in collaborative filtering looks like a technical detail but is actually a structural commitment about what the data represents. Gaussian likelihoods model each interaction as an independent observation of a continuous quantity. Logistic likelihoods model each interaction as an independent binary classification. Both treat items as separate prediction targets.

Liang et al. argue the multinomial likelihood is structurally correct for click data because of competition. The model has a probability budget that must sum to 1 across all items. Putting probability on one item necessarily takes it away from others. This forces the model to assign more mass to items that are more likely to be clicked, which is exactly what top-N ranking metrics reward. Gaussian and logistic models can assign high probability to many items simultaneously without penalty, so they don't optimize for the relative ordering that recommendation actually requires.

The deeper point is that the likelihood is a closer proxy to the evaluation metric than logistic or Gaussian. Top-N ranking loss is hard to optimize directly, but multinomial likelihood induces the same kind of competition implicitly. The match between training objective and evaluation objective is doing the work — not anything specific to neural networks.

Source: Recommenders Architectures