Generalized CP (GCP)

Generalized CP — keep the CP model, replace the loss, one element at a time. Spanish: CP generalizado.

The prediction in each cell is still the same sum of rank-1 terms, and the factors are still the profiles you read in deep dive 14. What changes is the one line that says how bad a prediction is: GCP minimises the sum over every entry of any elementwise loss f(x, m).

Each choice of f is the negative log-likelihood of a different model of the data. The notebook’s three-row table is cut down from Table 1 of Hong, Kolda and Duersch (2020), which also lists Gamma, Rayleigh, negative binomial, Huber and more — and the machinery does not care which one you hand it.