15 · Generalized CP for Counts and Binary Data

Deep dive 15 of Tensors for Machine Learning. Every decomposition so far minimised squared error. This one asks what that choice was assuming:

Least squares is maximum likelihood under Gaussian noise of constant variance.

Counts are not that. Generalized CP keeps the CP model and replaces the loss — Poisson for counts, Bernoulli for 0/1 data — one element at a time.

The tensor is real: one year of Chicago crime reports, day-of-week × hour × community area × crime type. A squared-error fit predicts negative crimes on more than a thousand cells. And one of the components the Poisson fit finds is not a pattern in the city at all — it is what a form does when nobody knows the time.

A take-home deep dive, not one of the live labs of the six-hour workshop.

Study here, then run the real thing: notebook 15 on Colab · all the notebooks

Built from the workshop’s own material by Ravi Kalia and Sebastian Laverde Chunza, CC BY 4.0.