Squared error is an assumption

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

Every fit in the workshop — the pseudoinverse in section 07, the SVD in 09, Tucker in 10, CP in deep dive 14 — minimised squared error. That is not what “fit” means; it is one answer to how surprised should I be by this residual?

Both halves of the assumption are wrong for counts. The spread is not constant: a Poisson count’s variance equals its mean. The support is wrong: a Gaussian lives on the whole number line, so the model is free to predict negative crimes.

The loss is where you tell the decomposition what kind of number it is looking at.