we posit a family of approximate densities Q. This is a set of densities over the latent variables. Then, we try to find the member of that family that minimizes the Kullback-Leibler(KL) divergence to the exact posterior,
Why is it called "family"? Why don't we call it "assumptions" on the joint distribution of latent variables.
For example, Why don't we say:
"In the mean field approximation we assume that the latent variables are independent and we try to find the best approximation of the joint distribution of latent variables to minimizes the $KL$ divergence"