Make function to estimate number of columns HMA produces.

[amontanez24]

Problem Description

As a user, I'd like to know as soon as possible if HMA will be slow so that I can properly decide whether or not to use it.

Expected behavior

• Inside HMASynthesizer, add a function that can estimate the number or columns that will be modeled for each root table. We will use this later to give alerts.

It is understood that the exact number of rows varies depending on the transformers, constraints etc. For this reason, we only need an estimate. You can make the following assumptions:

• Assume the default transformers are being used
• Assume no constraints

Requirements

• The estimate should be the same order of magnitude as the actual answer.
• It should be performant (don't go overboard on trying to make calculations more precise at the cost of performance).

Additional context

The following tips may help:

• If a parent has a child with n columns
  • A covariance matrix with O(n^2) columns will be added to it
  • A column for the mean and standard deviation of the parent row will be added to it
  • At least n columns will be added for the marginal distribution parameters
  • At least one column will be added for the cardinality