`FixedCombinations` implementation may lose correlations

[npatki]

Problem Description

Under the hood, the FixedCombinations constraint concatenates the columns to produce unique identifiers (and drops the individual columns). This solves the constraint, but in doing so, it may lose correlations that exist between original columns.

Expected behavior

Consider a table of users belong to different cities & states in the US. There is a fixed combinations constraint between the city & state.

User ID	City	State	Tax Rate
1	San Francisco	CA	7.2%
2	Los Angeles	CA	7.5%
3	Seattle	WA	2.1%
4	Seattle	WA	2.5%
5	Spokane	WA	3.1%
...	...	...	...

There is correlation where CA corresponds to higher tax rates (regardless of which city in CA). The model should be able to capture this.

With FixedCombinations, the model never looks at CA as common feature. Rather it looks at SanFrancisco+CA and LosAngeles+CA as separate categories. (This may be good enough for certain cases, but IMO it's missing a key input that both locations have a commonality.)

Possible Solutions

1. Do not drop the city and state columns when modeling. The model may synthesize some unexpected output (eg. CA+SanFrancisco, Boston, NY) but that can be fixed later through some logic.
2. Create a new table to identify a City, State pair. For eg. Location ID, City, State. Then use that identifier (Location ID) as a primary key to reference in the Users table.

[npatki]

Updated title and task since the constraint has been renamed to FixedCombinations. Issue still holds.