IDS

[zenna]

IDS are integral to many components of Omega but there's a few things we haven't figured out?

What are IDS?

What are ids?

Originally they were identifiers used to make random variables distinct. Now that are indexes into (conditional) independence classes. That is, a class c expresses an infinite set of random variables and the idth element of that class is \omega -> class(id, \omega).

Nested Plates

Say we have a nested plate

child1(id, w) = w |> (1, id) ~ Normal(0, 1)
child2(id, w) = w |> (2, id) ~ Uniform(0, 1)
parent(id, w) = child1(id, w) + child2(id, w)

Lower Level type

At one level we agree that an id is just a symbol, it really just needs to be distinct from other ids. At a lower level, we might make some representational choices -- should ids be:

• Integers
• Sequences of integers
• Anything
• Sequences of anything

The reason we are talking about sequences at all is because of the projection mechanism used in independence, which relies on combining two ids into a unique one. Mathematically this can be done using pairing functions but the precision in practice means we should use sequences.