design system for symbolically identifying GP covariance kernel structure

[riastradh-probcomp]

Various desiderata:

1. Use a principled mechanism other than VentureFunction.stuff['name'] to represent it.
2. Readable display for names, including parameters.
3. Enable structure learning to distinguish composition/base kernel/parameter/hyperparameter inference.
4. Maybe enable simplification of phrase generated from PCFG after the fact?

Various candidates:

• Concatenate nested string representation in VentureFunction.stuff['name']. Pro: Easy, already done in matrixGP. Con: Not amenable to writing code that reliably works for GP covariance kernels and noisily fails for other things (1). No post-generation simplification (4).
• Compound (k, "k") structure for the above, maybe introducing tagged records to Venture. Pro: Fixes (1) and (4). Con: Need to invent tagged records. Extra verbiage for everything.
• Add purely symbolic representation separately, with a function mapping symbolic representation to functional representation. Pro: Fixes (1) and (4). Con: Still need to invent tagged records. Extra verbiage for everything. Explicit step to instantiate functional representation.

[axch]

Venture Lite has implementer-definable tagged records in backend/lite/record.py. Porting them to Puma would be useful (#224). Not clear whether adding user-definable tagged records is necessary for the present purpose.

[axch]

Presumably (3) can be accomplished with suitable uses of tag regardless of the in-model symbolic identification? Does that require #421?

[riastradh-probcomp]

(3) is indeed an independent issue but something relevant that is worth articulating somewhere and for some reason I had in my head that there are ways you might go about doing this that don't satisfy (3). #421 would help, yes.