Make it easier to select expression from Pareto front for evaluation

[MilesCranmer]

This enables the following syntax:

model = SRRegressor()
mach = machine(model, X, y)
fit!(mach)

# Predict with 3rd equation:
predict(mach, (data=X, idx=3))

# Predict with most complex equation:
r = report(mach)
predict(mach, (data=X, idx=lastindex(r.equations)))

which lets the user specify the equation they wish to use for prediction from the Pareto front.

For multiple outputs:

model = MultitargetSRRegressor()
mach = machine(model, X, y)
fit!(mach)


# Choose the 1st equation for output 1, 10th for output 2, and 5th for output 3:
predict(mach, (data=X, idx=[1, 10, 5]))

TODO:

• Add example to documentation
• Add example to README
• Remove discussion of modifying selection_method (Seems to not work, see Issues with making predictions using the expression selected using the function passed to selection_method PySR#543 by @MrChewi)

---

@ablaom I would be interested to know if there is any way to make this sort of behavior compatible with MLJ? As it stands I think this might break some MLJ interfaces for users who wish to use this. (They would still be able to use selection_method parameter, but only before fit!)

[github-actions]

Benchmark Results

	master	b5d56e0...	t[master]/t[b5d56e0...]
search/multithreading	24 ± 0.19 s	24.4 ± 1.8 s	0.985
search/serial	33.8 ± 0.62 s	33.9 ± 1.2 s	0.995
utils/best_of_sample	1.44 ± 0.58 μs	1.36 ± 0.49 μs	1.06
utils/check_constraints_x10	12.9 ± 3.4 μs	12.6 ± 3.4 μs	1.02
utils/compute_complexity_x10/Float64	2.25 ± 0.11 μs	2.27 ± 0.13 μs	0.992
utils/compute_complexity_x10/Int64	2.26 ± 0.12 μs	2.27 ± 0.12 μs	1
utils/compute_complexity_x10/nothing	1.44 ± 0.1 μs	1.44 ± 0.13 μs	0.999
utils/optimize_constants_x10	31.3 ± 6.8 ms	30.6 ± 7.1 ms	1.02
time_to_load	1.37 ± 0.052 s	1.39 ± 0.056 s	0.983

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[ablaom]

Sorry for not catching this earlier. This looks very breaking to me. In MLJ you cannot attach metadata to data at predict time.

[MilesCranmer]

I wasn't sure the proper way to incorporate this. SRRegressor basically fits an ensemble of models (each equation) and the user requires an interface to specify which model they wish to evaluate. The default behavior (predict(mach, X)) uses some selection method for picking from the ensemble. But I wasn't sure how to let the user decide themselves.

[ablaom]

Something similar was encountered in hierarchical clustering. In that case we wanted the user to choose, after fitting, the height of the dendrogram. There was quite a bit of discussion and the best we came up with was to return a method in the report to let the user predict with a user-specified height. (A hyperparameter controls the default height for the ordinary predict).

I do have the idea to allow more flexible predict arguments in the LearnAPI.jl proposal, but I think it's difficult to justify in MLJ for small number of use-cases, as adding this is quite complicated.