PySR VS Bigsimr.jl

> Yes, julia can be called from other languages rather easily

This seems false to me. StaticCompiler.jl [1] puts in their limitations that "GC-tracked allocations and global variables do not work with compile_executable or compile_shlib. This has some interesting consequences, including that all functions within the function you want to compile must either be inlined or return only native types (otherwise Julia would have to allocate a place to put the results, which will fail)." PackageCompiler.jl [2] has the same limitations if I'm not mistaken. So then you have to fall back to distributing the Julia "binary" with a full Julia runtime, which is pretty heavy. There are some packages which do this. For example, PySR [3] does this.

There is some word going around though that there is an even better static compiler in the making, but as long as that one is not publicly available I'd say that Julia cannot easily be called from other languages.

[1]: https://github.com/tshort/StaticCompiler.jl

[2]: https://github.com/JuliaLang/PackageCompiler.jl

[3]: https://github.com/MilesCranmer/PySR

I first learned about it with PySR https://github.com/MilesCranmer/PySR, they have an arxiv paper with some use cases as well.

I encourage everyone to read this paper. It's well written and easy to follow along. To the uninitiated, SR is the problem of finding a mathematical (symbolic) expression that most accurately describes a dataset of input-output examples (regression). The most naive implementation of SR is basically a breath first search starting from the simplest program tree: x -> sin(x) -> cos(x) ... sin(cos(tan(x))) until timeout. However, we can prune out equivalent expressions and, in general, the problem is embarrassingly parallel which alludes to some hope that we can solve this pretty fast (check out PySR[1] for a modern implementation). I find SR fascinating because it can be used for model distillation: learn a DNN approximation and "distill" it to a symbolic program.

Note that the paper talks about the decision version of the SR problem. ie: can we discover the global optimum expression. I think this proof is important for the SR community but not particularly surprising (to me). However, I'm excited by the potential future work for this paper! A couple of discussion points:

* First, SR is technically a bottom up program synthesis problem where the DSL (math) has an equivalence operator. Can we use this proof to impose stronger guarantees on the "hyperparameters" for bottom up synthesis. Conversely, does the theoretical foundation of the inductive synthesis literature [2] help us define tighter bounds?

* Second, while SR itself is NP hard, can we say anything about the approximate algorithms (eg: distilling a deep neural network to find a solution[3])? Specifically, what proof tell us about the PAC learnability of SR?

Anyhow, pretty cool seeing such work getting more attention!

[1] https://github.com/MilesCranmer/PySR

[2] https://susmitjha.github.io/papers/togis17.pdf

[3] https://astroautomata.com/paper/symbolic-neural-nets/

I found it curious that one of the implementations of symbolic regression (the "machine scientist" referenced in the article) is a Python wrapper on Julia: https://github.com/MilesCranmer/PySR

I don't think I've seen a Python wrapper on Julia code before.

This is really neat! Since you're interested in this subject, you may also appreciate PySR and the corresponding paper which uses Graph Neural Networks to perform symbolic regression.

One more example for you. Our group wrote our core package in Julia called Bigsimr.jl (here) and then wrote interfaces to it for R (here and on cran) and Python (here and on PyPi)

Mostly, but I used it to write a package that does multivariate simulation via gaussian copulas with correlation matching. You can find it here.

We wrote a Julia package that can do this called Bigsimr which also has an R interface. Message me if you have more questions.

I wrote a Julia library that basically applies this idea, but extends it to multivariate distributions. We sample from a multivariate normal, transform the margins to uniform (via the normal cdf), and then transform to the desired distribution using the margins inverse cdf's (called the NORTA algorithm). The caveat is that this transformation is non-linear, so the correlation matrix used to generate the multivariate normal samples is generally not the same as the correlation after transformation. We account for this by numerically solving for the n*(n-1)/2 double integrals to determine what input correlation is necessary to get the desired output correlation. This paper describes the full problem and method for solving.