Use InverseFunctions

[devmotion]

The package InverseFunctions.jl will be available in the registry soon and contain inverse + definitions for functions in base. If other packages such as LogExpFunctions implement this interface we could replace GPLikelihoods.inverse with InverseFunctions.inverse and remove our definitions.

[devmotion]

Note: We can't switch before LogExpFunctions and StatsFuns support it though (if we don't want to introduce type piracy).

[oschulz]

Do we already have something pending on StatsFuns?

[devmotion]

No, I didn't push this issue the last weeks. I am up for reviewing a PR though.

[oschulz]

I am up for reviewing a PR though.

Sure, I can do one. Which functions in StatsFuns should be targeted?

[oschulz]

I guess the relevant functions in StatsFuns are the cdf, ccdf, logcdf and logccdf and their inverses, right (since the log/exp functions live in LogExpFunctions now)?

[devmotion]

Yes, I guess everything that's defined in StatsFuns and not in LogExpFunctions.

[oschulz]

Uh, I was just about to get started, and then realized that those function do of course all take multiple arguments - InverseFunctions.inverse doesn't support that (would be tricky to define what inverse means). We could define InverseFunctions.inverse (and even ChangesOfVariables.with_logabsdet_jacobian if we want) for Base.Fix1(Distributions.cdf) and so on in a generic fashion, though.

Or would it be fine to just do normcdf & friends?

What does GPLikelihoods need, here?

[oschulz]

And I just saw sqrt/square in inverse.jl here. I actually had that in an eary draft of InverseFunctions, but then took it out because Base has no inverse of sqrt and hadn't seen sqrt/square used in variable trafos.

We should add square to InverseFunctions, though, if it's useful here.

[devmotion]

Ah true, yes, it only makes sense for one-argument functions. We only need normcdf and norminvcdf here.

[oschulz]

What about sqrt? Is it used, or just in inverse.jl for completeness?

[devmotion]

No, everything in inverse.jl is used. It is needed for the SquareLink (alias and constructor might be removed at some point but we still want to support it).

[oschulz]

Ok, then let's just add square to InverseFunctions. Should it be exported, you think?

Also - should we support it in ChangesOfVariables? Would require it to depend on InverseFunctions, but I don't think that should be a problem.

[oschulz]

InverseFunctions supports sqrt now (JuliaRegistries/General#48374).