Extreme Vertex Designs

[caseykneale]

Hi again,

I, with the help of some others, was able to whip up some entry point code for making extreme vertex candidate sets. Maybe we can find a way to work together to flesh out this area of the ecosystem?

[caseykneale]

https://github.com/caseykneale/ExtremeVertexDesigns.jl

[phrb]

Hey, that looks nice, especially your implementations of federov's and K-exchange!

I've implemented KL-exchange (https://github.com/phrb/ExperimentalDesign.jl/blob/master/src/kl_exchange.jl#L109), although not so cleanly as you did. I tried to use matrix and vector views to save on memory, and I can run this for relatively large candidate sets (n = 300000) and numbers of factors (k = 50), if the factors are all of the same type.

I also have some types for designs, Plackett-Burman designs, and random designs using arbitrary distributions from Distributions.jl.

I had not planned to include constraints directly, but I saw you've found a nice way to do it, although I'm not sure I understand how that works. Does it sample candidates respecting the constraints and then optimize, or do you sample uniformly then filter? I was hoping I could use the different distribution mixes for random designs to do some sort of "constrained sampling".

Regarding ideas to move forward, I would certainly be willing to add code to this package to interface with yours, and I plan to do that. Another option would be you contributing your code to this package, but it seems it would make sense to create a Julia Experimental Design organization on GitHub or something like that, to gather all efforts.

What do you think?

[caseykneale]

I really like that you have Plackett-Burman and factorial designs. I think your package is/should be the main hub for DoE stuff. I think you've done a really good job implementing things - I don't fully understand all of the design decisions you made but it looks good overall. I'm not 100% confident in my K-exchange algorithms. I think they are correct, but, that was my first try to implement them.

So the way extreme vertex designs work, my understanding anyways, is, they are mostly used for mixture designs. So the values of the design points need to sum to 1.0 (or 100%). So if a user says component A will only be at 20-80% concentration than theres no reason to sample beyond that range. That makes a constraint in the design space. Now in mixture DoE's more often than not there is a limitation in the number of samples allowable. A full simplex design or simplex centroid design would be ideal with no constraints.

What many people do - is they admit that the extreme vertices are sufficient. So Federov in this case just shuffles the extreme edges of the design space to optimize some criterion. I only found equations for D optimality, but surely, A, E, I, etc optimality could also be used.

So your package is less specific, the unreleased package I made is pretty specific to mixture design. It currently lacks interior point sampling, but that could be included as well.

I think an Organization is a great idea! This could allow us to break up the space a bit and map it out more. I've also noticed - we don't have a MANOVA/MANCOVA or even a working ANOVA package in the latest Julia. That's something we probably need to correct as well