I asked this question on Cross Validated a few days ago, but didn't really get a favorable response, so asking here to see if I get any.

I'm looking at the description of a short-term position in statistical machine learning, which states that the main mission is the theme of estimation in algebraically structured models. I did a search but couldn't come up with something relevant, as the name didn't seem to be universal it seems: articles like these did come up but they're about model theory, not statistical models.

The position also mentions in the required skills the concepts of group actions, linear representations and Fourier transformations on finite or compact groups, etc. I'm well familiar with the context of group action and Fourier transforms, but I'm having difficulty connecting it with the term algebraically structured (statistical) models, about which I don't have any idea either.

I'd appreciate if you could post some beginner's references on algebraically structured (statistical) models and if not done in these references already, point out the connection between these models and the context of group action, linear representations and Fourier transformations on finite or compact groups.

I did some more search and found this paper named "ALGEBRAIC STATISTICAL MODELS" and this paper named "Learning rates for Gaussian mixtures under group invariance", could they be possibly in the right direction?

Thanks a lot in advance!