I'd like to hear people's thoughts on the general topic of representing (or approximating) given functions as compositions of others.(adsbygoogle = window.adsbygoogle || []).push({});

Of course, one task is define precisely what this means. What are some interesting problems (theoretical or statistical) that require it?

Perhaps a Google virtuoso can do better than my attempts. I've used terms like "function decomposition" and I get lots of hits, but they are mostly about organizing businesses or computer programs. Abstractly, such problems do have some relevance. For example, a typical computer program needs to compute some function F(x,y,z,w...) and it's useful to do this in steps that compute simpler functions like g(x,y), h(z,w) and thus F becomes F(g(x,y),h(z,w)).

Several years ago, I saw a paper where some people were analying a way to evaluate the creditworthiness of loan applicants in a baltic country and they proposed a method of decomposing a function F(x,y,z,...) specified by a numerical table into simpler functions, also given by tables. I don't recall the specifics.

Writing a function as a multivariate Taylor series is a decomposition. I'm curious if there is interesting math besides that approach and besides the more general approach of representing a function as a summation over a set of orthogonal functions. Or maybe someone has proven that all approaches amount to these summation approaches?

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# Math related to representing functions as compositions of others?

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