On Tuesday, October 16, 2018, Greg Ewing <greg.ewing@canterbury.ac.nz> wrote:
Wes Turner wrote:
Is there a name for an iteration of the powerset which is more useful for binary search? I.e. instead of starting with null set, start with the "middle" ( r/2 ).

You'll have to provide more detail about what you want to search
and how you intend to search it. There isn't a single "middle" to
the set of powersets, since in general there are many subsets with
about half the elements of the original set. Also there is no
obvious ordering to use for bisection.

When searching for combinations of factors which most correlate to the dependent variable, it doesn't always make sense to start with single factors; especially when other factors 'cancel out'.

For example, in clinical medicine, differential diagnosis is a matter of determining what the most likely diagnosis/es is/are; given lots of noise and one or more differentiating factors.

Testing individual factors first may not be the most efficient because combinations/permutations are more likely to be highly correlated with specific diagnoses. 

Random search of the powerset and mutation (or a neuralnet) may be faster anyways. Just wondering whether there's a name for differently ordered powerset (and Cartesian product) traversals?

Obviously, this is combinatorics and set theory (category theory (HOTT)); here in the itertools library for iterables.

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