Finiteness for the k-factor model and chirality varieties
Advances in Mathematics , Volume 223 - Issue 0811.3503 p. 243- 256
This paper deals with two families of algebraic varieties arising from applications. First, the k-factor model in statistics, consisting of n-times-n covariance matrices of n observed Gaussian variables that are pairwise independent given k hidden Gaussian variables. Second, chirality varieties inspired by applications in chemistry. A point in such a chirality variety records chirality measurements of all k-subsets among an n-set of ligands. Both classes of varieties are given by a parameterisation, while for applications having polynomial equations would be desirable. For instance, such equations could be used to test whether a given point lies in the variety. We prove that in a precise sense, which is different for the two classes of varieties, these equations are finitely characterisable when k is fixed and n grows.
|Keywords||algebraic factor analysis, Noetherianity|
|MSC||Toric varieties, Newton polyhedra (msc 14M25), Polytopes and polyhedra (msc 52Bxx), Representation theory (msc 20G05)|
|THEME||Logistics (theme 3)|
|Journal||Advances in Mathematics|
|Note||(Link is to arxiv preprint.)|
Draisma, J. (2010). Finiteness for the k-factor model and chirality varieties. Advances in Mathematics, 223(0811.3503), 243–256.