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Algebraic tests of general Gaussian latent tree models

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

  • Dennis Leung
  • Mathias Drton
We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any such model. In other words, we find polynomial constraints that characterize when a matrix is the covariance matrix of a distribution in a given latent tree model. However, leveraging these constraints to test a given such model is often complicated by the number of constraints being large and by singularities of individual polynomials, which may invalidate standard approximations to relevant probability distributions. Illustrating with the star tree, we propose a new testing methodology that circumvents singularity issues by trading off some statistical estimation efficiency and handles cases with many constraints through recent advances on Gaussian approximation for maxima of sums of high-dimensional random vectors. Our test avoids the need to maximize the possibly multimodal likelihood function of such models and is applicable to models with larger number of variables. These points are illustrated in numerical experiments.
OriginalsprogEngelsk
TitelAdvances in Neural Information Processing Systems 31 (NIPS 2018)
Antal sider10
ForlagNeural Information Processing Systems Foundation
Publikationsdato2018
StatusUdgivet - 2018
BegivenhedTwenty-Second Annual Conference on Neural Information Processing Systems - Hyatt Regency, Vancouver, Canada
Varighed: 8 dec. 200813 dec. 2008
Konferencens nummer: 22

Konference

KonferenceTwenty-Second Annual Conference on Neural Information Processing Systems
Nummer22
LokationHyatt Regency
LandCanada
ByVancouver
Periode08/12/200813/12/2008

ID: 215135290