Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic tests of general Gaussian latent tree models   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.

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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg