Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Half-Trek Criterion for Identifiability of Latent Variable Models   We consider linear structural equation models with latent variables and
develop a criterion to certify whether the direct causal effects between the
observable variables are identifiable based on the observed covariance matrix.
Linear structural equation models assume that both observed and latent
variables solve a linear equation system featuring stochastic noise terms. Each
model corresponds to a directed graph whose edges represent the direct effects
that appear as coefficients in the equation system. Prior research has
developed a variety of methods to decide identifiability of direct effects in a
latent projection framework, in which the confounding effects of the latent
variables are represented by correlation among noise terms. This approach is
effective when the confounding is sparse and effects only small subsets of the
observed variables. In contrast, the new latent-factor half-trek criterion
(LF-HTC) we develop in this paper operates on the original unprojected latent
variable model and is able to certify identifiability in settings, where some
latent variables may also have dense effects on many or even all of the
observables. Our LF-HTC is an effective sufficient criterion for rational
identifiability, under which the direct effects can be uniquely recovered as
rational functions of the joint covariance matrix of the observed random
variables. When restricting the search steps in the LF-HTC to consider subsets
of latent variables of bounded size, the criterion can be verified in time that
is polynomial in the size of the graph.

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The categories of this paper are: cs
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
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The categories of this paper are: physics
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga