Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Maximum Likelihood Threshold of a Path Diagram   Linear structural equation models postulate noisy linear relationships
between variables of interest. Each model corresponds to a path diagram, which
is a mixed graph with directed edges that encode the domains of the linear
functions and bidirected edges that indicate possible correlations among noise
terms. Using this graphical representation, we determine the maximum likelihood
threshold, that is, the minimum sample size at which the likelihood function of
a Gaussian structural equation model is almost surely bounded. Our result
allows the model to have feedback loops and is based on decomposing the path
diagram with respect to the connected components of its bidirected part. We
also prove that if the sample size is below the threshold, then the likelihood
function is almost surely unbounded. Our work clarifies, in particular, that
standard likelihood inference is applicable to sparse high-dimensional models
even if they feature feedback loops.

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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci