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2019

Algebraic Properties of Gaussian HTC-identifiable Graphs

Yao, Bohao, Evans, Robin

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In this paper, we explore some algebraic properties of linear structural equation modelsthat can be represented by an HTC-identifiable graph.

In particular, we prove that all mixedgraphs are HTC-identifiable if and only if all the regression coefficients can be recovered fromthe covariance matrix using straightforward linear algebra operations.
We also find a set ofpolynomials that generates the ideal that encompasses all the equality constraints of the modelon the cone of positive definite matrices.
We further prove that this set of polynomials are theminimal generators of said ideal for a subset of HTC-identifiable graphs.

Algebraic Properties of Gaussian HTC-identifiable Graphs · Around

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The method of path coefficients
Original
S. Wright · 1911
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Structural equations with latent variables
K. A. Bollen · 1989
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Identifying independence in bayesian networks
D. Geiger, T. Verma, and J. Pearl · 1990
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Equivalence and synthesis of causal models
T. Verma and J. Pearl · 1990
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Causation, Prediction, and Search
P. Spirtes, C. N. Glymour, and R. Scheines · 1993
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