Abstract
Latent variables represent unmeasured causal factors. Some, such as intelligence, cannot be directly measured; others may be, but we do not know about them or know how to measure them when making our observations. Regardless, in many cases, the influence of latent variables is real and important, and optimal modeling cannot be done without them. However, in many of those cases the influence of latent variables reveals itself in patterns of measured dependency that cannot be reproduced using the observed variables alone, under the assumptions of the causal Markov property and faithfulness. In such cases, latent variables may be posited to the advantage of the causal discovery process. All latent variable discovery takes advantage of this; we make the process explicit.
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- 1.
Indeed, Friedman applied SEM to the problem of latent variable discovery as well. Our empirical results here don’t include SEM due to time constraints after some initial difficulty in obtaining SEM code.
- 2.
Note that we will indifferently refer to the causal models that generate these dependency patterns triggers as well.
- 3.
Note that these restrictions imply, for example, that we would not be finding any such latent variable model as that in Fig. 1. However, these restrictions apply only to our search for useful triggers and their models; subsequent search through the latent variable model space can find these models, as Friedman’s work [5] demonstrates.
- 4.
The datasets are available at: https://sourceforge.net/projects/triggers-of-bn-latent- variable/.
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Zhang, X., Korb, K.B., Nicholson, A.E., Mascaro, S. (2017). Applying Dependency Patterns in Causal Discovery of Latent Variable Models. In: Wagner, M., Li, X., Hendtlass, T. (eds) Artificial Life and Computational Intelligence. ACALCI 2017. Lecture Notes in Computer Science(), vol 10142. Springer, Cham. https://doi.org/10.1007/978-3-319-51691-2_12
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