Learning the Structure of Linear Latent Variable Models

  • Authors:
  • Ricardo Silva;Richard Scheines;Clark Glymour;Peter Spirtes

  • Affiliations:
  • -;-;-;-

  • Venue:
  • The Journal of Machine Learning Research
  • Year:
  • 2006

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Abstract

We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems.