Learning Measurement Models

Ricardo Silva

Abstract

Graphical models such as Bayesian networks and structural equation models are widely used as representations for causal relations. A fundamental issue when expressing causality in graphical models is how to deal with possible hidden common causes. We introduce and evaluate a new principled way of discovering latent causes of set of observed variables under the rather common assumption that all observed variables are continuous linear measures, but never causes, of the underlying latents. In other words, the observed variables define a measurement model of the latents and the learning task can be seen as clustering variables according to their common causes. By carefully choosing which identifiability constraints to assume, the described methodology has the theoretical strength of not requiring knowledge about the number of latents, the distribution of any variable, independence of latents or even if latents are linearly related among themselves. An empirical study with simulated data is performed in order to identify situations where this approach can be robust against effects of sample variability. Joint work with Richard Scheines, Peter Spirtes and Clark Glymour

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