Learning Associations by Discrete Measurement Models

Discovering interesting associations in discrete databases is a key task in data mining. Association rules and graphical models among observed variables are standard tools in this analysis, but in problems where associations are due to hidden common causes not recorded in the database, the resulting models are overly complex and offer no picture of the causes of such dependencies. For instance, the pattern of answers in a large marketing survey might be explained by a few latent traits of the population. A large set of association rules might offer little insight on this process. Instead, one can model the observed variables as measurements of latent concepts, such as in discrete principal component analysis. However, discrete PCA and its variations rely on the assumption that latents are independent. While such an assumption might be reasonable in, e.g., black box models for classification, it makes little sense if the goal is understanding the real causes for the associations. We present in this paper a method for finding hidden common causes that explain observed associations of subsets of the given variables without imposing independence constraints over latents. Variables should be binary or ordinal.