Exact and near compatibility of discrete conditional distributions
Computational Statistics & Data Analysis
Dependency networks for inference, collaborative filtering, and data visualization
The Journal of Machine Learning Research
Compatibility of discrete conditional distributions with structural zeros
Journal of Multivariate Analysis
Probabilistic self-organizing maps for qualitative data
Neural Networks
Gibbs ensembles for nearly compatible and incompatible conditional models
Computational Statistics & Data Analysis
A simple algorithm for checking compatibility among discrete conditional distributions
Computational Statistics & Data Analysis
On compatibility of discrete full conditional distributions: A graphical representation approach
Journal of Multivariate Analysis
Compatibility results for conditional distributions
Journal of Multivariate Analysis
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Most work on conditionally specified distributions has focused on approaches that operate on the probability space, and the constraints on the probability space often make the study of their properties challenging. We propose decomposing both the joint and conditional discrete distributions into characterizing sets of canonical interactions, and we prove that certain interactions of a joint distribution are shared with its conditional distributions. This invariance opens the door for checking the compatibility between conditional distributions involving the same set of variables. We formulate necessary and sufficient conditions for the existence and uniqueness of discrete conditional models, and we show how a joint distribution can be easily computed from the pool of interactions collected from the conditional distributions. Hence, the methods can be used to calculate the exact distribution of a Gibbs sampler. Furthermore, issues such as how near compatibility can be reconciled are also discussed. Using mixed parametrization, we show that the proposed approach is based on the canonical parameters, while the conventional approaches are based on the mean parameters. Our advantage is partly due to the invariance that holds only for the canonical parameters.