Bayesian test of significance for conditional independence: The multinomial model
This work addresses the need for robust conditional independence tests in machine learning, particularly for structure learning in probabilistic graphical models, but it appears incremental as it adapts an existing Bayesian test to a specific domain.
The paper tackles the problem of testing conditional independence in discrete datasets by proposing the Full Bayesian Significance Test (FBST) as a Bayesian alternative to frequentist p-value methods, with a focus on applications in probabilistic graphical models like Bayesian Networks.
Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Networks (BN) models--CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Significance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist's significance tests (characterized by the calculation of the \emph{p-value}).