Algebraic statistics in model selection
Luis David García Puente · Uncertainty in Artificial Intelligence · 2004
We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics. We present an algebra-statistics dictionary focused on statistical modeling. In particular, we link the notion of effective dimension of a Bayesian network with the notion of algebraic dimension of a variety. We also obtain the independence and non-independence constraints on the distributions over the observable variables implied by a Bayesian network with hidden variables, via a generating set of an ideal of polynomials associated to the network. These results extend previous work on the subject. Finally, the relevance of these results for model selection is discussed.