Selection Criterion for Log-Linear Models Using Statistical Learning Theory

摘要

Log-linear models are a well-established method for describing statisticaldependencies among a set of n random variables. The observed frequencies of then-tuples are explained by a joint probability such that its logarithm is a sumof functions, where each function depends on as few variables as possible. Weobtain for this class a new model selection criterion using nonasymptoticconcepts of statistical learning theory. We calculate the VC dimension for theclass of k-factor log-linear models. In this way we are not only able to selectthe model with the appropriate complexity, but obtain also statements on thereliability of the estimated probability distribution. Furthermore we show thatthe selection of the best model among a set of models with the same complexitycan be written as a convex optimization problem.