We discuss a problem of selecting active predictors for the response with no parametric assumptions on their joint dependence. We show that two popular information-based selection criteria which are both derived as approximations of Conditional Mutual Information CMI may exhibit different behaviour in Generative Tree Models resulting in different orders in which predictors are chosen in variable selection process. We also show that in certain situations Positive Selection Rate of one of the approximations, a popular selection method Conditional Infomax Feature Extraction (CIFE) may become arbitrarily small. Explicit formulae for CMI and its two approximations in the generative tree model are obtained. As a by product, we establish expressions for entropy of a multivariate gaussian mixture and its mutual information with mixing distribution.