Sample-based estimators for the instrinsically multivariate prediction score

Canalizing genes possess broad regulatory power over gene regulatory networks. In a previous publication, the concept of intrinsically multivariate predictive (IMP) genes was introduced and analyzed in the context of stochastic logic models. Furthermore, based on an empirical study of the DUSP gene, a canalizing gene in melanoma, it was hypothesized that canalizing genes possess IMP properties. In this paper, we study the problem of sample-based estimation of a gene IMP score. We study nonparametric IMP score estimators based on resubstitution, leave-one-out, cross-validation, and bootstrap, and introduce a maximum-likelihood IMP score estimator for a many-input stochastic logic model. Assuming a two-input, three-input and four-input stochastic AND model, performance metrics of these estimators are calculated by Monte Carlo sampling. Our results show that the ML IMP score estimator outperforms the other estimators in RMS, under the assumed stochastic logic model. It is followed by the resubstitution IMP score estimator. This indicates that, provided one has information about regulatory relationships in the network, the ML IMP score estimator is the estimator of choice, whereas resubstitution is to be preferred in the absence of prior knowledge.