The Chooser

The chooser procedure takes as its input the L hypothetical equiprobable networks generated by the predictor. Its goal is to choose a new perturbation p, from a set of allowed perturbations P, which best discriminates between the L hypothetical networks. The following entropy-based algorithm is used for the chooser:

1.

For each perturbation $p \in P$ compute the network state resulting from p for each of the L networks. A given perturbation would result in a total of S distinct states over the L networks $(1 \leq S \leq L)$. Evaluate the following entropy score H_p, where l_s is the number of networks giving the state s $(1 \leq s \leq S)$, as follows:

$$H_p = -\Sigma_{s=1}^S \frac{l_s}{L} log_{2}(\frac{l_s}{L})$$ (1)

2.

Choose the perturbation p with the maximum score H_p as the next experiment.

The entropy measure H_p describes expected gain in information when performing the perturbation p. The more distinct states the networks produce, the more information is obtained. According to the predictor procedure, a network may have the "*" symbol in its truth table, meaning that any function value is equally probably for a given node and input. In this case the chooser randomly assigns either 0 or 1 to to replace the "*". In addition, when L is large, it may be infeasible to calculate the entropy for all the hypothetical networks. In this case the entropy is calculate by Monte-Carlo procedure, over a random sample. The best perturbation returned by the chooser is then performed on the network, and the new measured gene expression values are added to E. A new, narrower set of parsimonious networks is then inferred by the predictor, and so on. This design process proceeds iteratively, choosing a new perturbation experiment in each iteration, until either a single parsimonious network remains (L = 1), or no perturbation in P can discriminate between any of the L networks (H_p = 0).