We develop an approach utilizing randomized genotypes to rigorously infer causal regulatory relationships among genes at the transcriptional level. Based on experiments where large-scale genotyping and expression profiling are performed, we calculate the probability that a given gene has a regulatory effect on each other gene, for all pairs of genes. These probabilities can be used to build transcriptional regulatory networks and to identify putative regulators of genes, providing direct detection of the genes inducing variation in these ``expression traits.'' Since the method is based on randomized variables (genotypes), it avoids the usual pitfalls of correlation and model-selection based construction of networks. We apply the method to an experiment in yeast, where genes known to be in the same processes and functions are recovered in the resulting transcriptional regulatory network. We estimate a lower bound on the total number of regulatory relationships, yielding new insights into the topology of the yeast transcriptional regulatory network.
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