Generating a comprehensive map of molecular interactions in living cells is difficult and great efforts are undertaken to infer molecular interactions from large-scale perturbation experiments. Here, we develop the analytical and numerical tools to quantify the fundamental limits for inferring transcriptional networks from gene knockout screens and introduce a network inference method that is unbiased with respect to measurement noise and scalable to large network sizes. We show that network asymmetry, knockout coverage and measurement noise are central determinants that limit prediction accuracy, whereas the knowledge about gene-specific variability among biological replicates can be used to eliminate noise-sensitive nodes and thereby boost the performance of network inference algorithms.