Just: Data requirements Data requirements of reverse-engineering algorithms

Data sets used in reverse-engineering of biochemical networks contain usually relatively few high-dimensional data points, which makes the problem in general vastly underdetermined. It is therefore important to estimate the probability that a given algorithm will return a model of acceptable quality when run on a data set of small size but high dimension. We propose a mathematical framework for investigating such questions. We then demonstrate that without assuming any prior biological knowledge, in general no theoretical distinction between the performance of different algorithms can be made. We also give an example of how expected algorithm performance can in principle be altered by utilizing certain features of the data collection protocol. We conclude with some examples of theorems that were proven within the proposed framework.