Regularization and Noise Injection for Improving Genetic Network Models

The most fundamental problem in genetic network modeling is generally known as the dimensionality problem. Typical time-course gene expression data sets contain measurements of thousands of genes taken over fewer than twenty time-steps. A large dynamic network cannot be learned from data with such a limited number of time-steps without the use of additional constraints, preferably derived from biological knowledge. In this chapter, we present an approach that can nd rough estimates of the underlying genetic network based on limited time-course gene expression data by employing the fact that gene expression measurements are relatively noisy and genetic networks are thought to be robust. The method expands the data set by adding noisy duplicates, thereby simultaneously tackling the dimensionality problem and making the solutions more robust against (the already large) noise in the data. For linear models, this concept is strongly related to shrinkage methods, such as ridge regression and lasso regression, and in the limiting case equivalent to the Moore-Penrose pseudoinverse. The strength of the proposed concept of noise injection lies, however, in the fact that it can be employed to any modelling approach, including non-linear models.