Chapter 4: Nonlinear signal modelling and structure selection with applications to genomics

Modeling is a prerequisite for the most fundamental signal processing tasks of signal analysis, detection, classification, denoising, and compression. While linear models are widely used, and they allow elegant theoretical and algorithmic developments, their nonlinear alternatives offer advantages in terms of modeling power and improved performance, which often eclipse the extra cost due to increased complexity. In this chapter we discuss nonlinear signal modeling with two main goals. The first is to present several examples of nonlinear models arising naturally in processing genomic data. The second is to discuss methods for evaluating the complexity of these nonlinear models with information theoretic methods. Several signal processing methods are useful for processing genomic data. Microarray data come originally in the form of microarray images, which need to be preprocessed (denoised and segmented) before the quantities of interest, the gene expression ratios, are estimated from the image. All these stages benefit greatly from nonlinear techniques. The stages involving statistical inference on the gene expression values, can also be formulated as optimal design problems for the structure and the parameters of certain nonlinear predictors. In this chapter we investigate