Model validation for gene selection and regulation maps

Consider the problem of investigating the structure of a set of sample points in a very high dimensional (Euclidean) space. This case is paradigmatic, for instance, in postgenomic applications. The high dimensionality and small sample size make statistical inference and optimization difficult problems, such that selecting a model or choosing a learning algorithm face the evidence that currently no consensus guidelines exist. Usually, the intervention of linear or nonlinear projection method is required to map the observations into a low-dimensional space with the most salient data features preserved. This step usually involves computing statistics from the low-dimensional projected space of features and then inferring on the highly dimensional original structures (the genes). This work deals with model validation for gene selection and regulation dynamics. The analysis is conducted through a mix of quantitative methods and qualitative aspects. A regularized inference approach is employed based on dimensionality reduction, data denoising, and feature extraction tasks. Each task requires the implementation of statistics and machine learning algorithms. We focus on the complex problem of inferring the coregulation from the coexpression gene dynamics in the presence of limited biological information and time course perturbation experiments. In particular, both separation and interference gene dynamics are considered and validated to design the most coherent underlying transcriptional regulatory map.