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In this paper we study the identification of sparse interaction networks as a machine learning problem. Sparsity mean that we are provided with a small data set and a high number of unknown components of the system, most of which are zero. Under these circumstances, a model needs to be learned that fits the underlying system, capable of generalization. This corresponds to the student-teacher setting in machine learning. In the first part of this paper we introduce a learning algorithm, based on L1-minimization, to identify interaction networks from poor data and analyze its dynamics with respect to phase transitions. The efficiency of the algorithm is measured by the generalization error, which represents the probability that the student is a good fit to the teacher. In the second part of this paper we show that from a system with a specific system size value the generalization error of other system sizes can be estimated. A comparison with a set of simulation experiments show a very good fit. [ABSTRACT FROM AUTHOR]

In this study we will focus on piecewise linear state space models for gene-protein interaction networks. We will follow the dynamical systems approach with special interest for partitioned state spaces. From the observation that the dynamics in natural systems tends to punctuated equilibria, we will focus on piecewise linear models and sparse and hierarchic interactions, as, for instance, described by Glass, Kauffman, and de Jong. Next, the paper is concerned with the identification (also known as reverse engineering and reconstruction) of dynamic genetic networks from microarray data. We will describe exact and robust methods for computing the interaction matrix in the special case of piecewise linear models with sparse and hierarchic interactions from partial observations. Finally, we will analyze and evaluate this approach with regard to its performance and robustness towards intrinsic and extrinsic noise. [ABSTRACT FROM AUTHOR]