Information Theoretic Modeling of Dynamical Systems: Estimation and Experimental Design @bullet Free Software Foundation Europe @bullet Free Software Foundation @bullet European Science Foundation

Dynamical systems are mathematical models expressing cause-e ect relations of time-varying phenomena. This thesis focuses on learning dynamical systems from empirical observations. Three settings are considered: unsupervised, supervised, and active learning. The unifying goal is to extract predictive information from data. A method is introduced to cluster time-series and perform model validation. The method addresses order and model selection with the principle of Approximation Set Coding [Buhmann (2010)]. Experimental veri cation is performed in the context of relational clustering of temporal gene expression pro les. The results demonstrate wide applicability and consistency with the Bayesian Information Criterion. Then, discrete dynamic transitions are reconstructed from high-dimensional time-series with an unsupervised approach. The approach, based on Hidden Markov Models over Gaussian Mixtures, is applied to predict cell morphology classes from time-resolved microscopy data. Experimental validation with uorescent markers and screening data demonstrates accurate identi cation of human cell phenotypes. Reported results highlight competitiveness and increased objectivity in comparison to supervised approaches based on user labeling. In the supervised setting, clustering is employed to improve conventional particle ltering for generalized state estimation. Preventive clustering mitigates the inevitable divergence of resampling for sequential Monte Carlo methods. Supervised learning with dynamic