Identification of non-linear system structure and parameters using regime decomposition
Automatica (Journal of IFAC)
Nonlinear black-box modeling in system identification: a unified overview
Automatica (Journal of IFAC) - Special issue on trends in system identification
Nonlinear black-box models in system identification: mathematical foundations
Automatica (Journal of IFAC) - Special issue on trends in system identification
Prediction with Gaussian processes: from linear regression to linear prediction and beyond
Learning in graphical models
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
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This paper investigates new ways of inferring nonlinear dependence from measured data. The existence of unique linear and nonlinear sub-spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub-spaces are derived. The importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task. Specifically, once the linear/nonlinear sub-spaces are known, by definition the explanatory variables may be transformed to form two disjoint sub-sets spanning, respectively, the linear and nonlinear sub-spaces. The nonlinear modelling task is confined to the latter sub-set, which will typically have a smaller number of elements than the original set of explanatory variables. Constructive algorithms are proposed for inferring the linear and nonlinear sub-spaces from noisy data.