1,721,209 research outputs found
Regularization and A-Priori Bounds on Complexity in Learning from Data by Kernel Methods
No full text
Model complexities of shallow neural networks for the approximation of input-output mappings with large variations
No full textInput-output stability for optimal estimation problems
No full textOptimal estimation problems for a class of dynamic systems described
by nonlinear differential equations are considered under the effect
of disturbances. The estimator is a Luenberger observer that depends
on an innovation function to be suitably chosen. The optimality criterion is taken as the norm of the estimation error in a function space and is expressed by means of a cost functional dependent on the innovation function. The well-definiteness of such a functional can be guaranteed via a Lyapunov approach and in terms of input-output stability of mappings between function spaces, where the disturbances are the input and the estimation error is the output. In particular, Lp and Sobolev optimality criteria are adopted. In these cases, relationships between internal (asymptotic and exponential) stability and input-output stability are studied and upper bounds on the estimation error are given. The bounds are illustrated by an example and a converse result is presented. In summary, the paper provides conditions for the well-definiteness of a class of optimal estimation problems and represents departure point to develop efficient solution methodologies
Approximate Minimization of the Regularized Expected Error Over Kernel Models
No full textLearning from data under constraints on model complexity is studied in terms of rates of approximate minimization of the
regularized expected error functional. For kernel models with an increasing number n of kernel functions, upper bounds on
such rates are derived. The bounds are of the form a/n+b/
√
n, where a and b depend on the regularization parameter and
on properties of the kernel, and of the probability measure defining the expected error. As a special case, estimates of rates of approximate minimization of the regularized empirical error are derived
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