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Various regularization techniques are investigated in supervised learning from data. Theoretical features of the associated optimization problems are studied, and sparse suboptimal solutions are searched for. Rates of approximate optimization are estimated for sequences of suboptimal solutions formed by linear combinations of n-tuples of computational… (More)

Approximation properties of some connectionistic models, commonly used to construct approximation schemes for optimization problems with multivariable functions as admissible solutions, are investigated. Such models are made up of linear combinations of computational units with adjustable parameters. The relationship between model complexity (number of… (More)

Kernel machines traditionally arise from an elegant formulation based on measuring the smoothness of the admissible solutions by the norm in the reproducing kernel Hilbert space (RKHS) generated by the chosen kernel. It was pointed out that they can be formulated in a related functional framework, in which the Green's function of suitable differential… (More)

Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being… (More)

—Two criteria are proposed to characterize and improve suboptimal coordinate-convex (c.c.) policies in Call Admission Control (CAC) problems with nonlinearly-constrained feasibility regions. Then, a structural property of the optimal c.c. policies is derived. This is expressed in terms of constraints on the relative positions of successive corner points.

— In the " consensus problem " on multi-agent systems , in which the states of the agents are " opinions " , the agents aim at reaching a common opinion (or " consensus state ") through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems so as to achieve a good trade-off between a small… (More)

Approximation capabilities of two types of computational models are explored: dictionary-based models (i.e., linear combinations of n-tuples of basis functions computable by units belonging to a set called "dictionary") and linear ones (i.e., linear combinations of n fixed basis functions). The two models are compared in terms of approximation rates, i.e.,… (More)

Keywords: Supervised learning Kernel machines Propositional rules Variational calculus Infinite-dimensional optimization Representer theorems a b s t r a c t Supervised learning is investigated, when the data are represented not only by labeled points but also labeled regions of the input space. In the limit case, such regions degenerate to single points… (More)