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The degree of approximation of infinite-dimensional function classes using finite n -dimensional manifolds has been the subject of a classical field of study in the area of mathematical approximation theory. In Ratsaby and Maiorov (1997), a new quantity ρ n ( F , L q ) which measures the degree...
The classical binary classification problem is investigated when it is known in advance that the posterior probability function (or regression function) belongs to some class of functions. We introduce and analyze methods which effectively exploit this knowledge. These methods are based on...
We define embeddings between concept classes that are meant to reflect certain aspects of their combinatorial structure. Furthermore, we introduce a notion of universal concept classes - classes into which any member of a given family of classes can be embedded. These universal classes play a...
Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in particular when time is a relevant parameter. This paper provides lower and upper bounds for the VC...
We show a natural graph-theoretic generalization of the Sauer-Shelah lemma. This result is applied to bound the ℓ ∞ and L 1 packing numbers of classes of functions whose range is an arbitrary, totally bounded metric space.
We consider the class M of monotonically increasing binary output functions. M has considerable practical significance in machine learning and pattern recognition because prior information often suggests a monotonic relationship between input and output variables. The decision boundaries of...
Using standard methods from empirical-process theory, in particular symmetrization, we derive exponential bounds on the fluctuations of stochastic processes which may be represented as the averages of many small functions. As examples, self-service queueing and storage problems are analyzed. We...
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