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Statistical Theory of Learning Curves
"... Behaviors of a learning machine depends on its complexity and the number of training examples. A learning curve shows how fast a neural network or a general learning machine can improve its behavior as the number of training examples increases. This is also related to the complexity of a learning ma ..."
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Behaviors of a learning machine depends on its complexity and the number of training examples. A learning curve shows how fast a neural network or a general learning machine can improve its behavior as the number of training examples increases. This is also related to the complexity of a learning machine. The characteristic of the learning curve is studied from the statisticalmechanical, information theoretic and statistical points of view. The present paper summarizes universal as well as specific properties of learning curves of both deterministic and stochastic pattern classifiers from the statistical point of view. 1 Introduction Learning is an important subject of research studied by various methods of approach such as algorithm theory, stochastic gradient method, statistical mechanics, information theory, statistics, etc. Statistical mechanics and information theory have proved its wide applicability in the field of machine learning. The present paper intends to elucidate the ch...
On the Vapnik–Chervonenkis dimension of the Ising perceptron
, 1996
"... The Vapnik–Chervonenkis (VC) dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N � 31. It is significantly larger than 1 2 N. The data suggest that there is probably no welldefined asymptotic behaviour for N →∞. ..."
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The Vapnik–Chervonenkis (VC) dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N � 31. It is significantly larger than 1 2 N. The data suggest that there is probably no welldefined asymptotic behaviour for N →∞.