Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-02-03
Physics
Condensed Matter
Disordered Systems and Neural Networks
14 pages, 3 figures, submitted to Physical Review E
Scientific paper
10.1143/JPSJ.74.2966
Within the framework of on-line learning, we study the generalization error of an ensemble learning machine learning from a linear teacher perceptron. The generalization error achieved by an ensemble of linear perceptrons having homogeneous or inhomogeneous initial weight vectors is precisely calculated at the thermodynamic limit of a large number of input elements and shows rich behavior. Our main findings are as follows. For learning with homogeneous initial weight vectors, the generalization error using an infinite number of linear student perceptrons is equal to only half that of a single linear perceptron, and converges with that of the infinite case with O(1/K) for a finite number of K linear perceptrons. For learning with inhomogeneous initial weight vectors, it is advantageous to use an approach of weighted averaging over the output of the linear perceptrons, and we show the conditions under which the optimal weights are constant during the learning process. The optimal weights depend on only correlation of the initial weight vectors.
Hara Kazuyuki
Okada Masato
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