Playing Billiard in Version Space

Details Playing Billiard in Version Space Playing Billiard in Version Space

1995-08-29

arxiv.org/abs/cond-mat/9508130v1

Physics

Condensed Matter

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Scientific paper

A ray-tracing method inspired by ergodic billiards is used to estimate the theoretically best decision rule for a set of linear separable examples. While the Bayes-optimum requires a majority decision over all Perceptrons separating the example set, the problem considered here corresponds to finding the single Perceptron with best average generalization probability. For randomly distributed examples the billiard estimate agrees with known analytic results. In real-life classification problems the generalization error is consistently reduced compared to the maximal stability Perceptron.

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