How to Implement A Priori Information: A Statistical Mechanics Approach

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dc.creatorLemm, Joerg C.
dc.date1998-08-04
dc.date1998-12-14
dc.date.accessioned2026-07-07T03:11:14Z
dc.date.available2026-07-07T03:11:14Z
dc.descriptionA new general framework is presented for implementing complex a priori knowledge, having in mind especially situations where the number of available training data is small compared to the complexity of the learning task. A priori information is hereby decomposed into simple components represented by quadratic building blocks (quadratic concepts) which are then combined by conjunctions and disjunctions to built more complex, problem specific error functionals. While conjunction of quadratic concepts leads to classical quadratic regularization functionals, disjunctions, representing ambiguous priors, result in non--convex error functionals. These go beyond classical quadratic regularization approaches and correspond, in Bayesian interpretation, to non--gaussian processes. Numerical examples show that the resulting stationarity equations, despite being in general nonlinear, inhomogeneous (integro--)differential equations, are not necessarily difficult to solve. Appendix A relates the formalism of statistical mechanics to statistics and Appendix B describes the framework of Bayesian decision theory.
dc.description88 pages, 9 figures (enlarged version)
dc.identifierhttps://arxiv.org/abs/cond-mat/9808039
dc.identifierhttp://arxiv.org/abs/cond-mat/9808039
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/28495
dc.subjectDisordered Systems and Neural Networks
dc.subjectAdaptation and Self-Organizing Systems
dc.subjectStatistical Mechanics
dc.titleHow to Implement A Priori Information: A Statistical Mechanics Approach
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