STATISTICAL-MECHANICS OF HYPOTHESIS EVALUATION

Following ideas of Gull, Skilling and MacKay, we develop and explore a statistical-mechanics framework through which one may assign values t o the parameters of a model for a 'rule' (instanced, here, by the nois y linear perceptron), on the basis of data instancing the rule. The 'e vidence' which the data offers in support of a given assignment, is li kened to the free energy of a system with quenched variables (the data ): the most probable (MAP) assignments of parameters are those which m inimize this free-energy; tracking the free-energy minimum may lead to 'phase transitions' in the preferred assignments. We explore the exte nt to which the MAP assignments lead to optimal performance.