PAC learning with generalized samples and an applicaiton to stochastic geometry

An extension of the standard probably approximately correct (PAC) learning model that allows the use of generalized samples is introduced. A generalized sample is viewed as a pair consisting of a functional on the concept class together with the value obtained by the functional operating on the unknown concept. It appears that this model can be applied to a number of problems in signal processing and geometric reconstruction to provide sample size bounds under a PAC criterion. A specific application of the generalized model to a problem of curve reconstruction is considered, and some connections with a result from stochastic geometry are discussed