To what extent is learnability impeded when information is missing in learning instances? We present relevant known results and concrete open problems, in the context of a natural extension of the PAC learning model that accounts for arbitrarily missing information.

Previous results on nonlearnability of visual concepts relied on the assumption that such concepts are represented as sets of pixels [l]. This correspondence uses an approach developed by Haussler [2] to show that under an alternative, feature-based representation, recognition is PAC learnable from a feasible number of examples in a distribution-free manner.

We introduce and study the notions of a PAC substructure of a stable structure, and a bounded substructure of an arbitrary substructure, generalizing [8]. We give precise definitions and equivalences, saying what it means for properties such as PAC to be first order, study some examples (such as differentially closed fields) in detail, relate the material to generic automorphisms, and generaliz...