Hints and the VC Dimension

Learning from hints is a generalization of learning from examples that allows for a variety of information about the unknown function to be used in the learning process. In this paper, we use the VC dimension, an established tool for analyzing learning from examples, to analyze learning from hints. In particular, we show how the VC dimension is affected by the introduction of a hint. We also derive a new quantity that defines a VC dimension for the hint itself. This quantity is used to estimate the number of examples needed to "absorb" the hint. We carry out the analysis for two types of hints, invariances and catalysts. We also describe how the same method can be applied to other types of hints.