Maximum entropy inference and stimulus generalization

Maximum entropy inference is a method for estimating a probability distribution based on limited information expressed in terms of the moments of that distribution. This paper presents such a maximum entropy characterization of Shepard's theory of generalization. Shepard's theory assumes that an object has an important consequence for an individual only if it falls in a connected set, called the consequential region, in the individual's representational space. The assumption yields a generalization probability that decays exponentially with an appropriate psychological distance metric-either the city-block or the Euclidean, depending on the correlational structure between extensions of the consequential region along the dimensions. In this note we show that a generalization function similar to that derived by Shepard (1987) can be obtained by applying maximum entropy inference on limited information about interstimulus distances between two objects having a common consequence. In particular, we show that different shapes of equal generalization contours may be interpreted as optimal utilization-in the maximum entropy sense-of the correlation structure of stimulus dimensions, similar to the explanation by Shepard's theory. (C) 1996 Academic Press