Technical Report CIS9715

Title: Partial Classification: The Benefit of Deferred Decision
Authors: Yoram Baram
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Abstract: It is shown that partial classification, which allows for indecision in certain domains of the data space, can increase a benifit function, defined as the difference between the probabilities of correct and incorrect decisions, joint with the event that a decision is made. This is particularly true for small data samples, which may cause a large deviations of the estimated separations surface from the intersection surface between the corresponding probability density functions. A density estimation method, based on maximizing the mutual information across a system of integrated Gaussians, is shown to yield a direct estimate of the density intersection surface, based on the first and second moments of the data. An indecision domain is naturally defined by a single parameter, whose optimal size, maximizing the benefit function, is derived from the data. The benefit function is shown to translate into profit in stock trading. Employing medical and economic data, it is shown that partial classification producers, on average, higher benefit values than full classification, assigning each new object to a class, and that the marginal benefit of partial classification reduces without vanishing, as the data size increases.
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