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Bounds on memory versus error trade-offs in question-answering systems

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A question-answering (QA) system answers queries from a given set about data sets drawn from a given ensemble. Shannon's rate-distortion function R(D) provides the minimum amount of memory that a QA system must employ in order to achieve an average distortion less than D (the distortion can, for example, be the average proportion of erroneous answers produced by the system). The ability of a system to convert an amount D of distortion into a saving in memory is measured by the ratio R(D)/R(0) . A system will be called elastic if this ratio goes to zero as M , the size of the data set ensemble, tends to infinity. The asymptotic bounds to R(D) are derived, giving rise to elasticity conditions which involve only general system parameters.

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Information Theory, IEEE Transactions on  (Volume:25 ,  Issue: 2 )