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Storage space versus validity of answers in probabilistic question-answering systems

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The trade-offs between the required storage space and the validity of answers produced by probabilistic question-answering (PQA) systems are studies. If the correct answer to a given query is "yes" and the system, instead, issues the estimate that the query has a probability \pi of being true, then the economic loss to the user can be measured by a distortion function that decreases monotonically with \pi . A system will be called elastic if a drastic memory saving may be achieved by tolerating a small level of average distortion. The main result reported is that for a large class of distortion measures (i.e., measures exceeding (1-\pi)^{\alpha } with \alpha > 0) , if a binary QA system (true-false answers) is inelastic then the corresponding probabilistic QA system must also be inelastic. This result implies, for example, that a PQA system that is designed to answer all binary questions on an arbitrary dataset is inelastic. Similarly a PQA system admitting singly conjunctive questions such as "Are both x and y in the dataset?" is also inelastic.

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Information Theory, IEEE Transactions on  (Volume:26 ,  Issue: 6 )