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Optimum Probability Estimation from Empirical Distributions
 Information Processing and Management
, 1989
"... Probability estimation is important for the application of probabilistic models as well as for any evaluation in IR. We discuss the interdependencies between parameter estimation and certain properties of probabilistic models: dependence assumptions, binary vs. nonbinary features, estimation sample ..."
Abstract

Cited by 7 (4 self)
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Probability estimation is important for the application of probabilistic models as well as for any evaluation in IR. We discuss the interdependencies between parameter estimation and certain properties of probabilistic models: dependence assumptions, binary vs. nonbinary features, estimation sample selection. Then we define an optimum estimate for binary features which can be applied to various typical estimation problems in IR. A method for computing this estimate using empirical data is described. Some experiments show the applicability of our method, whereas comparable approaches are partially based on false assumptions or yield biased estimates. 1 Parameter estimation in IR In IR the development of theoretical models and their evaluation in experiments is of equal importance: A model which cannot be evaluated (applied) is of very little use, while an evaluation can show its weaknesses and strengths and give evidence for further developments. As will be discussed below, any evaluation in IR involves some kind of parameter estimation, even for nonprobabilistic models. So it is interesting to note that the problem of parameter estimation has been discussed only by a few authors ( [Rijsbergen 77], [Robertson & Bovey 82], [Bookstein 83], [?]). In this paper, an attempt is