SP500215 Bayesian Inference with Node Aggregation for Information Retrieval chapter B. Del Favero R. Fung National Institute of Standards and Technology D. K. Harman In conjunction with these representational improvements, we would like to design a complete user interface that would allow users to make the needed probabilistic judgements easily and intuitively. We would also like to develop an explanation facility that could describe why one document was preferred over another. There are new exact and inexact algorithms that could handle these representational modifications. We would like to experiment with these algorithms to see if they are suitable. We would also like to implement a relevance feedback mechanism based on the Bayesian concept of equivalent sample size. Finally, while the information retrieval problem has been viewed primarily (and rightly so) as an evidential reasoning problem, we take the position that a decision-theoretic perspective is more accurate since information retrieval is a decision process. We believe that this perspective can provide additional insight and eventually improve upon the probabilistic approaches that have been developed. Acknowledgment We would like the thank Dr. Richard Tong for his assistance and guidance. Appendix Bayesian Inference We calculate the posterior probability that a document is relevant to a state using Bayes' rule and an assumption of conditional independence between the features. The Bayesian inversion formula is this: p(sldocument)=p(s IF) = p(FIs)p(s) p(F) where 5 is the state, and F is a binary feature vector with = 1 if feature i is present (the event fj+) F[OCRerr]= 0 if feature i is absent (the event [OCRerr] The set of all features that are present is denoted F+. All other features are absent and are in the set denoted F-. The first term in the numerator is expanded under the assumption that the features are conditionally independent given the state. p(FIs)= [1 p(ij+ Is) Y' p(Ij Is) iinF+ iinF[OCRerr] The second term in the numerator is the state prior, p( s), which can be estimated as described in Section 3.2. 160 The denominator is a normalization constant obtained by summing over the values for the numerator for all the states. p(F)= [OCRerr] p(FIs)p(s) all 5 p( F) is the probability that one would observe the particular set of features F. References Chang, K. C., & Fung, R. M. (1989). Node Aggregation for Distributed Inference in Bayesian Networks. In IJCAI 89. Detroit: Morgan Kaufmann. Fung, R. M., & Chang, K. C. (1989). Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks. In R. D. S. M. Henrion L.N. Kanal and J.F. Lemmer (Eds.), Uncertainty and Artificial Intelligence 5 Elsevier Science Publishers B.V. (North-Holland). Fung, R. M., Crawford, S. L., Appelbaum, L., & Tong, R. M. (1990). A Probabilistic Concept-based Architecture for Information Retrieval. In Proceedings of the ACM International Conference on Information Retrieval Brussels, Belgium. Heckerman, D. E. (1989). A tractable algorithm for diagnosing multiple diseases. In Proceedings of the Fifth Workshop on Uncertainty in Artificial Intelligence, (pp. 162-173). Detroit, MI. Heckerman, D. E. (1991). Probabilistic Similarity Networks. The MIT Press. Howard, R. A., & Matheson, J. E. (1981). Influence diagrams. In R. A. Howard & J. E. Matheson (Eds.), Readings on the Principles and Applications of Decision Analysis (pp.721-762). Menlo Park, Ca.: Strategic Decisions Group. Lauritzen, S. L., & Spiegelhalter, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems. JRSS[OCRerr] 50, 157-224. Maron, M. E., & Kuhns, J. L. (1960). On relevance, probabilistic indexing and information retrieval. Journal of the ACM, 7, 216-244. Paice, C. D. (1977). Information Retrieval and the Computer. London. Pearl, I. (1988). Probabilistic Reasoning in Intelligent Systems. San Mateo, Ca.: Morgan Kaufman.