Combining expert knowledge with data based on belief function theory: an application in waste water treatment

This paper presents a methodology for combining expert knowledge with information from statistical data, in classification and prediction problems. The method is based on (1) a case-based approach allowing to predict a quantity of interest from past cases in the form of a belief function, (2) Bayesian networks for modelling expert knowledge and (3) a tuning mechanism allowing to optimally discount information sources by optimizing a performance criterion. This methodology is applied to the prediction of chemical oxygen demand solubility in wastewater. The approach is expected to be useful in situations where both small databases and partial expert knowledge are available.

[1]  Khaled Mellouli,et al.  The Evaluation of Sensors' Reliability and Their Tuning for Multisensor Data Fusion within the Transferable Belief Model , 2001, ECSQARU.

[2]  Silja Renooij,et al.  Probabilities for a probabilistic network: a case study in oesophageal cancer , 2002, Artif. Intell. Medicine.

[3]  Eugene Charniak,et al.  Bayesian Networks without Tears , 1991, AI Mag..

[4]  Marek J. Druzdzel,et al.  Knowledge Engineering for Very Large Decision-analytic Medical Models , 1999, AMIA.

[5]  Philippe Smets,et al.  The Transferable Belief Model , 1994, Artif. Intell..

[6]  Michael P. Wellman.  Fundamental Concepts of Qualitative Probabilistic Networks , 1990, Artif. Intell..

[7]  Marek J. Druzdzel,et al.  Building Probabilistic Networks: "Where Do the Numbers Come From?" Guest Editors Introduction , 2000, IEEE Trans. Knowl. Data Eng..

[8]  Thierry Denoeux,et al.  An evidence-theoretic k-NN rule with parameter optimization , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[9]  Philippe Smets,et al.  The transferable belief model and random sets , 1992, Int. J. Intell. Syst..

[10]  L. C. van der Gaag,et al.  Probabilities for a Probabilistic Network : A Case-study in Oesophageal Carcinoma , 2001 .

[11]  Marek J. Druzdzel,et al.  GeNIe: A Development Environment for Graphical Decision-Analytic Models , 1999, AMIA.

[12]  Thierry Denoeux,et al.  A k-nearest neighbor classification rule based on Dempster-Shafer theory , 1995, IEEE Trans. Syst. Man Cybern..

[13]  Silja Renooij,et al.  Talking probabilities: communicating probabilistic information with words and numbers , 1999, Int. J. Approx. Reason..

[14]  Thierry Denoeux,et al.  Handling possibilistic labels in pattern classification using evidential reasoning , 2001, Fuzzy Sets Syst..

[15]  Max Henrion,et al.  Some Practical Issues in Constructing Belief Networks , 1987, UAI.

[16]  Marek J. Druzdzel,et al.  Learning Bayesian network parameters from small data sets: application of Noisy-OR gates , 2001, Int. J. Approx. Reason..

[17]  L. C. van der Gaag,et al.  Building probabilistic networks: Where do the numbers come from? - a guide to the literature , 2000 .