When do Numbers Really Matter?

Common wisdom has it that small distinctions in the probabilities quantifying a belief network do not matter much for the results of probabilistic queries. Yet, one can develop realistic scenarios under which small variations in network probabilities can lead to significant changes in computed queries. A pending theoretical question is then to analytically characterize parameter changes that do or do not matter. In this paper, we study the sensitivity of probabilistic queries to changes in network parameters and prove some tight bounds on the impact that such parameters can have on queries. Our analytical results pinpoint some interesting situations under which parameter changes do or do not matter. These results are important for knowledge engineers as they help them identify influential network parameters. They also help explain some of the previous experimental results and observations with regards to network robustness against parameter changes.

[1]  Adnan Darwiche,et al.  A differential approach to inference in Bayesian networks , 2000, JACM.

[2]  Niels Peek,et al.  Using sensitivity analysis for efficient quantification of a belief network , 1999, Artif. Intell. Medicine.

[3]  Linda C. van der Gaag,et al.  Making Sensitivity Analysis Computationally Efficient , 2000, UAI.

[4]  Silja Renooij,et al.  Analysing Sensitivity Data from Probabilistic Networks , 2001, UAI.

[5]  Enrique F. Castillo,et al.  Sensitivity analysis in discrete Bayesian networks , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[6]  Finn Verner Jensen,et al.  Gradient Descent Training of Bayesian Networks , 1999, ESCQARU.

[7]  Kathryn B. Laskey.  Sensitivity analysis for probability assessments in Bayesian networks , 1995, IEEE Trans. Syst. Man Cybern..

[8]  David Poole,et al.  Context-specific approximation in probabilistic inference , 1998, UAI.

[9]  Stuart J. Russell,et al.  Local Learning in Probabilistic Networks with Hidden Variables , 1995, IJCAI.

[10]  Dale Schuurmans,et al.  Learning Bayesian Nets that Perform Well , 1997, UAI.

[11]  Gregory M. Provan,et al.  The Sensitivity of Belief Networks to Imprecise Probabilities: An Experimental Investigation , 1996, Artif. Intell..

[12]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[13]  Finn V. Jensen,et al.  Bayesian Networks and Decision Graphs , 2001, Statistics for Engineering and Information Science.

[14]  Finn Verner Jensen,et al.  Introduction to Bayesian Networks , 2008, Innovations in Bayesian Networks.