Sensitivity Analysis in Bayesian Networks: From Single to Multiple Parameters

Previous work on sensitivity analysis in Bayesian networks has focused on single parameters, where the goal is to understand the sensitivity of queries to single parameter changes, and to identify single parameter changes that would enforce a certain query constraint. In this paper, we expand the work to multiple parameters which may be in the CPT of a single variable, or the CPTs of multiple variables. Not only do we identify the solution space of multiple parameter changes that would be needed to enforce a query constraint, but we also show how to find the optimal solution, that is, the one which disturbs the current probability distribution the least (with respect to a specific measure of disturbance). We characterize the computational complexity of our new techniques and discuss their applications to developing and debugging Bayesian networks, and to the problem of reasoning about the value (reliability) of new information.

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

[2]  Haiqin Wang,et al.  User Interface Tools for Navigation in Conditional Probability Tables and Elicitation of Probabilities in Bayesian Networks , 2000, UAI.

[3]  Steffen L. Lauritzen,et al.  Bayesian updating in causal probabilistic networks by local computations , 1990 .

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

[5]  Joseph Y. Halpern,et al.  A Logic for Reasoning about Evidence , 2002, UAI.

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

[7]  Prakash P. Shenoy,et al.  Propagating Belief Functions with Local Computations , 1986, IEEE Expert.

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

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

[10]  Adnan Darwiche,et al.  A distance measure for bounding probabilistic belief change , 2002, Int. J. Approx. Reason..

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

[12]  Adnan Darwiche,et al.  When do Numbers Really Matter? , 2001, UAI.

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

[14]  L. C. van der Gaag,et al.  A Computational Architecture for N-Way Sensitivity Analysis of Bayesian Networks , 2000 .