An Experimental Comparison of Numerical and Qualitative Probabilistic Reasoning
This work addresses the challenge of simplifying probabilistic modeling for machine diagnosis, but it is incremental as it builds on existing qualitative probability frameworks.
The paper tackled the problem of reducing knowledge engineering effort in probabilistic reasoning by comparing qualitative (infinitesimal) probabilities to numerical methods for car troubleshooting, finding that infinitesimal schemes performed as well as numerical ones for identifying faults with small prior probabilities (below 0.03).
Qualitative and infinitesimal probability schemes are consistent with the axioms of probability theory, but avoid the need for precise numerical probabilities. Using qualitative probabilities could substantially reduce the effort for knowledge engineering and improve the robustness of results. We examine experimentally how well infinitesimal probabilities (the kappa-calculus of Goldszmidt and Pearl) perform a diagnostic task - troubleshooting a car that will not start by comparison with a conventional numerical belief network. We found the infinitesimal scheme to be as good as the numerical scheme in identifying the true fault. The performance of the infinitesimal scheme worsens significantly for prior fault probabilities greater than 0.03. These results suggest that infinitesimal probability methods may be of substantial practical value for machine diagnosis with small prior fault probabilities.