Balanced sensitivity functions for tuning multi-dimensional Bayesian network classifiers

Multi-dimensional Bayesian network classifiers are Bayesian networks of restricted topological structure, which are tailored to classifying data instances into multiple dimensions. Like more traditional classifiers, multi-dimensional classifiers are typically learned from data and may include inaccuracies in their parameter probabilities. We will show that the graphical properties and dedicated use of these classifiers induce higher-order sensitivity functions of a highly constrained functional form in these parameters. We then introduce the concept of balanced sensitivity function in which multiple parameters are functionally related by the odds ratios of their original and new values, and argue that these functions provide for a suitable heuristic for tuning multi-dimensional classifiers with guaranteed bounds on the effects on their output probabilities. We demonstrate the practicability of our heuristic by means of a classifier for a real-world application in the veterinary field.