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Sensitivity analysis in probabilistic discrete graphical models is usuallyconducted by varying one probability value at a time and observing how thisaffects output probabilities of interest. When one probability is varied thenothers are proportionally covaried to respect the sum-to-one condition ofprobability laws. The choice of proportional covariation is justified by avariety of optimality conditions, under which the original and the varieddistributions are as close as possible under different measures of closeness.For variations of more than one parameter at a time proportional covariation isjustified in some special cases only. In this work, for the large class ofdiscrete statistical models entertaining a regular monomial parametrisation, wedemonstrate the optimality of newly defined proportional multi-way schemes withrespect to an optimality criterion based on the notion of I-divergence. Wedemonstrate that there are varying parameters choices for which proportionalcovariation is not optimal and identify the sub-family of model distributionswhere the distance between the original distribution and the one whereprobabilities are covaried proportionally is minimum. This is shown by adoptinga new formal, geometric characterization of sensitivity analysis in monomialmodels, which include a wide array of probabilistic graphical models. We alsodemonstrate the optimality of proportional covariation for multi-way analysesin Naive Bayes classifiers.

A geometric characterisation of sensitivity analysis in monomial models