Zusammenfassung für den Vortrag am 16.11.2017 (11:00 Uhr)Seminar on Nonlinear Algebra
Eva Riccomagno (Università Degli Studi Di Genova)
Sensitivity analysis for monomial models
Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability value at a time and observing how this affects output probabilities of interest. When one probability is varied then others are proportionally covaried to respect the sum-to-one condition of probability laws. The choice of proportional covariation is justified by a variety of optimality conditions, under which the original and the varied distributions are as close as possible under different measures of closeness. For variations of more than one parameter at a time proportional covariation is justified only in some special cases. In this work, for the large class of models entertaining a monomial parametrisation, we demonstrate the optimality of newly defined proportional multi-way schemes with respect to an optimality criterion based on the notion of I-divergence. Furthermore we introduce a condition that any proportional covariation needs to respect in order to be optimal. This is shown by adopting a new formal, geometric characterization of sensitivity analysis in monomial models, which include a wide array of probabilistic graphical models. We also demonstrate the optimality of proportional covariation for multi-way analyses in Naive Bayes classifiers.
This is joint work with Manuele Leonelli, University of Glasgow, UK