Graphical models and their (un)certainties
M.A.R. Leisink · Radboud Repository (Radboud University) · 2004
'A graphical models is a powerful tool to deal with complex probability models. Although in principle any set of probabilistic relationships can be modelled, the calculation of the actual numbers can be very hard. Every graphical model suffers from a phenomenon known as exponential scaling. To circumvent this problem one need to approximate the model with mathematical techniques. This thesis is subdivided in two parts. The first part explains linear response, an extension of the mean field approximation, that provides a fast and usable method to approximate means of and correlations between variables in the network. The second part deals with bounding techniques. Approximations tend to be as good as possible without defining what 'good' is. Bounds, on the other hand, try to enclose the quantity of interest as tight as possible from above or below.'