Possibilistic networks are belief graphical models based on possibility theory. A possibilistic network either represents experts' epistemic uncertainty or models uncertain information from poor, scarce or imprecise data. Learning possibilistic networks from data in general and from imperfect or scarce datasets in particular, has not received enough attention. This work focuses on parameter learning of possibilistic networks. The main contributions of the paper are i) a study of an extension of the information affinity measure to assess the similarity of possibilistic networks and ii) a comparative empirical evaluation of two approaches for learning the parameters of a possibilistic network from empirical data.

Graphical belief models are compact and powerful tools for representing and reasoning under uncertainty. Possibilistic networks are graphical belief models based on possibility theory. In this paper, we address reasoning under uncertain inputs in both quantitative and qualitative possibilistic networks. More precisely, we first provide possibilistic counterparts of Pearl's methods of virtual evidence then compare them with the possibilistic counterparts of Jeffrey's rule of conditioning. As in the probabilistic setting, the two methods are shown to be equivalent in the quantitative setting regarding the existence and uniqueness of the solution. However in the qualitative setting, Pearl's method of virtual evidence which applies directly on graphical models disagrees with Jeffrey's rule and the virtual evidence method. The paper provides the precise situations where the methods are not equivalent. Finally, the paper addresses related issues like transformations from one method to another and commutativity.

Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of information can be described by different measures: possibility measures, necessity measures and more recently, guaranteed possibility measures, denoted by Delta. This paper first proposes the use of guaranteed possibility measures to define a so-called Delta-based possibilistic network. This graphical representation tries to express and to deal with the minimal (lower-bound) possibility degree guaranteed for each variable. We then establish relationships between graphical and logical-based representations of uncertain information encoded by guaranteed possibility measures. We show that possibilistic networks based on guaranteed possibility measures can be easily transformed, in a polynomial time, in Delta-based knowledge bases. Then we analyze propagation algorithms in Delta-based possibilistic networks. In fact, standard possibilistic propagation algorithms can be re-used since we show that a simple rewriting of the chain rule allows the transformation of the initial Delta-based possibilistic networks into standard min-based possibilistic networks.