Belief Revision with Uncertain Inputs in the Possibilistic Setting

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal scale only, and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning. Besides, revision under uncertain inputs can be understood in two different ways depending on whether the input is viewed, or not, as a constraint to enforce. Moreover, it is shown that M.A. Williams' transmutations, originally defined in the setting of Spohn's functions, can be captured in this framework, as well as Boutilier's natural revision.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

New Graphical Model for Computing Optimistic Decisions in Possibility Theory Framework

This paper first proposes a new graphical model for decision making under uncertainty based on min-based possibilistic networks. A decision problem under uncertainty is described by means of two distinct min-based possibilistic networks: the first one expresses agent's knowledge while the second one encodes agent's preferences representing a qualitative utility. We then propose an efficient algorithm for computing optimistic optimal decisions using our new model for representing possibilistic decision making under uncertainty. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph resulting from the fusion of agent's beliefs and preferences. This paper also proposes an alternative way for computing optimal optimistic decisions. The idea is to transform the two possibilistic networks into two equivalent possibilistic logic knowledge bases, one representing agent's knowledge and the other represents agent's preferences. We show that computing an optimal optimistic decision comes down to compute the inconsistency degree of the union of the two possibilistic bases augmented with a given decision

The Basic Principles of Uncertain Information Fusion. An organized review of merging rules in different representation frameworks

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings

Toward a General Framework for Information Fusion

National audienceDepending on the representation setting, different combination rules have been proposed for fusing information from distinct sources. Moreover in each setting, different sets of axioms that combination rules should satisfy have been advocated, thus justifying the existence of alternative rules (usually motivated by situations where the behavior of other rules was found unsatisfactory). These sets of axioms are usually purely considered in their own settings, without in-depth analysis of common properties essential for all the settings. This paper introduces core properties that, once properly instantiated, are meaningful in different representation settings ranging from logic to imprecise probabilities. The following representation settings are especially considered: classical set representation, possibility theory, and evidence theory, the latter encompassing the two other ones as special cases. This unified discussion of combination rules across different settings is expected to provide a fresh look on some old but basic issues in information fusion

Learning Possibilistic Logic Theories

Vi tar opp problemet med å lære tolkbare maskinlæringsmodeller fra usikker og manglende informasjon. Vi utvikler først en ny dyplæringsarkitektur, RIDDLE: Rule InDuction with Deep LEarning (regelinduksjon med dyp læring), basert på egenskapene til mulighetsteori. Med eksperimentelle resultater og sammenligning med FURIA, en eksisterende moderne metode for regelinduksjon, er RIDDLE en lovende regelinduksjonsalgoritme for å finne regler fra data. Deretter undersøker vi læringsoppgaven formelt ved å identifisere regler med konfidensgrad knyttet til dem i exact learning-modellen. Vi definerer formelt teoretiske rammer og viser forhold som må holde for å garantere at en læringsalgoritme vil identifisere reglene som holder i et domene. Til slutt utvikler vi en algoritme som lærer regler med tilhørende konfidensverdier i exact learning-modellen. Vi foreslår også en teknikk for å simulere spørringer i exact learning-modellen fra data. Eksperimenter viser oppmuntrende resultater for å lære et sett med regler som tilnærmer reglene som er kodet i data.We address the problem of learning interpretable machine learning models from uncertain and missing information. We first develop a novel deep learning architecture, named RIDDLE (Rule InDuction with Deep LEarning), based on properties of possibility theory. With experimental results and comparison with FURIA, a state of the art method, RIDDLE is a promising rule induction algorithm for finding rules from data. We then formally investigate the learning task of identifying rules with confidence degree associated to them in the exact learning model. We formally define theoretical frameworks and show conditions that must hold to guarantee that a learning algorithm will identify the rules that hold in a domain. Finally, we develop an algorithm that learns rules with associated confidence values in the exact learning model. We also propose a technique to simulate queries in the exact learning model from data. Experiments show encouraging results to learn a set of rules that approximate rules encoded in data.Doktorgradsavhandlin

Other uncertainty theories based on capacities

International audienceThe two main uncertainty representations in the literature that tolerate imprecision are possibility distributions and random disjunctive sets. This chapter devotes special attention to the theories that have emerged from them. The first part of the chapter discusses epistemic logic and derives the need for capturing imprecision in information representations. It bridges the gap between uncertainty theories and epistemic logic showing that imprecise probabilities subsume modalities of possibility and necessity as much as probability. The second part presents possibility and evidence theories, their origins, assumptions and semantics, discusses the connections between them and the general framework of imprecise probability. Finally, chapter points out the remaining discrepancies between the different theories regarding various basic notions, such as conditioning, independence or information fusion and the existing bridges between them