Magdalena Ivanovska

Information and Computation 303 Doi: https://doi.org/10.1016/j.ic.2024.105256

Probabilistic judgment aggregation is concerned with aggregating judgments about probabilities of logically related issues. It takes as input imprecise probabilistic judgments over the issues given by a group of agents and defines rules of aggregating the individual judgments into a collective opinion representative for the group. The process of aggregation can be subject to constraints, i.e., aggregation rules can be required to satisfy certain properties. We explore how probabilistic independence constraints can be represented and incorporated into the aggregation process.

2022 25th International Conference on Information Fusion - FUSION Doi: https://doi.org/10.23919/FUSION49751.2022.9841392

In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to propagate both means and variances through sum-product networks derived from Bayesian networks, thereby characterizing epistemic uncertainty, or the uncertainty in the model itself. Alternatively, second-order belief propagation has been demonstrated for polytrees but not for general directed acyclic graph structures. In this work, we extend Loopy Belief Propagation to the setting of second-order Bayesian networks, giving rise to Second-Order Loopy Belief Propagation (SOLBP). For second-order Bayesian networks, SOLBP generates inferences consistent with those generated by sum-product networks, while being more computationally efficient and scalable.

Modeling Decisions for Artificial Intelligence 19th International Conference, MDAI 2022, Sant Cugat, Spain, August 30 – September 2, 2022, Proceedings s. 26-37 Doi: https://doi.org/10.1007/978-3-031-13448-7_3

We consider a situation where agents are updating their probabilistic opinions on a set of issues with respect to the confidence they have in each other’s judgements. We adapt the framework for reaching a consensus introduced in [2] and modified in [1] to our case of uncertain probabilistic judgements on logically related issues. We discuss possible alternative solutions for the instances where the requirements for reaching a consensus are not satisfied.

European Journal of Operational Research 297(3) s. 1030-1041 Doi: https://doi.org/10.1016/j.ejor.2021.05.030

Preference aggregation in Group Decision Making (GDM) is a substantial problem that has received a lot of research attention. Decision problems involving fuzzy preference relations constitute an important class within GDM. Legacy approaches dealing with the latter type of problems can be classified into indirect approaches, which involve deriving a group preference matrix as an intermediate step, and direct approaches, which deduce a group preference ranking based on individual preference rankings. Although the work on indirect approaches has been extensive in the literature, there is still a scarcity of research dealing with the direct approaches. In this paper we present a direct approach towards aggregating several fuzzy preference relations on a set of alternatives into a single weighted ranking of the alternatives. By mapping the pairwise preferences into transitions probabilities, we are able to derive a preference ranking from the stationary distribution of a stochastic matrix. Interestingly, the ranking of the alternatives obtained with our method corresponds to the optimizer of the Maximum Likelihood Estimation of a particular Bradley-Terry-Luce model. Furthermore, we perform a theoretical sensitivity analysis of the proposed method supported by experimental results and illustrate our approach towards GDM with a concrete numerical example. This work opens avenues for solving GDM problems using elements of probability theory, and thus, provides a sound theoretical fundament as well as plausible statistical interpretation for the aggregation of expert opinions in GDM.

Electronic Proceedings in Theoretical Computer Science (EPTCS) 297 s. 273-292 Doi: https://doi.org/10.4204/EPTCS.297.18

In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way that allows handling probabilistic judgments and then define probabilistic aggregation functions obtained by generalization of the classical ones. In addition, we discuss essential desirable properties for the aggregation functions and explore impossibility results.