Quantifying Degrees of E-admissibility in Decision Making with Imprecise Probabilities

Abstract

This paper is concerned with decision making using imprecise probabilities. In the first part, we introduce a new decision criterion that allows for explicitly modeling how far decisions that are optimal in terms of Walley's maximality are accepted to deviate from being optimal in the sense of Levi's E-admissibility. For this criterion, we also provide an efficient and simple algorithm based on linear programming theory. In the second part of the paper, we propose two new measures for quantifying the extent of E-admissibility of an E-admissible act, i.e. the size of the set of measures for which the corresponding act maximizes expected utility. The first measure is the maximal diameter of this set, while the second one relates to the maximal barycentric cube that can be inscribed into it. Also here, for both measures, we give linear programming algorithms capable to deal with them. Finally, we discuss some ideas in the context of ordinal decision theory. The paper concludes with a stylized application example illustrating all introduced concepts.

Decision Making Under Severe Uncertainty on a Budget

“…We have adopted two different views: one where we consider a regret-based argument, and the other where we want to have alternatives that are well-dispersed in the space of alternatives. This second approach is very close in spirit to some recent work bearing on E-admissibility (another well-known decision rule) [7] as well as to space-filling designs.…”

“…In this section, we demonstrate how our method can be applied in practice. The first example is inspired from Jansen et al [10], but adapted to provide more than 3 maximal acts, while the second one concerns a situation where we must predict binary vectors over a set of labels, which is the situation encountered in multi-label learning, a specific multi-task machine learning problem.…”

“…Financial investment example. We follow the financial application example in [10], where a subject wants to invest her money in some stocks. An act corresponds to investing in a specific stock.…”

“…In addition, based on the decision maker's experience in the financial market, she specifies her credal set through probability bounds as follows (note these are slightly wider than the ones from Jansen et al [10] to better demonstrate the benefits of our method):…”

Modular Graph Transformer Networks for Multi-Label Image Classification

“…Thus, BR can be seen as a credal classifier and would be useful when targeting reliable set-valued predictions[4,33,62].…”