Learning from Imprecise Data: Adjustments of Optimistic and Pessimistic Variants

Abstract

The problem of learning from imprecise data has recently attracted increasing attention, and various methods to tackle this problem have been proposed. In this paper, we discuss and compare two quite opposite approaches, an “optimistic” one that interprets imprecise data in a way that is most favourable for a candidate model, and a “pessimistic” one in which model choice is guided by the most unfavourable interpretation. To avoid an overly extreme behaviour, a modified version of the latter has recently been proposed, which we complement by an adjusted version of the optimistic approach. By presenting the various methods within a common (loss minimization) framework and discussing illustrative examples, we hope to provide some insight into important properties and differences, thereby paving the way for a more formal analysis.