# Expected utility theory and clustering

## MAP-PDMA

Irene Brito

CMAT - University of Minho

Abstract ::

In decision theory, for example in the actuarial and economic context, the expected utility model describes how individuals choose between uncertain or risky prospects [1]. According to that model, there exists a utility function to appraise different risky outcomes and a decision maker chooses the outcome which maximizes expected utility. The utility function is used to model the individual’s preferences. Several problems in machine learning, for example data classification problems, rely on partitioning a given data set into disjoint, non-empty subsets. Clustering is a process of organizing a data set into subsets – clusters – in such a way that objects belonging to the same cluster are similar [2]. The aim is to form a partition, where the clusters are constructed using a metric (for example the Euclidean metric), minimizing the dissimilarity between elements belonging to the same cluster. The aim of utility clustering is to solve classification problems taking into account the preferences of decisions, by replacing the usual metrics with utility functions [3]. In this seminar I will present a brief introduction to the theory of expected utility and to clustering and explain then the fundamentals of the utility clustering theory. The equivalence of the traditional K-means clustering and the utility clustering with a quadratic utility function will be shown [3].

References

[1] R. Kaas et al., Modern actuarial risk theory, 2nd ed., Springer, 2008.

[2] B.S. Everitt et al., Cluster Analysis, 5th Edition, Wiley and Sons, 2011.

[3] S. Clain, I. Brito, Utility clustering, in preparation, 2021.

Seminar for the Doctoral Program in Applied Mathematics (MAP-PDMA Seminar)