On the decomposition of Generalized Additive Independence models

TL;DR

This paper studies a specific subclass of GAI models, providing a decomposition that simplifies optimization problems from exponential to quadratic complexity, thereby enhancing their practical usability.

Contribution

It introduces a decomposition for discrete 2-additive GAI models into nonnegative monotone terms, reducing computational complexity.

Findings

Decomposition into nonnegative monotone terms achieved

Complexity reduced from exponential to quadratic

Facilitates practical application of GAI models

Abstract

The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive utility model, which need not satisfy mutual preferential independence. Its great generality makes however its application and study difficult. We consider a significant subclass of GAI models, namely the discrete 2-additive GAI models, and provide for this class a decomposition into nonnegative monotone terms. This decomposition allows a reduction from exponential to quadratic complexity in any optimization problem involving discrete 2-additive models, making them usable in practice.