Learning Inconsistent Preferences with Gaussian Processes

TL;DR

This paper introduces a generalized Gaussian process model that captures inconsistent preferences and non-rankable data, enabling better modeling of real-world preference structures and discovering item clusters.

Contribution

It extends preferential Gaussian processes to handle inconsistent preferences and non-rankable data, with a new covariance kernel satisfying universality in preference function space.

Findings

The proposed model effectively captures inconsistent preferences.

It outperforms state-of-the-art methods on real-world datasets.

Violations of rankability are common in real-world preference data.

Abstract

We revisit widely used preferential Gaussian processes by Chu et al.(2005) and challenge their modelling assumption that imposes rankability of data items via latent utility function values. We propose a generalisation of pgp which can capture more expressive latent preferential structures in the data and thus be used to model inconsistent preferences, i.e. where transitivity is violated, or to discover clusters of comparable items via spectral decomposition of the learned preference functions. We also consider the properties of associated covariance kernel functions and its reproducing kernel Hilbert Space (RKHS), giving a simple construction that satisfies universality in the space of preference functions. Finally, we provide an extensive set of numerical experiments on simulated and real-world datasets showcasing the competitiveness of our proposed method with state-of-the-art. Our experimental findings support the conjecture that violations of rankability are ubiquitous in real-world preferential data.