# Learning Inconsistent Preferences with Gaussian Processes

arXiv: https://arxiv.org/abs/2006.03847 · HTML: https://mlsanity.com/paper/2006.03847/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2020.

## Built on by (most cited first, 12 of 12)

- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [Domain Generalisation via Imprecise Learning](https://mlsanity.com/paper/2404.04669/) (2024)
- [Explaining Preferences with Shapley Values](https://mlsanity.com/paper/2205.13662/) (2022)
- [Learning Choice Functions with Gaussian Processes](https://mlsanity.com/paper/2302.00406/) (2023)
- [Principled Bayesian Optimisation in Collaboration with Human Experts](https://mlsanity.com/paper/2410.10452/) (2024)
- [ShaRP: Explaining Rankings and Preferences with Shapley Values](https://mlsanity.com/paper/2401.16744/) (2024)
- [Human-in-the-Loop Meta Bayesian Optimization for Fusion Energy and Scientific Applications](https://mlsanity.com/paper/2605.00068/) (2026)
- [Vector Optimization with Gaussian Process Bandits](https://mlsanity.com/paper/2412.02484/) (2024)
- [Post Hoc Regression Refinement via Pairwise Rankings](https://mlsanity.com/paper/2508.16495/) (2025)
- [DTI-GP: Bayesian operations for drug-target interactions using deep kernel Gaussian processes](https://mlsanity.com/paper/2512.24810/) (2025)
- [Aggregate-then-Calibrate for Human-centered Assessment with Theoretical Guarantees](https://mlsanity.com/paper/2608.02455/) (2026)
- [Targeted Active Learning for Preference-Based Treatment Effects on Multivariate Outcomes](https://mlsanity.com/paper/2610.03824/) (2026)

## Abstract (arXiv)

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.