# Learning Choice Functions with Gaussian Processes

arXiv: https://arxiv.org/abs/2302.00406 · HTML: https://mlsanity.com/paper/2302.00406/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 53 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 16 of 16)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Preferential Batch Bayesian Optimization](https://mlsanity.com/paper/2003.11435/) (2020)
- [Preferential Bayesian optimisation with Skew Gaussian Processes](https://mlsanity.com/paper/2008.06677/) (2020)
- [Statistical comparison of classifiers through Bayesian hierarchical modelling](https://mlsanity.com/paper/1609.08905/) (2016)
- [Learning Inconsistent Preferences with Gaussian Processes](https://mlsanity.com/paper/2006.03847/) (2020)
- [Recursive Estimation for Sparse Gaussian Process Regression](https://mlsanity.com/paper/1905.11711/) (2019)
- [Scalable Gaussian Process Classification via Expectation Propagation](https://mlsanity.com/paper/1507.04513/) (2015)
- [Skew Gaussian Processes for Classification](https://mlsanity.com/paper/2005.12987/) (2020)
- [Learning Context-Dependent Choice Functions](https://mlsanity.com/paper/1901.10860/) (2019)
- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)
- [A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes](https://mlsanity.com/paper/2012.06846/) (2020)
- [Prior Specification for Bayesian Matrix Factorization via Prior Predictive Matching](https://mlsanity.com/paper/1910.12263/) (2019)
- [Learning Choice Functions via Pareto-Embeddings](https://mlsanity.com/paper/2007.06927/) (2020)

## Built on by (most cited first, 5 of 5)

- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [Principled Bayesian Optimisation in Collaboration with Human Experts](https://mlsanity.com/paper/2410.10452/) (2024)
- [Leveraging Sparsity for Sample-Efficient Preference Learning: A Theoretical Perspective](https://mlsanity.com/paper/2501.18282/) (2025)
- [Interactive Multi-Objective Probabilistic Preference Learning with Soft and Hard Bounds](https://mlsanity.com/paper/2506.21887/) (2025)
- [The AI off-switch problem as a signalling game: bounded rationality and incomparability](https://mlsanity.com/paper/2502.06403/) (2025)

## Abstract (arXiv)

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not able to select a single most preferred object. To address these situations, we need a choice-model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice-data. The proposed model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.