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arxiv: 2403.11782 · v6 · pith:7PDMUM37new · submitted 2024-03-18 · 💻 cs.LG · stat.ML

A tutorial on learning from preferences and choices with Gaussian Processes

Alessio Benavoli , Dario Azzimonti This is my paper

Pith reviewed 2026-05-24 03:23 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords preference learningGaussian processeslikelihood functionsrandom utility modelsdecision theoryobject preferencelabel preferencemachine learning
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The pith

Tailoring the likelihood function allows Gaussian Process models to incorporate economic rationality principles for preference learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This tutorial establishes a unified framework for preference and choice modeling with Gaussian Processes. The central move is to encode rationality principles from economics and decision theory directly into the likelihood function rather than altering the GP prior or kernel. Doing so produces models that cover random utility theory, limits of discernment, and multiple conflicting utilities, and that handle both object preferences and label preferences. A reader would care because the resulting models retain full probabilistic uncertainty quantification while remaining compatible with standard GP inference.

Core claim

By suitably tailoring the likelihood function, this framework enables the construction of preference learning models that encompass random utility models, limits of discernment, and scenarios with multiple conflicting utilities for both object- and label-preference.

What carries the argument

The tailored likelihood function that encodes rationality principles from economics and decision theory inside Gaussian Process preference models.

If this is right

  • Random utility models become expressible as GP preference models.
  • Limits of discernment can be directly modeled within the same framework.
  • Scenarios with multiple conflicting utilities are covered for both objects and labels.
  • Standard GP inference and uncertainty quantification remain available after the likelihood change.
  • The same construction applies uniformly to object-preference and label-preference tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The likelihood-tailoring strategy could be tested on sequential choice data to check whether the resulting posteriors match observed human inconsistency rates.
  • If the approach works, it supplies a route to embed other decision-theoretic constraints, such as stochastic dominance, without redesigning the covariance function.
  • The framework's uniformity across object and label preferences suggests it may simplify hybrid recommendation systems that mix both types of feedback.

Load-bearing premise

Rationality principles from economics and decision theory can be incorporated into Gaussian Process models simply by tailoring the likelihood function without requiring additional structural changes or losing key GP properties such as uncertainty quantification.

What would settle it

An explicit example of a rationality axiom that cannot be represented by any choice of likelihood while keeping the rest of the GP model unchanged, or a case where uncertainty quantification is demonstrably lost after tailoring the likelihood.

Figures

Figures reproduced from arXiv: 2403.11782 by Alessio Benavoli, Dario Azzimonti.

Figure 3.1
Figure 3.1. Figure 3.1: Alice’s utility for home temperature. tures (objects) X = {10,11,12,...,25} and asks her preferences for 19 pairs of temperatures. This results in the dataset: D19 ={12 ≻ 10,13 ≻ 25,14 ≻ 13,15 ≻ 22,15 ≻ 23,16 ≻ 11,19 ≻ 15, 19 ≻ 21,19 ≻ 22,19 ≻ 24,20 ≻ 10,20 ≻ 14,20 ≻ 21,20 ≻ 24, 20 ≻ 25,21 ≻ 13,21 ≻ 25,23 ≻ 25,24 ≻ 25}. (3.1) We aim to learn Alice’s utility function for home-temperature from D19 and pred… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Sampling from a constrained region using lin-ess, [PITH_FULL_IMAGE:figures/full_fig_p019_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Left: learned utility functions, the mean is the continuous line and [PITH_FULL_IMAGE:figures/full_fig_p020_3_3.png] view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Left: learned utility functions under Luce’s model, the mean is the [PITH_FULL_IMAGE:figures/full_fig_p025_3_4.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Φ(∆u/σ) for different values of σ. (3.18) is known as probit. Hereafter we exploit a result derived in Benavoli et al. [2021b] to show that, assuming a GP prior on u and the likelihood (3.18), the predictive posterior for u is a Skew-GP. Model 3: Probit model for erroneous preferences Consider a vector X = [x1,x2,...,xr ] ⊤ of objects such that xi ∈ R c for all i = 23 [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 3
Figure 3. Figure 3: a-left shows the predictive posterior mean and 95% credible interval [PITH_FULL_IMAGE:figures/full_fig_p027_3.png] view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: Left: learned utility functions under the probit model for erroneous [PITH_FULL_IMAGE:figures/full_fig_p028_3_6.png] view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: Left: learned utility functions under the probit model for erroneous [PITH_FULL_IMAGE:figures/full_fig_p029_3_7.png] view at source ↗
Figure 3.8
Figure 3.8. Figure 3.8: Left: learned utility functions under the Gaussian-noise model for pref [PITH_FULL_IMAGE:figures/full_fig_p032_3_8.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Alice’s true utilities for brownie, fruit cake and ice cream. [PITH_FULL_IMAGE:figures/full_fig_p040_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Top: mean of the predicted posterior utilities for the three desserts. Bot [PITH_FULL_IMAGE:figures/full_fig_p041_4_2.png] view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Posterior distributions of the differences [PITH_FULL_IMAGE:figures/full_fig_p042_4_3.png] view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Top: mean of the predicted posterior utilities for the three desserts. Bot [PITH_FULL_IMAGE:figures/full_fig_p044_4_4.png] view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Predicted ranking distribution at day x = 0.25. The string ‘ibf’ stays for icecream ≻ brownie ≻ fruitcake. The most probable ordering is ‘fib’ fruitcake ≻ icecream ≻ brownie. would order them on any other day of the year [PITH_FULL_IMAGE:figures/full_fig_p045_4_5.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: True latent utilities function that underlay Alice’s Pareto-rational [PITH_FULL_IMAGE:figures/full_fig_p056_5_1.png] view at source ↗
Figure 5
Figure 5. Figure 5: -left shows the posterior-mean of the utilities and 95% credible inter [PITH_FULL_IMAGE:figures/full_fig_p056_5.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Learned utilities from rational choice data using Model 9 with ratio [PITH_FULL_IMAGE:figures/full_fig_p057_5_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: and, respectively, 5.4. In Figure 5.3, it can be noticed that the relative [PITH_FULL_IMAGE:figures/full_fig_p057_5.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Learned utilities from pseudo-rational choice data using Model 9 with [PITH_FULL_IMAGE:figures/full_fig_p058_5_3.png] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Learned utilities from pseudo-rational choice data using Model 9 with [PITH_FULL_IMAGE:figures/full_fig_p058_5_4.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Predicted utilities for the Transportation modes in Table 6.2 for the lin [PITH_FULL_IMAGE:figures/full_fig_p061_6_1.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Predicted utilities for the Transportation modes in Table 6.2 for the SE [PITH_FULL_IMAGE:figures/full_fig_p062_6_2.png] view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Predictive posterior for the utilities of the platforms. Covariates [PITH_FULL_IMAGE:figures/full_fig_p065_6_3.png] view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Thumbnail images of the 50 ellipses [PITH_FULL_IMAGE:figures/full_fig_p065_6_4.png] view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: Ellipses shown to the student (ID=32, 15, 25 from left to right). The [PITH_FULL_IMAGE:figures/full_fig_p065_6_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: b showcases the utilities for a case of incomparability. Ellipse ID=15 [PITH_FULL_IMAGE:figures/full_fig_p066_6.png] view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: Predictive posterior for the two latent utilities (top and bottom plot) for [PITH_FULL_IMAGE:figures/full_fig_p067_6_6.png] view at source ↗
read the original abstract

Preference modelling lies at the intersection of economics, decision theory, machine learning and statistics. By understanding individuals' preferences and how they make choices, we can build products that closely match their expectations, paving the way for more efficient and personalised applications across a wide range of domains. The objective of this tutorial is to present a cohesive and comprehensive framework for preference learning with Gaussian Processes (GPs), demonstrating how to seamlessly incorporate rationality principles (from economics and decision theory) into the learning process. By suitably tailoring the likelihood function, this framework enables the construction of preference learning models that encompass random utility models, limits of discernment, and scenarios with multiple conflicting utilities for both object- and label-preference. This tutorial builds upon established research while simultaneously introducing some novel GP-based models to address specific gaps in the existing literature.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript is a tutorial on a Gaussian Process framework for preference learning. It claims that tailoring the likelihood function allows incorporation of rationality principles from economics and decision theory, enabling models that recover random utility models, limits of discernment, and multi-utility scenarios for both object- and label-preferences, while building on prior work and introducing some novel GP-based models.

Significance. If the constructions hold, the tutorial offers a unified, likelihood-focused approach to embedding decision-theoretic principles into GPs while retaining uncertainty quantification, which could aid development of personalized systems. Credit is due for its expository synthesis of established literature with targeted novel models addressing literature gaps.

minor comments (2)
  1. The abstract states that novel GP-based models are introduced to address gaps; the main text should explicitly flag which sections present new derivations versus syntheses of prior work, with clear citations to the latter.
  2. Ensure that all likelihood constructions are accompanied by explicit statements confirming that standard GP properties (e.g., posterior uncertainty) remain intact after tailoring, to avoid reader uncertainty about the framework's scope.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading and positive evaluation of the manuscript. We are pleased that the unified likelihood-based framework for embedding decision-theoretic principles into Gaussian process preference models was viewed as a useful expository contribution, and we appreciate the recommendation for minor revision.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper is an expository tutorial whose central claim is that preference learning models encompassing random utility models, limits of discernment, and multi-utility scenarios can be obtained by tailoring the likelihood function within a fixed GP prior. This is a standard model-construction technique that does not reduce any prediction or result to a quantity defined by the authors' own inputs or prior self-citations; the derivation chain consists of explicit likelihood choices that recover known models from economics and decision theory without circular redefinition or fitted-input renaming. The work explicitly positions itself as building on established literature while adding some novel models, with no load-bearing uniqueness theorems or ansatzes imported from the authors' own prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no specific free parameters, axioms or invented entities are described. The framework relies on standard Gaussian Process properties and likelihood tailoring drawn from prior literature in the field.

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    DT-PBO is a tree-based surrogate for preferential Bayesian optimization that matches GP performance on benchmarks while remaining inherently interpretable.

Reference graph

Works this paper leans on

137 extracted references · 137 canonical work pages · cited by 1 Pith paper · 3 internal anchors

  1. [1]

    Osborne, Sebastian Orbell, Natalia Ares, Krikamol Muandet, and Siu Lun Chau

    Masaki Adachi, Brady Planden, David Howey, Michael A. Osborne, Sebastian Orbell, Natalia Ares, Krikamol Muandet, and Siu Lun Chau. Looping in the human: Collaborative and explainable bayesian optimization. In Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, pages 505--513. PMLR, 4 2024. URL https://proceedings.ml...

    work page 2024

  2. [2]

    Lo \" c Adam and S \'e bastien Destercke. Incremental elicitation of preferences: optimist or pessimist? In Algorithmic Decision Theory: 7th International Conference, ADT 2021, Toulouse, France, November 3--5, 2021, Proceedings 7, pages 71--85. Springer, 2021 a

    work page 2021

  3. [3]

    Possibilistic preference elicitation by minimax regret

    Lo \" c Adam and S \'e bastien Destercke. Possibilistic preference elicitation by minimax regret. In Uncertainty in artificial intelligence, pages 718--727. PMLR, 2021 b

    work page 2021

  4. [4]

    Accelerated spectral ranking

    Arpit Agarwal, Prathamesh Patil, and Shivani Agarwal. Accelerated spectral ranking. In International Conference on Machine Learning, pages 70--79. PMLR, 2018

    work page 2018

  5. [5]

    Aggarwal

    Charu C. Aggarwal. Recommender Systems. Springer International Publishing, Cham, 2016. ISBN 978-3-319-29657-9. doi:10.1007/978-3-319-29659-3

    work page doi:10.1007/978-3-319-29659-3 2016

  6. [6]

    Learning preferences for multiclass problems

    Fabio Aiolli and Alessandro Sperduti. Learning preferences for multiclass problems. Advances in neural information processing systems, 17, 2004

    work page 2004

  7. [7]

    General theory of best variants choice: Some aspects

    Mark Aizerman and Andrew Malishevski. General theory of best variants choice: Some aspects. IEEE Transactions on Automatic Control, 26 0 (5): 0 1030--1040, 1981

    work page 1981

  8. [8]

    Gaussian process regression with skewed errors

    MT Alodat and Mohammed K Shakhatreh. Gaussian process regression with skewed errors. Journal of Computational and Applied Mathematics, 370: 0 112665, 2020

    work page 2020

  9. [9]

    Statistical methods for ranking data, volume 1341

    Mayer Alvo and LH Philip. Statistical methods for ranking data, volume 1341. Springer, 2014

    work page 2014

  10. [10]

    Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results

    Niccol \`o Anceschi, Augusto Fasano, Daniele Durante, and Giacomo Zanella. Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results. Journal of the American Statistical Association, 118 0 (542): 0 1451--1469, 2023

    work page 2023

  11. [11]

    B Arellano and Adelchi Azzalini

    R. B Arellano and Adelchi Azzalini. On the unification of families of skew-normal distributions. Scandinavian Journal of Statistics, 33 0 (3): 0 561--574, 2006

    work page 2006

  12. [12]

    Pareto rationalizability by two single-peaked preferences

    Ricardo Arlegi and Miriam Teschl. Pareto rationalizability by two single-peaked preferences. Mathematical Social Sciences, 118: 0 1--11, 2022

    work page 2022

  13. [13]

    Social choice and individual values

    Kenneth J Arrow. Social choice and individual values. Yale university press, 1963

    work page 1963

  14. [14]

    Random utility theory for social choice

    Hossein Azari, David Parks, and Lirong Xia. Random utility theory for social choice. Advances in Neural Information Processing Systems, 25, 2012

    work page 2012

  15. [15]

    Generalized method-of-moments for rank aggregation

    Hossein Azari Soufiani, William Chen, David C Parkes, and Lirong Xia. Generalized method-of-moments for rank aggregation. Advances in Neural Information Processing Systems, 26, 2013

    work page 2013

  16. [16]

    The skew-normal and related families, volume 3

    Adelchi Azzalini. The skew-normal and related families, volume 3. Cambridge University Press, 2013

    work page 2013

  17. [17]

    Understanding probabilistic sparse G aussian process approximations

    Matthias Bauer, Mark van der Wilk, and Carl Edward Rasmussen. Understanding probabilistic sparse G aussian process approximations. In Advances in neural information processing systems, pages 1533--1541, 2016

    work page 2016

  18. [18]

    prefGP : A python package for preference and choice learning with gaussian processes

    Alessio Benavoli and Dario Azzimonti. prefGP : A python package for preference and choice learning with gaussian processes. https://github.com/benavoli/prefGP, 2024

    work page 2024

  19. [19]

    Skew Gaussian Processes for Classification

    Alessio Benavoli, Dario Azzimonti, and Dario Piga. Skew Gaussian Processes for Classification . Machine Learning, 109: 0 1877–1902, 2020. doi:10.1007/s10994-020-05906-3. URL https://arxiv.org/abs/2005.12987

    work page doi:10.1007/s10994-020-05906-3 1902

  20. [20]

    Preferential Bayesian optimisation with Skew Gaussian Processes

    Alessio Benavoli, Dario Azzimonti, and Dario Piga. Preferential Bayesian optimisation with Skew Gaussian Processes . In 2021 Genetic and Evolutionary Computation Conference Companion (GECCO '21 Companion), July 10--14, 2021, Lille, France, New York, NY, USA, 2021 a . ACM

    work page 2021

  21. [21]

    A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes

    Alessio Benavoli, Dario Azzimonti, and Dario Piga. A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes . Machine Learning, pages 1--39, 2021 b . doi:10.1007/s10994-021-06039-x. URL https://link.springer.com/article/10.1007/s10994-021-06039-x

    work page doi:10.1007/s10994-021-06039-x 2021

  22. [22]

    Preferential bayesian optimisation with skew gaussian processes

    Alessio Benavoli, Dario Azzimonti, and Dario Piga. Preferential bayesian optimisation with skew gaussian processes. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, pages 1842--1850, 2021 c

    work page 2021

  23. [23]

    Learning choice functions with gaussian processes

    Alessio Benavoli, Dario Azzimonti, and Dario Piga. Learning choice functions with gaussian processes. In Robin J. Evans and Ilya Shpitser, editors, Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, volume 216 of Proceedings of Machine Learning Research, pages 141--151. PMLR, 2023 a . URL https://proceedings.mlr.press/v2...

    work page 2023

  24. [24]

    Bayesian optimization for choice data

    Alessio Benavoli, Dario Azzimonti, and Dario Piga. Bayesian optimization for choice data. In 2023 Genetic and Evolutionary Computation Conference Companion (GECCO '23 Companion), July 15--19, 2023, Lisbon, 2023 b . doi:10.1145/3583133.3596324

    work page doi:10.1145/3583133.3596324 2023

  25. [25]

    A discrete choice model for subset selection

    Austin R Benson, Ravi Kumar, and Andrew Tomkins. A discrete choice model for subset selection. In Proceedings of the eleventh ACM international conference on web search and data mining, pages 37--45, 2018

    work page 2018

  26. [26]

    Pandasbiogeme: a short introduction

    Michel Bierlaire. Pandasbiogeme: a short introduction. Report TRANSP-OR: Lausanne, Switzerland, 181219, 2018

    work page 2018

  27. [27]

    The normal law under linear restrictions: simulation and estimation via minimax tilting

    Zdravko I Botev. The normal law under linear restrictions: simulation and estimation via minimax tilting. Journal of the Royal Statistical Society Series B: Statistical Methodology, 79 0 (1): 0 125--148, 2017

    work page 2017

  28. [28]

    Incremental elicitation of rank-dependent aggregation functions based on bayesian linear regression

    Nadjet Bourdache, Patrice Perny, and Olivier Spanjaard. Incremental elicitation of rank-dependent aggregation functions based on bayesian linear regression. In IJCAI-19-Twenty-Eighth International Joint Conference on Artificial Intelligence, pages 2023--2029. International Joint Conferences on Artificial Intelligence Organization, 2019

    work page 2023

  29. [29]

    Computational decision support: Regret-based models for optimization and preference elicitation, 2013

    Craig Boutilier. Computational decision support: Regret-based models for optimization and preference elicitation, 2013

    work page 2013

  30. [30]

    Constraint-based optimization and utility elicitation using the minimax decision criterion

    Craig Boutilier, Relu Patrascu, Pascal Poupart, and Dale Schuurmans. Constraint-based optimization and utility elicitation using the minimax decision criterion. Artificial Intelligence, 170 0 (8-9): 0 686--713, 2006

    work page 2006

  31. [31]

    Rank analysis of incomplete block designs: I

    Ralph Allan Bradley and Milton E Terry. Rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika, 39 0 (3/4): 0 324--345, 1952

    work page 1952

  32. [32]

    Asymmetric, closed-form, finite-parameter models of multinomial choice

    Timothy Brathwaite and Joan L Walker. Asymmetric, closed-form, finite-parameter models of multinomial choice. Journal of choice modelling, 29: 0 78--112, 2018

    work page 2018

  33. [33]

    Learning to rank using gradient descent

    Chris Burges, Tal Shaked, Erin Renshaw, Ari Lazier, Matt Deeds, Nicole Hamilton, and Greg Hullender. Learning to rank using gradient descent. In Proceedings of the 22nd international conference on Machine learning, pages 89--96, 2005

    work page 2005

  34. [34]

    From ranknet to lambdarank to lambdamart: An overview

    Christopher JC Burges. From ranknet to lambdarank to lambdamart: An overview. Learning, 11 0 (23-581): 0 81, 2010

    work page 2010

  35. [35]

    Procaccia, and Nisarg Shah

    Ioannis Caragiannis, Ariel D. Procaccia, and Nisarg Shah. When do noisy votes reveal the truth? ACM Transactions on Economics and Computation, 4 0 (3): 0 1–30, 6 2016. ISSN 2167-8375, 2167-8383. doi:10.1145/2892565

    work page doi:10.1145/2892565 2016

  36. [36]

    Efficient bayesian inference for generalized bradley--terry models

    Francois Caron and Arnaud Doucet. Efficient bayesian inference for generalized bradley--terry models. Journal of Computational and Graphical Statistics, 21 0 (1): 0 174--196, 2012

    work page 2012

  37. [37]

    Learning Inconsistent Preferences with Gaussian Processes

    Siu Lun Chau, Javier Gonzalez, and Dino Sejdinovic. Learning Inconsistent Preferences with Gaussian Processes . In Gustau Camps-Valls, Francisco J. R. Ruiz, and Isabel Valera, editors, Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, volume 151 of Proceedings of Machine Learning Research, pages 2266--2281. PMLR, ...

    work page 2022

  38. [38]

    Rational selection of decision functions

    Herman Chernoff. Rational selection of decision functions. Econometrica: journal of the Econometric Society, pages 422--443, 1954

    work page 1954

  39. [39]

    Deep reinforcement learning from human preferences

    Paul F Christiano, Jan Leike, Tom Brown, Miljan Martic, Shane Legg, and Dario Amodei. Deep reinforcement learning from human preferences. Advances in neural information processing systems, 30, 2017

    work page 2017

  40. [40]

    Preference Learning with Gaussian Processes

    Wei Chu and Zoubin Ghahramani. Preference Learning with Gaussian Processes . In Proceedings of the 22nd International Conference on Machine Learning, ICML ’05, page 137–144, New York, NY, USA, 2005. Association for Computing Machinery. ISBN 1595931805. doi:10.1145/1102351.1102369

    work page doi:10.1145/1102351.1102369 2005

  41. [41]

    Learning to order things

    William W Cohen, Robert E Schapire, and Yoram Singer. Learning to order things. Advances in neural information processing systems, 10, 1997

    work page 1997

  42. [42]

    Paired comparison, triple comparison, and ranking experiments as generalized linear models, and their implementation on glim

    Douglas E Critchlow and Michael A Fligner. Paired comparison, triple comparison, and ranking experiments as generalized linear models, and their implementation on glim. Psychometrika, 56 0 (3): 0 517--533, 1991

    work page 1991

  43. [43]

    Estimation of random utility models in r: the mlogit package

    Yves Croissant. Estimation of random utility models in r: the mlogit package. Journal of Statistical Software, 95: 0 1--41, 2020

    work page 2020

  44. [44]

    Interpreting, axiomatising and representing coherent choice functions in terms of desirability

    Jasper De Bock and Gert De Cooman. Interpreting, axiomatising and representing coherent choice functions in terms of desirability. In International Symposium on Imprecise Probabilities: Theories and Applications, pages 125--134. PMLR, 2019

    work page 2019

  45. [45]

    Representation of a preference ordering by a numerical function

    Gerard Debreu. Representation of a preference ordering by a numerical function. Decision processes, 3: 0 159--165, 1954

    work page 1954

  46. [46]

    Torch-choice: A pytorch package for large-scale choice modelling with python

    Tianyu Du, Ayush Kanodia, and Susan Athey. Torch-choice: A pytorch package for large-scale choice modelling with python. arXiv preprint arXiv:2304.01906, 2023

    work page arXiv 2023

  47. [47]

    Conjugate Bayes for probit regression via unified skew-normal distributions

    Daniele Durante. Conjugate Bayes for probit regression via unified skew-normal distributions . Biometrika, 106 0 (4): 0 765--779, 08 2019

    work page 2019

  48. [48]

    Indifference or indecisiveness? choice-theoretic foundations of incomplete preferences

    Kfir Eliaz and Efe A Ok. Indifference or indecisiveness? choice-theoretic foundations of incomplete preferences. Games and economic behavior, 56 0 (1): 0 61--86, 2006

    work page 2006

  49. [49]

    Active preference learning with discrete choice data

    Brochu Eric, Nando Freitas, and Abhijeet Ghosh. Active preference learning with discrete choice data. Advances in neural information processing systems, 20, 2007

    work page 2007

  50. [50]

    Generalized robust conjoint estimation

    Theodoros Evgeniou, Constantinos Boussios, and Giorgos Zacharia. Generalized robust conjoint estimation. Marketing Science, 24 0 (3): 0 415--429, 2005

    work page 2005

  51. [51]

    Learning subjective functions with large margins

    Claude-Nicolas Fiechter and Seth Rogers. Learning subjective functions with large margins. In ICML, pages 287--294, 2000

    work page 2000

  52. [52]

    Fishburn

    Peter C. Fishburn. Nonlinear preference and utility theory. Johns Hopkins series in the mathematical sciences. Johns Hopkins University Press, Baltimore, 1988. ISBN 978-0-8018-3598-8

    work page 1988

  53. [53]

    Posterior probabilities for a consensus ordering

    Michael A Fligner and Joseph S Verducci. Posterior probabilities for a consensus ordering. Psychometrika, 55: 0 53--63, 1990

    work page 1990

  54. [54]

    A rank-ordered logit model with unobserved heterogeneity in ranking capabilities

    Dennis Fok, Richard Paap, and Bram Van Dijk. A rank-ordered logit model with unobserved heterogeneity in ranking capabilities. Journal of applied econometrics, 27 0 (5): 0 831--846, 2012

    work page 2012

  55. [55]

    Application and interpretation of nested logit models of intercity mode choice

    Christopher V Forinash and Frank S Koppelman. Application and interpretation of nested logit models of intercity mode choice. Transportation research record, 0 (1413), 1993

    work page 1993

  56. [56]

    u rnkranz and Eyke H \

    Johannes F \"u rnkranz and Eyke H \"u llermeier. Preference learning. Springer, 2010

    work page 2010

  57. [57]

    R., Pleiss, G., Bindel, D., Weinberger, K

    Jacob R. Gardner, Geoff Pleiss, David Bindel, Kilian Q. Weinberger, and Andrew Gordon Wilson. Gpytorch: Blackbox matrix-matrix gaussian process inference with gpu acceleration. Advances in Neural Information Processing Systems, 2018-Decem 0 (NeurIPS): 0 7576–7586, 2018. ISSN 10495258. arXiv: 1809.11165

    work page arXiv 2018

  58. [58]

    Integrals over Gaussians under Linear Domain Constraints

    Alexandra Gessner, Oindrila Kanjilal, and Philipp Hennig. Integrals over Gaussians under Linear Domain Constraints . In Silvia Chiappa and Roberto Calandra, editors, Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, volume 108, pages 2764--2774. PMLR, 8 2020

    work page 2020

  59. [59]

    Variational Gaussian process classifiers

    Mark N Gibbs and David JC MacKay. Variational Gaussian process classifiers . IEEE Transactions on Neural Networks, 11 0 (6): 0 1458--1464, 2000

    work page 2000

  60. [60]

    Lawrence

    Javier González, Zhenwen Dai, Andreas Damianou, and Neil D. Lawrence. Preferential Bayesian Optimization . In Proceedings of the 34th International Conference on Machine Learning, pages 1282--1291. PMLR, 2017. URL https://proceedings.mlr.press/v70/gonzalez17a.html

    work page 2017

  61. [61]

    Bayesian inference for plackett-luce ranking models

    John Guiver and Edward Snelson. Bayesian inference for plackett-luce ranking models. In proceedings of the 26th annual international conference on machine learning, pages 377--384, 2009

    work page 2009

  62. [62]

    Constraint classification: A new approach to multiclass classification

    Sariel Har-Peled, Dan Roth, and Dav Zimak. Constraint classification: A new approach to multiclass classification. In International conference on algorithmic learning theory, pages 365--379. Springer, 2002

    work page 2002

  63. [63]

    Maxwell Harper and Joseph A

    F. Maxwell Harper and Joseph A. Konstan. The MovieLens Datasets: History and Context . ACM Transactions on Interactive Intelligent Systems, 5 0 (4): 0 19:1--19:19, 2015. ISSN 2160-6455. doi:10.1145/2827872

    work page doi:10.1145/2827872 2015

  64. [64]

    Lawrence

    James Hensman, Nicol\` o Fusi, and Neil D. Lawrence. Gaussian processes for big data. In Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, UAI'13, pages 282--290, Arlington, Virginia, USA, 2013. AUAI Press

    work page 2013

  65. [65]

    Learning preference relations for information retrieval

    Ralf Herbrich, Thore Graepel, Peter Bollmann-Sdorra, and Klaus Obermayer. Learning preference relations for information retrieval. In ICML-98 Workshop: text categorization and machine learning, pages 80--84, 1998

    work page 1998

  66. [66]

    Scalable gaussian process classification via expectation propagation

    Daniel Hernandez-Lobato and Jose Miguel Hernandez-Lobato. Scalable gaussian process classification via expectation propagation. In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, page 168–176. PMLR, 2016. URL https://proceedings.mlr.press/v51/hernandez-lobato16.html

    work page 2016

  67. [67]

    Apollo: A flexible, powerful and customisable freeware package for choice model estimation and application

    Stephane Hess and David Palma. Apollo: A flexible, powerful and customisable freeware package for choice model estimation and application. Journal of choice modelling, 32: 0 100170, 2019

    work page 2019

  68. [68]

    Bayesian Active Learning for Classification and Preference Learning

    Neil Houlsby, Ferenc Husz \'a r, Zoubin Ghahramani, and M \'a t \'e Lengyel. Bayesian active learning for classification and preference learning. arXiv preprint arXiv:1112.5745, 2011

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  69. [69]

    Explaining preferences with shapley values

    Robert Hu, Siu Lun Chau, Jaime Ferrando Huertas, and Dino Sejdinovic. Explaining preferences with shapley values. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 27664--27677. Curran Associates, Inc., 2022. URL https://proceedings.neurips.cc/paper_files/pape...

    work page 2022

  70. [70]

    u llermeier, Johannes F \

    Eyke H \"u llermeier, Johannes F \"u rnkranz, Weiwei Cheng, and Klaus Brinker. Label ranking by learning pairwise preferences. Artificial Intelligence, 172 0 (16-17): 0 1897--1916, 2008

    work page 1916

  71. [71]

    MM algorithms for generalized Bradley-Terry models

    David R Hunter. MM algorithms for generalized Bradley-Terry models . The Annals of Statistics, 32 0 (1): 0 384--406, 2004

    work page 2004

  72. [72]

    Gibbs sampling approach for generation of truncated multivariate gaussian random variables

    Jayesh H Kotecha and Petar M Djuric. Gibbs sampling approach for generation of truncated multivariate gaussian random variables. In 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No. 99CH36258), volume 3, pages 1757--1760. IEEE, 1999

    work page 1999

  73. [73]

    A course in microeconomic theory

    David M Kreps et al. A course in microeconomic theory. Princeton university press, 1990

    work page 1990

  74. [74]

    Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithms

    Gael Lederrey, Virginie Lurkin, Tim Hillel, and Michel Bierlaire. Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithms. Journal of Choice Modelling, 38: 0 100226, 2021. ISSN 1755-5345

    work page 2021

  75. [75]

    Antithetic and monte carlo kernel estimators for partial rankings

    Maria Lomeli, Mark Rowland, Arthur Gretton, and Zoubin Ghahramani. Antithetic and monte carlo kernel estimators for partial rankings. Statistics and Computing, 29: 0 1127--1147, 2019

    work page 2019

  76. [76]

    Semiorders and a theory of utility discrimination

    R Duncan Luce. Semiorders and a theory of utility discrimination. Econometrica, Journal of the Econometric Society, pages 178--191, 1956

    work page 1956

  77. [77]

    Individual Choice Behavior: A Theoretical Analysis

    R Duncan Luce. Individual Choice Behavior: A Theoretical Analysis . Wiley, New York, 1959

    work page 1959

  78. [78]

    Bayesian methods for backpropagation networks

    David JC MacKay. Bayesian methods for backpropagation networks. In Models of neural networks III, pages 211--254. Springer, 1996

    work page 1996

  79. [79]

    Advanced conjoint analysis using feature selection via support vector machines

    Sebasti \'a n Maldonado, Ricardo Montoya, and Richard Weber. Advanced conjoint analysis using feature selection via support vector machines. European Journal of Operational Research, 241 0 (2): 0 564--574, 2015

    work page 2015

  80. [80]

    Non-null ranking models

    Colin L Mallows. Non-null ranking models. i. Biometrika, 44 0 (1/2): 0 114--130, 1957

    work page 1957

Showing first 80 references.