Pseudo-Mallows for Efficient Probabilistic Preference Learning

Sylvia Qinghua Liu, Valeria Vitelli, Carlo Mannino, Arnoldo Frigessi, Ida Scheel
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:78648-78680, 2026.

Abstract

We propose the Pseudo-Mallows distribution over the set of all permutations of $n$ items, to approximate the posterior distribution of the Bayesian Mallows model. The Bayesian Mallows model has been successfully used for recommender systems to learn personal preferences from highly incomplete users data. However current inference algorithms do not scale, preventing its use in real-time applications. The Pseudo-Mallows distribution is a product of univariate discrete Mallows-like distributions, where the quality of the approximation depends on the order of the $n$ items in the factorization sequence. In a variational setting, we optimize the variational order parameter by minimising a marginalized KL-divergence, conjecturing a certain form of the optimal variational order that depends on the data, and proposing an approximation algorithm for this discrete optimization. Empirical evidence and some theory support our conjecture. We demonstrate on clicking data that variational inference via the Pseudo-Mallows distribution allows much faster probabilistic preference learning compared to alternative MCMC-based options.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-liu26ee, title = {Pseudo-Mallows for Efficient Probabilistic Preference Learning}, author = {Liu, Sylvia Qinghua and Vitelli, Valeria and Mannino, Carlo and Frigessi, Arnoldo and Scheel, Ida}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {78648--78680}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/liu26ee/liu26ee.pdf}, url = {https://proceedings.mlr.press/v306/liu26ee.html}, abstract = {We propose the Pseudo-Mallows distribution over the set of all permutations of $n$ items, to approximate the posterior distribution of the Bayesian Mallows model. The Bayesian Mallows model has been successfully used for recommender systems to learn personal preferences from highly incomplete users data. However current inference algorithms do not scale, preventing its use in real-time applications. The Pseudo-Mallows distribution is a product of univariate discrete Mallows-like distributions, where the quality of the approximation depends on the order of the $n$ items in the factorization sequence. In a variational setting, we optimize the variational order parameter by minimising a marginalized KL-divergence, conjecturing a certain form of the optimal variational order that depends on the data, and proposing an approximation algorithm for this discrete optimization. Empirical evidence and some theory support our conjecture. We demonstrate on clicking data that variational inference via the Pseudo-Mallows distribution allows much faster probabilistic preference learning compared to alternative MCMC-based options.} }
Endnote
%0 Conference Paper %T Pseudo-Mallows for Efficient Probabilistic Preference Learning %A Sylvia Qinghua Liu %A Valeria Vitelli %A Carlo Mannino %A Arnoldo Frigessi %A Ida Scheel %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-liu26ee %I PMLR %P 78648--78680 %U https://proceedings.mlr.press/v306/liu26ee.html %V 306 %X We propose the Pseudo-Mallows distribution over the set of all permutations of $n$ items, to approximate the posterior distribution of the Bayesian Mallows model. The Bayesian Mallows model has been successfully used for recommender systems to learn personal preferences from highly incomplete users data. However current inference algorithms do not scale, preventing its use in real-time applications. The Pseudo-Mallows distribution is a product of univariate discrete Mallows-like distributions, where the quality of the approximation depends on the order of the $n$ items in the factorization sequence. In a variational setting, we optimize the variational order parameter by minimising a marginalized KL-divergence, conjecturing a certain form of the optimal variational order that depends on the data, and proposing an approximation algorithm for this discrete optimization. Empirical evidence and some theory support our conjecture. We demonstrate on clicking data that variational inference via the Pseudo-Mallows distribution allows much faster probabilistic preference learning compared to alternative MCMC-based options.
APA
Liu, S.Q., Vitelli, V., Mannino, C., Frigessi, A. & Scheel, I.. (2026). Pseudo-Mallows for Efficient Probabilistic Preference Learning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:78648-78680 Available from https://proceedings.mlr.press/v306/liu26ee.html.

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