A Statistical Framework for Learning Preferences from the Past
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911670604922880 |
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| author | Sadhukhan, Tamojit Banerjee, Moulinath Maulik, Krishanu Roy, Parthanil |
| author_facet | Sadhukhan, Tamojit Banerjee, Moulinath Maulik, Krishanu Roy, Parthanil |
| contents | In many real-world settings such as online recommendation or consumer choice modeling, individuals make repeated choices from a fixed set of options. Accurately estimating their underlying preferences is essential for generating personalized future recommendations. Probabilistic models for understanding user choice behavior from past decisions can serve as a valuable addition to existing recommender systems and choice prediction methods. To this end, in this article, we introduce a novel statistical framework for predicting user preferences based on their past choices, under a natural monotonicity assumption: options that were chosen more frequently or more intensely in the past are more likely to be chosen again in the future. Our approach builds on a parametric model proposed by Le Goff and Soulier (2017), originally used to describe how ants in an ant colony select a path among many pre-existing paths. We propose a non-parametric generalization of this model, drawing inspiration from the generalized elephant random walk introduced by Maulik et al. (2024). We develop a method of maximum likelihood estimation of the user preference probabilities under the above-mentioned monotonicity constraint. We also derive theoretical guarantees for our estimator and demonstrate the effectiveness of our method through both simulated experiments and real-world datasets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10042 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Statistical Framework for Learning Preferences from the Past Sadhukhan, Tamojit Banerjee, Moulinath Maulik, Krishanu Roy, Parthanil Methodology Probability Applications 62G05 (Primary) 62M05, 62M20, 60G25 (Secondary) In many real-world settings such as online recommendation or consumer choice modeling, individuals make repeated choices from a fixed set of options. Accurately estimating their underlying preferences is essential for generating personalized future recommendations. Probabilistic models for understanding user choice behavior from past decisions can serve as a valuable addition to existing recommender systems and choice prediction methods. To this end, in this article, we introduce a novel statistical framework for predicting user preferences based on their past choices, under a natural monotonicity assumption: options that were chosen more frequently or more intensely in the past are more likely to be chosen again in the future. Our approach builds on a parametric model proposed by Le Goff and Soulier (2017), originally used to describe how ants in an ant colony select a path among many pre-existing paths. We propose a non-parametric generalization of this model, drawing inspiration from the generalized elephant random walk introduced by Maulik et al. (2024). We develop a method of maximum likelihood estimation of the user preference probabilities under the above-mentioned monotonicity constraint. We also derive theoretical guarantees for our estimator and demonstrate the effectiveness of our method through both simulated experiments and real-world datasets. |
| title | A Statistical Framework for Learning Preferences from the Past |
| topic | Methodology Probability Applications 62G05 (Primary) 62M05, 62M20, 60G25 (Secondary) |
| url | https://arxiv.org/abs/2605.10042 |