A Statistical Framework for Learning Preferences from the Past

2026-05-11

AI Summary

This study addresses the problem of accurately estimating users’ latent preferences from their historical choice behavior to support personalized recommendation and choice prediction. Building on the monotonicity assumption that options selected more frequently or intensely in the past are more likely to be chosen in the future, the authors propose a nonparametric statistical framework. This approach extends the ant-path selection model of Le Goff and Soulier (2017) by incorporating ideas from generalized elephant random walks, enabling maximum likelihood estimation of preference probabilities under monotonicity constraints. The method requires no prespecified parametric form, enjoys theoretical convergence guarantees, and demonstrates strong empirical performance and superiority over baselines in both simulated and real-world datasets.

Abstract

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.

Problem

• preference learning
• choice modeling
• recommender systems
• user behavior
• statistical estimation

Innovation

• non-parametric preference learning
• monotonicity constraint
• generalized elephant random walk
• maximum likelihood estimation
• choice modeling