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.

翻译：在许多现实场景中，例如在线推荐或消费者选择建模，个体从一组固定的选项中进行重复选择。准确估计其潜在偏好对于生成个性化的未来推荐至关重要。基于过去决策理解用户选择行为的概率模型，可作为现有推荐系统和选择预测方法的有益补充。为此，本文引入了一种新颖的统计框架，用于根据用户过去的选择预测其偏好，并遵循一个自然的单调性假设：过去更频繁或更强烈被选择的选项，在未来也更有可能被再次选择。我们的方法建立在Le Goff和Soulier（2017）提出的参数模型基础上，该模型最初用于描述蚁群中的蚂蚁如何在众多已有路径中选择一条路径。我们受Maulik等人（2024）引入的广义大象随机游走模型启发，提出了该模型的非参数泛化形式。我们开发了一种在上述单调性约束下对用户偏好概率进行极大似然估计的方法。我们还为估计量提供了理论保证，并通过模拟实验和真实数据集证明了我们方法的有效性。