你吃什么就是什么：一种偏好感知的逆Optimization方法
You Are What You Eat: A Preference-Aware Inverse Optimization Approach
摘要：
新兴的精准营养领域的一个关键挑战是提供饮食建议，这些建议既反映了不同患者群体的饮食偏好（通常是未知的），也反映了人类专家指定的已知饮食限制。出于这一挑战，我们开发了一种偏好感知的约束推理方法，其中最优化问题的目标函数不是预先指定的，并且可以在各个部分中有所不同。在现有的方法中，来自机器学习的聚类模型并不自然地适合于恢复约束最优化问题，而约束推理模型（诸如逆优化）并不明确地解决给定数据集中的非同质性。通过利用集群和逆优化技术的优势，我们开发了一种新的方法，恢复跨集群的约束优化过程的效用函数，同时提供最佳的饮食建议作为集群代表。使用患者每日食物摄入量的数据集，我们展示了我们的方法如何分别在遵守饮食指南和分区观察方面推广独立聚类和逆优化方法。该方法通过结合患者偏好和专家对更健康饮食的建议来提供饮食建议，从而在患者划分和每个聚类的营养建议方面实现结构性改进。我们的方法的一个吸引人的特点是它能够考虑不可行的，但翔实的意见，为一组给定的饮食限制。由此产生的建议对应于更广泛的饮食选择，即使它们限制了不健康的选择。
英文摘要：
A key challenge in the emerging field of precision nutrition entails providing diet recommendations that reflect both the (often unknown) dietary preferences of different patient groups and known dietary constraints specified by human experts. Motivated by this challenge, we develop a preference-aware constrained-inference approach in which the objective function of an optimization problem is not pre-specified and can differ across various segments. Among existing methods, clustering models from machine learning are not naturally suited for recovering the constrained optimization problems, whereas constrained inference models such as inverse optimization do not explicitly address non-homogeneity in given datasets. By harnessing the strengths of both clustering and inverse optimization techniques, we develop a novel approach that recovers the utility functions of a constrained optimization process across clusters while providing optimal diet recommendations as cluster representatives. Using a dataset of patients' daily food intakes, we show how our approach generalizes stand-alone clustering and inverse optimization approaches in terms of adherence to dietary guidelines and partitioning observations, respectively. The approach makes diet recommendations by incorporating both patient preferences and expert recommendations for healthier diets, leading to structural improvements in both patient partitioning and nutritional recommendations for each cluster. An appealing feature of our method is its ability to consider infeasible but informative observations for a given set of dietary constraints. The resulting recommendations correspond to a broader range of dietary options, even when they limit unhealthy choices.
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