What Do Customers Like: A New Approach That Lets The Data Decide

该奖项的研究目标是为从有限数据中学习客户选择的非参数模型问题建立理论基础并构建算法。用于这项任务的现有工具假定选择参数模型，这些模型随后与数据拟合。相比之下，本研究的出发点将是与任何可用数据一致的所有可能选择模型集的特征。鉴于这样的特征，研究将为从这一组中选择适当的选择模型的几个不同标准产生方法并确立其优点。按照奥卡姆剃刀的精神，我们要考虑的一个标准是从这个集合中找到“最稀疏”的模型。对这一标准的研究将确定选择模型识别的限制，这是任何学习理论的关键组成部分。这将通过使用和开发来自压缩感知领域的工具来实现。模型选择的第二个标准将来自于在许多收益优化应用中出现的选择模型的某个函数。利用这一准则来选择选择模型的算法将需要新的优化技术来进行鲁棒优化。如果成功，这项研究将推进从现有的部分数据中获得选择模型的基本技术。选择模型是对消费者如何从提供给他们的选项中进行选择的概率描述。这项研究将使学习这种选择模型的“黑箱”方法成为可能，这在专家输入困难或昂贵的应用程序中是有价值的。这种类型的应用包括大型汽车公司和在线零售商所面临的库存和分类优化问题。这项研究将为这些问题提供一个可行的方法，其中消费者需求的复杂性被明确地考虑在内。这些方法的实施将导致收入和效率的增加。与此同时，这项研究代表了统计推断、信号处理和机器学习社区的一个有希望的方向，这些社区最近开始在压缩感知的保护下探索方法上的挑战。从这个意义上说，这项工作将推进压缩感知和非参数学习的理论。

The research objective of this award is to establish theoretical foundations and build algorithms for the problem of learning non-parametric models of customer choice from limited data. Existing tools for this task posit parametric models of choice which are subsequently fit to data. In contrast, the starting point for this research will be a characterization of the set of all possible choice models consistent with any data that might be available. Given such a characterization, the research will produce methodologies for, and establish the merits of, several distinct criteria for selecting an appropriate choice model from this set. In the spirit of Occam's razor, one criterion that will be considered is finding the "sparsest" model from this set. The study of this criterion will establish the limits to choice model identification, a key component of any theory of learning. This will be accomplished via the use and development of tools from the area of compressive sensing. A second criterion for model selection will be derived from a certain function of the choice model sought that arises in numerous revenue optimization applications. Algorithms that utilize this criterion to select a choice model will require new optimization techniques for robust optimization. If successful, this research will advance the fundamental techniques used in obtaining choice models from available partial data. Choice models are probabilistic descriptions of how consumers choose from options presented to them. This research will make possible a "black box" approach to the problem of learning such choice models that will be valuable in applications where expert input is difficult or expensive to obtain. Applications in this genre include problems of inventory and assortment optimization faced by large auto companies and online retailers alike. This research will provide a viable methodology for such problems wherein the complex nature of consumer demand is explicitly accounted for. The implementation of such methodologies will lead to increased revenues and efficiencies. At the same time, this investigation represents a promising direction within the statistical inference, signal processing and machine learning communities, which have recently begun to explore the methodological challenges herein under the umbrella of compressive sensing. In that sense, this work will advance the theory of compressed sensing and non-parametric learning.