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的数据中学习客户选择的非参数模型的问题建立理论基础并构建算法。现有的工具，这项任务的参数模型的选择，随后拟合数据。相比之下，本研究的出发点将是与任何可能可用的数据一致的所有可能的选择模型的集合的表征。鉴于这样的特征，研究将产生的方法，并建立优点，几个不同的标准，从这一套选择一个适当的选择模型。在奥卡姆剃刀的精神，将被考虑的一个标准是从这个集合中找到“稀疏”模型。对这一标准的研究将建立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压缩传感领域的工具来实现。模型选择的第二个标准将从在许多收入优化应用中出现的所寻求的选择模型的某个函数导出。利用该标准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。如果成功的话，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呈现给他们的选项中进行选择的概率描述。这项研究将有可能是一个“黑箱”的方法来学习这样的选择模型，这将是有价值的应用程序中的专家输入是困难的或昂贵的。这类应用包括大型汽车公司和在线零售商面临的库存和分类优化问题。这项研究将提供一个可行的方法来解决这些问题，其中消费者需求的复杂性是明确占。采用这些方法将增加收入和提高效率。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内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伞下探索本文的方法学挑战。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.