CIF: Medium: Collaborative Research: Nonasymptotic Analysis of Feature-Rich Decision Problems with Applications to Computer Vision

该项目涉及统计决策问题的理论和有效算法，这些问题在两个关键方面与迄今为止研究的问题完全不同：第一，决策者可以在不同复杂性和质量的一大类观测通道（特征）中进行选择;第二，在做出决策之前可以使用的计算资源的总成本是有限的。计算机视觉是这种特征丰富的决策问题的典型来源，需要使用多种异构特征类型，整合不同来源的上下文信息，甚至可能是人类交互。该项目需要根据以下三个具体目标为特征丰富的决策问题开发一个严格的数学框架：（1）作为随机信念细化过滤器的特征的结构表征;（2）根据预期信息增益对特征进行数值比较的通用成本敏感标准;以及（3）用于顺序特征选择的最优信息值准则，该准则考虑了特征提取成本和终端决策损失。作为推论，本研究探讨连接到渐近信息理论的最佳特征选择规则和决策的表征。该项目的第四个具体目标是为两个具有挑战性的计算机视觉问题开发实用算法：主动视觉搜索和细粒度分类。该项目的这一部分利用理论目标（1）和（2）来开发实用的成本和损失敏感的特征压缩技术。理论目标（3）针对充当自主决策代理的算法。面对图像上的推理任务，他们应用成本敏感的非近视信息价值标准来决定在每个时间步是否从图像中提取新特征或停止并声明答案。

This project deals with theory and efficient algorithms for statistical decision problems that are radically different from those that have been studied to date in two key aspects: First, the decision-maker may choose among a large class of observation channels (features) of varying complexity and quality; and second, the total cost of computational resources that can be used prior to arriving at a decision is limited. Computer vision is a paradigmatic source of such feature-rich decision problems, requiring the use of multiple heterogeneous feature types, integration of diverse sources of contextual information, and possibly even human interaction. This project entails the development of a rigorous mathematical framework for feature-rich decision problems in accordance with three specific aims: (1) structural characterization of features as stochastic belief-refining filters; (2) universal cost-sensitive criteria for numerical comparison of features in terms of expected information gains; and (3) optimal value-of-information criteria for sequential feature selection that take into account both feature extraction costs and terminal decision losses. As corollaries, this research investigates connections to asymptotic information-theoretic characterizations of optimal feature selection rules and decisions. The fourth specific aim of the project is the development of practical algorithms for two challenging computer vision problems: active visual search and fine-grained categorization. This component of the project leverages theoretical aims (1) and (2) to develop practical cost- and loss-sensitive feature compression techniques. Theoretical aim (3) targets algorithms that function as autonomous decision-making agents. Faced with an inference task on an image, they apply cost-sensitive non-myopic value- of-information criteria to decide at each time step whether to extract a new feature from the image or to stop and declare an answer.