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

这个项目研究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研究的统计决策问题截然不同：第一，决策者可以从一大类复杂和质量不同的观测通道(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范来源，需要使用多种不同的特征类型，集成不同的上下文信息来源，甚至可能需要人类交互。本项目需要根据三个具体目标为特征丰富的决策问题制定一个严格的数学框架：(1)将特征的结构表征为随机信念精化过滤器；(2)根据预期信息收益对特征进行数值比较的通用成本敏感标准；(3)同时考虑特征提取成本和最终决策损失的顺序特征选择的最佳信息价值标准。作为推论，本研究调查了与最优特征选择规则和决策的渐近信息论特征之间的联系。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)来开发实用的对成本和损失敏感的特征压缩技术。理论目标(3)以充当自主决策代理的算法为目标。面对对图像的推理任务，他们应用成本敏感、非近视的信息价值标准，在每个时间步决定是从图像中提取新特征，还是停下来宣布答案。

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.