CIF: Small: Distribution-Adaptive Prediction and Classification

模式分类在许多应用中都是一个基本问题，从检测心脏病患者的异常心跳，到识别微芯片制造中的缺陷芯片，再到防扩散任务中的核源分类。设计分类器的传统方法是利用由所考虑的不同对象类的标记样本组成的训练数据。然而，标准方法的一个基本假设是，训练数据代表将对其应用分类器的未来观测。在越来越多的应用中，包括上面提到的那些，由于生物、技术或环境因素引起的主体对主体的可变性，这一假设是不合理的。作为回应，本研究正在开发新的基本分类和预测方法，使训练的分类器适应未来模式的特征。特别是，本研究开发了一个用于分布自适应预测和分类的理论和算法框架。该框架的一个关键特征是使用分布作为预测特征。研究了几个将分布作为特征的统计学习问题；一些是现有学习问题的推广，而另一些是由分布自适应问题独特地激发的新的学习问题。利用再生核Hilbert空间上的复杂性正则化框架，给出了这些问题的一般解。方法论上的贡献包括关于分布的新核和推广误差分析的新方法。这项工作是由流式细胞术的诊断应用具体激发和评估的，流式细胞术是一种用于血液相关疾病研究的高通量细胞分析方法。研究部分与涉及研究生、本科生和高中生的教育倡议相辅相成。

Pattern classification is a fundamental problem in a vast number of applications, ranging from detection of abnormal heartbeats in cardiac patients, to identification of defective chips in microchip manufacturing, to classification of nuclear sources in nonproliferation tasks. The conventional approach to designing classifiers is to leverage training data comprised of labeled examples of the different object classes under consideration. However, a fundamental assumption of standard approaches is that training data are representative of future observations to which the classifier will be applied. In a growing number of applications, including those mentioned above, this assumption cannot be justified because of subject-to-subject variability arising from biological, technological, or environmental factors. In response, this research is developing new fundamental approaches to classification and prediction that adapt trained classifiers to the characteristics of future patterns.In particular, this research develops a theoretical and algorithmic framework for distribution-adaptive prediction and classification. A critical feature of the framework is the use of distributions as predictive features. Several statistical learning problems are studied that incorporate distributions as features; some are generalizations of existing learning problems, while others are new and uniquely motivated by distribution-adaptive problems. General solutions are developed to these problems using the framework of complexity regularization over a reproducing kernel Hilbert space. Methodological contributions include novel kernels on distributions and new methods of generalization error analysis. The work is concretely motivated by and evaluated in diagnostic applications of flow cytometry, a high-throughput assay for cellular analysis used in the study of blood-related diseases. The research component is complemented by educational initiatives involving graduate, undergraduate, and high school students.