CIF: Small: Distribution-Adaptive Prediction and Classification

模式分类是大量应用中的基本问题，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示例组成的训练数据。 然而，标准方法的基本假设是训练数据代表分类器将应用于的未来观察。 在越来越多的应用中，包括上面提到的应用，由于生物、技术或环境因素引起的受试者之间的变异性，这种假设是不合理的。 作为回应，本研究正在开发新的分类和预测的基本方法，使训练的分类器适应未来模式的特征。特别是，本研究开发了一个理论和算法框架，用于分布自适应预测和分类。该框架的一个关键特征是使用分布作为预测特征。研究了几个统计学习问题，将分布作为特征;一些是现有学习问题的概括，而另一些是新的和独特的动机分布自适应问题。一般的解决方案，这些问题的再生核希尔伯特空间的复杂性正则化的框架。 方法上的贡献包括新的内核分布和新的方法的泛化误差分析。这项工作的具体动机和评估在诊断应用的流式细胞术，高通量分析用于细胞分析的血液相关疾病的研究。研究部分是由涉及研究生，本科生和高中学生的教育举措的补充。

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.