CIF: Small: Distribution-Adaptive Prediction and Classification

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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.