Adaptive Sequential Interval Estimation In Classification Problems

Classification is a hot topic both in research and applications such as medical science,social science and engineering.It is common for the learning related to a classification rule to take place under a training/testing framework using a given labeled dataset.Thus,having a sufficient amount of labeled data is essential to constructing a reliable classification rule.When the amount of labeled data is small and there is a considerable amount of unlabeled data,how to enlarge the training set to improve the classification rule is an important question.If examining the labels of those unlabeled data is costly and time-consuming,then how to first recruit those "crucial" data-which may largely change the classification rule-into training samples to accelerate the training process and reduce labeling costs becomes an important issue.In the machine learning literature,the term "active learning methods" refers to learning with aggressive subject selection strategies;in the statistical literature,from a data recruiting aspect,they relate to sequential methods.When we recruit new training samples by analyzing current data,stochastic regression can be useful for examining such active learning processes.If we use the criteria adopted by statistical experimental design methods to assess the unlabeled data and recruit only the most "informative" subjects into the training set,we can then accelerate the learning process and further reduce the labeling cost.The first chapter introduce the background knowledge and meaning,main references and innovations of this thesis.The second chapter consider about the active sequential estimation under multiclass classification.First,we propose a unified algorithm for both categorical and ordinal multi-class classification data.Then we prove the asymptotic properties under adaptive design.Based on the asymptotic properties,we give the sequential interval estimation and sampling strategy.The third chapter consider about the active sequential estimation for binary classification when label noise exists.First,we refine the binary logistic model with the misclassification rate.We propose two estimation methods for the refined model and prove the asymptotic properties under adaptive design.The forth chapter consider about the active sequential estimation for binary classification when label error and feature noise both exist.We give a constraint to feature noise to make sure the estimation methods proposed in chapter three still working.We also prove the asymptotic properties and give the sequential sampling method.