Abstract
Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be used, such as point estimators, confidence sets and decision theoretic approaches. For example, a classifier that classifies a future object as belonging to only one of several known classes is a point estimator. The purpose of this paper is to propose a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. An example is provided to illustrate the method, and a simulation study is included to highlight the desirable feature of the method.
Highlights
Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences, among others
Mimicking the confidence set in Equation (2), we construct the confidence set for the class c of y as: n o
The intuitive motivation underlying this method is that, when an object is judged to be possibly from several classes, we should accept this objectively rather than forcing ourselves to pick just one class, which entails a large chance of misclassification
Summary
Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences, among others. E.g., the recent books by [1,2,3,4]. Classical examples include medical diagnosis, automatic character recognition, data mining (such as credit scoring, consumer sales analysis and credit card transaction analysis) and artificial intelligence (such as the development of machines with brain-like performance). There have been many exciting new developments in both methodology and applications, taking advantage of increased computational power readily available nowadays. Classification methods can be divided into probabilistic methods (including Bayesian classifiers), regression methods (including logistic regression and regression trees), geometric methods (including support vector machines), and ensemble methods (combining classifiers for improved robustness)
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