Approximation Analysis of Classification with Deep Convolutional Neural Networks
DescriptionClassification is a classic problem in learning theory. Nowadays various classification algorithms have been developed and widely applied in AI (artificial intelligence). As deep neural networks have achieved great success in science and technology that involve large amounts of data, such as speech analysis, image and video analysis, finance and bioinformatics, rigorous mathematical analysis on classification methods by deep neural networks is in urgent demand.A classification algorithm usually involves a minimization based on training data with respect to a potentially rich hypothesis function space and a loss function. It is well known that algorithms with misclassification error are typically unfeasible. Instead, various loss functions have been proposed and applied. Therefore, to analyze different loss functions and characterize their classification behavior will have a great impact for classification problems. Statistical investigation in this direction has been extensive, especially for the binary scenario, which provides us a theoretical framework of classification learning methods. However, to obtain better understanding, more sophisticated and quantitative error analysis is needed as well.In this project, we shall focus on classification methods based on deep convolutional neural networks (CNNs). Precisely, we aim at establishing rigorous approximation analysis on the error in using classification algorithms for binary and multi-class scenarios with various loss function and deep CNNs. Also we shall consider gradient descent methods for a minimum error entropy principle in the framework. Analysis will be carried out by means of approximation theory of local polynomial reproduction and integral discretization. The desired results will have impact both for the theoretical analysis community and for the real practitioners in industries. In addition, the analysis produced in this project may help to design new network algorithms that are more efficient and accurate.
|Effective start/end date||1/01/22 → …|