Title: Convolutional neural networks estimation via Lipschitz loss functions with applications to biomedical studies
Authors: Shujie Ma - University of California-Riverside (United States)
Ke Huang - University of California, Riverside (United States) [presenting]
Abstract: The statistical learning theory of a convolutional neural networks (CNNs) estimator obtained from empirical risk minimization with a Lipschitz loss function is investigated. Our framework can be applied to both regression and classification problems. The CNNs estimator is constructed from a network architecture of CNNs followed by two fully connected layers. We establish an explicit bound for both the approximation error and the estimation error. The results provide theoretical guidance for selecting the number of convolutional layers and the number of nodes on each feed-forward layer in the considered network structure. For the purpose of alleviating ``the curse of dimensionality'', we further assume that the target function is defined on a low-dimensional manifold, and develop non-asymptotic excess risk bounds for our estimator. We illustrate the performance of the proposed method through Monte Carlo simulation experiments, and apply it to biomedical data applications.