A0491
Title: Learning rates of convolutional neural networks with correntropy induced loss
Authors: Yingqiao Zhang - Hong Kong Baptist University (Hong Kong) [presenting]
Abstract: Deep convolutional neural networks are widely used in practice, including image recognition, natural language processing, bioinformatics, and many other fields. Most recent convolutional neural network theory studies are based on the least square loss function. But the least square loss function could not handle the situation well when the noise is heavy-tailed noise which means the noise is only pth moment bounded. Deep convolutional neural networks are investigated with correntropy-induced loss function, assuming the noise is heavy-tailed. It is shown that, with target function in additive ridge functions format, convolutional neural networks followed by one fully connected layer with ReLU activation functions can reach optimal learning rate up to a logarithmic factor, and this rate could circumvent the curse of dimensionality at the same time. In addition, a more general error bound and learning rate are presented when the target function lies in a Sobolev space on the sphere.
