Generalization and Risk Bounds for Recurrent Neural Networks

Recurrent Neural Networks (RNNs) have achieved great success in the prediction of sequential data. However, their theoretical studies are still lagging behind because of their complex interconnected structures. In this paper, we establish a new generalization error bound for vanilla RNNs, and provide a unified framework to calculate the Rademacher complexity that can be applied to a variety of loss functions. When the ramp loss is used, we show that our bound is tighter than the existing bounds based on the same assumptions on the Frobenius and spectral norms of the weight matrices and a few mild conditions. Our numerical results show that our new generalization bound is the tightest among all existing bounds in three public datasets. Our bound improves the second tightest one by an average percentage of 13.80% and 3.01% when the $\tanh$ and ReLU activation functions are used, respectively. Moreover, we derive a sharp estimation error bound for RNN-based estimators obtained through empirical risk minimization (ERM) in multi-class classification problems when the loss function satisfies a Bernstein condition.

SleepEGAN: A GAN-enhanced Ensemble Deep Learning Model for Imbalanced Classification of Sleep Stages

Deep neural networks have played an important role in automatic sleep stage classification because of their strong representation and in-model feature transformation abilities. However, class imbalance and individual heterogeneity which typically exist in raw EEG signals of sleep data can significantly affect the classification performance of any machine learning algorithms. To solve these two problems, this paper develops a generative adversarial network (GAN)-powered ensemble deep learning model, named SleepEGAN, for the imbalanced classification of sleep stages. To alleviate class imbalance, we propose a new GAN (called EGAN) architecture adapted to the features of EEG signals for data augmentation. The generated samples for the minority classes are used in the training process. In addition, we design a cost-free ensemble learning strategy to reduce the model estimation variance caused by the heterogeneity between the validation and test sets, so as to enhance the accuracy and robustness of prediction performance. We show that the proposed method can improve classification accuracy compared to several existing state-of-the-art methods using three public sleep datasets.