How does Weight Correlation Affect the Generalisation Ability of Deep Neural Networks

This paper studies the novel concept of weight correlation in deep neural networks and discusses its impact on the networks' generalisation ability. For fully-connected layers, the weight correlation is defined as the average cosine similarity between weight vectors of neurons, and for convolutional layers, the weight correlation is defined as the cosine similarity between filter matrices. Theoretically, we show that, weight correlation can, and should, be incorporated into the PAC Bayesian framework for the generalisation of neural networks, and the resulting generalisation bound is monotonic with respect to the weight correlation. We formulate a new complexity measure, which lifts the PAC Bayes measure with weight correlation, and experimentally confirm that it is able to rank the generalisation errors of a set of networks more precisely than existing measures. More importantly, we develop a new regulariser for training, and provide extensive experiments that show that the generalisation error can be greatly reduced with our novel approach

Nonparametric Statistical Inference with an Emphasis on Information-Theoretic Methods

This book addresses contemporary statistical inference issues when no or minimal assumptions on the nature of studied phenomenon are imposed. Information theory methods play an important role in such scenarios. The approaches discussed include various high-dimensional regression problems, time series and dependence analyses