Mutual Information Learned Classifiers: an Information-theoretic Viewpoint of Training Deep Learning Classification Systems

Deep learning systems have been reported to achieve state-of-the-art performances in many applications, and a key is the existence of well trained classifiers on benchmark datasets. As a main-stream loss function, the cross entropy can easily lead us to find models which demonstrate severe overfitting behavior. In this paper, we show that the existing cross entropy loss minimization problem essentially learns the label conditional entropy (CE) of the underlying data distribution of the dataset. However, the CE learned in this way does not characterize well the information shared by the label and the input. In this paper, we propose a mutual information learning framework where we train deep neural network classifiers via learning the mutual information between the label and the input. Theoretically, we give the population classification error lower bound in terms of the mutual information. In addition, we derive the mutual information lower and upper bounds for a concrete binary classification data model in $\mathbb{R}^n$, and also the error probability lower bound in this scenario. Empirically, we conduct extensive experiments on several benchmark datasets to support our theory. The mutual information learned classifiers (MILCs) achieve far better generalization performances than the conditional entropy learned classifiers (CELCs) with an improvement which can exceed more than 10\% in testing accuracy.