Information Theoretic Representation Distillation

Despite the empirical success of knowledge distillation, current state-of-the-art methods are computationally expensive to train, which makes them difficult to adopt in practice. To address this problem, we introduce two distinct complementary losses inspired by a cheap entropy-like estimator. These losses aim to maximise the correlation and mutual information between the student and teacher representations. Our method incurs significantly less training overheads than other approaches and achieves competitive performance to the state-of-the-art on the knowledge distillation and cross-model transfer tasks. We further demonstrate the effectiveness of our method on a binary distillation task, whereby it leads to a new state-of-the-art for binary quantisation and approaches the performance of a full precision model. Code: www.github.com/roymiles/ITRDComment: BMVC 202

DiME: Maximizing Mutual Information by a Difference of Matrix-Based Entropies

We introduce an information-theoretic quantity with similar properties to mutual information that can be estimated from data without making explicit assumptions on the underlying distribution. This quantity is based on a recently proposed matrix-based entropy that uses the eigenvalues of a normalized Gram matrix to compute an estimate of the eigenvalues of an uncentered covariance operator in a reproducing kernel Hilbert space. We show that a difference of matrix-based entropies (DiME) is well suited for problems involving the maximization of mutual information between random variables. While many methods for such tasks can lead to trivial solutions, DiME naturally penalizes such outcomes. We compare DiME to several baseline estimators of mutual information on a toy Gaussian dataset. We provide examples of use cases for DiME, such as latent factor disentanglement and a multiview representation learning problem where DiME is used to learn a shared representation among views with high mutual information

Simple stopping criteria for information theoretic feature selection

Feature selection aims to select the smallest feature subset that yields the minimum generalization error. In the rich literature in feature selection, information theory-based approaches seek a subset of features such that the mutual information between the selected features and the class labels is maximized. Despite the simplicity of this objective, there still remain several open problems in optimization. These include, for example, the automatic determination of the optimal subset size (i.e., the number of features) or a stopping criterion if the greedy searching strategy is adopted. In this paper, we suggest two stopping criteria by just monitoring the conditional mutual information (CMI) among groups of variables. Using the recently developed multivariate matrix-based Renyi's \alpha-entropy functional, which can be directly estimated from data samples, we showed that the CMI among groups of variables can be easily computed without any decomposition or approximation, hence making our criteria easy to implement and seamlessly integrated into any existing information theoretic feature selection methods with a greedy search strategy.Comment: Paper published in the journal of Entrop