Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction
This work addresses the challenge of learning diverse and discriminative features for classification and clustering tasks, with broad applicability in machine learning, though it builds on existing information-theoretic frameworks.
The paper tackles the problem of learning intrinsic low-dimensional structures from high-dimensional data by proposing the principle of Maximal Coding Rate Reduction (MCR^2), which maximizes the coding rate difference between the whole dataset and individual classes, resulting in representations that are significantly more robust to label corruptions in classification and achieve state-of-the-art results in clustering mixed data.
To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.