Curvature Enhanced Manifold Sampling
Keywords: Manifold learning, Data augmentation, Regression
Abstract: Over-parameterized deep learning models, characterized by their large number of parameters, have demonstrated remarkable performance in various tasks. Despite the potential risk of overfitting, these models often generalize well to unseen data due to effective regularization techniques, with data augmentation being one of the most prominent methods. This strategy has proven effective in classification tasks, where label-preserving transformations are applicable. However, the application of data augmentation in regression problems remains underexplored. Recently, a new *manifold learning* approach for sampling synthetic data has been introduced, and it can be viewed as utilizing a first-order approximation of the data manifold. In this work, we propose to extend this direction by providing the fundamental theory and practical tools for approximating and sampling general data manifolds. Further, we introduce the curvature enhanced manifold sampling (CEMS) data augmentation method for regression. CEMS is based on a second-order encoding of the manifold, facilitating sampling and reconstruction of new points. Through extensive evaluations on multiple datasets and in comparison to several state-of-the-art approaches, we demonstrate that CEMS is superior in in-distribution and out-of-distribution tasks, while incurring only a mild computational overhead.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 6080
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