Geometry in Machine Learning
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (30 September 2020)
Special Issue Editors
Interests: optimization; machine learning; deep learning
Interests: Information theory; machine learning; convex geometry
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Recent years have seen a surge of interest in developing geometric techniques for analyzing machine learning algorithms. Much of this work is motivated by the need to understand the performance of deep learning-based algorithms that have revolutionized modern machine learning over the past decade. Methods from geometry have been successfully used to gain insight into three crucial aspects of modern machine learning: generalization, robustness, and optimization. Some examples include analyzing the generalization properties of interpolating classifiers, the relation between smoothness and curvature of classification boundaries to the robustness and generalization performance of the classifier, and the impact of parametrization and choice of optimization algorithm on the quality of a learned model. Optimal transport theory, which lies at the intersection of geometry and probability, has found applications in the theoretical analysis of machine learning algorithms and has also been used to propose novel generative models. Other mathematical areas such as differential geometry and information geometry have been applied to investigate learning and optimization on manifolds.
In this Special Issue, we welcome submissions related to the geometry of deep learning, applications of optimal transport, information geometry, and high-dimensional geometry for the theoretical analysis of machine learning algorithms. This is a highly interdisciplinary research topic, and we invite contributions from the mathematics, computer science, and engineering communities. Through this issue, we hope to highlight and strengthen the deep connections between geometry and machine learning.
Prof. Mikhail Belkin
Prof. Varun Jog
Guest Editors
Manuscript Submission Information
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Keywords
- manifold learning
- optimal transport
- differential geometry
- robust machine learning
- generalization
- optimization
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