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Sample Path Regularity of Gaussian Processes from the Covariance Kernel
While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i. e. the function spaces over which they define a probability measure, is lacking.
Differential geometry with extreme eigenvalues in the positive semidefinite cone
Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and machine learning.
The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle
On Euclidean spaces, the Gaussian kernel is one of the most widely used kernels in applications.
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