Manifold Density Estimation via Generalized Dequantization
Abstract: Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are not well-modeled by supposing
that their underlying geometry is Euclidean. Instead, it can be useful to model such data as lying on a manifold with some known structure. For instance, some kinds of data may be known to lie on the surface of a sphere. We propose a method for estimating densities on manifolds which combines normalized flows in a Euclidean space, a change of variables, and marginalization. The method is applicable where the appropriate change of variables is tractable, for example, the sphere, tori, and the orthogonal group.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=5Ltgy0q1Q5
Changes Since Last Submission: We addressed the editor's remarks about clarity and organization.
Assigned Action Editor: ~marco_cuturi2
Submission Number: 849
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