We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Sparse Regularized Optimal Transport with Deformed q -Entropy.
- Authors
Bao, Han; Sakaue, Shinsaku
- Abstract
Optimal transport is a mathematical tool that has been a widely used to measure the distance between two probability distributions. To mitigate the cubic computational complexity of the vanilla formulation of the optimal transport problem, regularized optimal transport has received attention in recent years, which is a convex program to minimize the linear transport cost with an added convex regularizer. Sinkhorn optimal transport is the most prominent one regularized with negative Shannon entropy, leading to densely supported solutions, which are often undesirable in light of the interpretability of transport plans. In this paper, we report that a deformed entropy designed by q-algebra, a popular generalization of the standard algebra studied in Tsallis statistical mechanics, makes optimal transport solutions supported sparsely. This entropy with a deformation parameter q interpolates the negative Shannon entropy ( q = 1 ) and the squared 2-norm ( q = 0 ), and the solution becomes more sparse as q tends to zero. Our theoretical analysis reveals that a larger q leads to a faster convergence when optimized with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. In summary, the deformation induces a trade-off between the sparsity and convergence speed.
- Subjects
UNCERTAINTY (Information theory); STATISTICAL mechanics; DISTRIBUTION (Probability theory); COMPUTATIONAL complexity; QUASI-Newton methods; ENTROPY; TOPOLOGICAL entropy; YANG-Baxter equation
- Publication
Entropy, 2022, Vol 24, Issue 11, p1634
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e24111634