Optimal Transport for Kernel Gaussian Mixture Models

The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT into widely used probabilistic models, such as Gaussian or G...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Oh, Jung Hun, Elkin, Rena, Simhal, Anish Kumar, Zhu, Jiening, Deasy, Joseph O, Tannenbaum, Allen
Format: Article
Language:English
Subjects:
Hilbert space
Kernels
Mass transport
Mathematical analysis
Probabilistic models
Statistical analysis
Online Access:Get full text
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Summary:The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT into widely used probabilistic models, such as Gaussian or Gaussian mixture, have been developed to enhance the capability of modeling complex multimodal densities of real datasets. However, very few studies have explored the OMT problems in a reproducing kernel Hilbert space (RKHS), wherein the kernel trick is utilized to avoid the need to explicitly map input data into a high-dimensional feature space. In the current study, we propose a Wasserstein-type metric to compute the distance between two Gaussian mixtures in a RKHS via the kernel trick, i.e., kernel Gaussian mixture models.
ISSN:2331-8422