@inproceedings{
oh2023optimal,
title={Optimal Transport for Kernel Gaussian Mixture Models},
author={Jung Hun Oh and Rena Elkin and Anish Kumar Simhal and Jiening Zhu and Joseph O Deasy and Allen Tannenbaum},
booktitle={OPT 2023: Optimization for Machine Learning},
year={2023},
url={https://openreview.net/forum?id=37Oh63lj1x}
}
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.
Optimal Transport for Kernel Gaussian Mixture Models
Jung Hun Oh Rena Elkin Anish Kumar Simhal Jiening Zhu Joseph O Deasy Allen Tannenbaum