NeurIPS 2019poster47 citations
Large-scale optimal transport map estimation using projection pursuit
Cheng Meng, Yuan Ke, Jingyi Zhang, Mengrui Zhang, Wenxuan Zhong, Ping Ma
Abstract
This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a series of one-dimensional OTM problems through iterative random projection. Such methods, however, suffer from slow or none convergence in practice due to the nature of randomly selected projection directions. Instead, we propose an estimation method of large-scale OTM by combining the idea of projection pursuit regression and sufficient dimension reduction. The proposed method, named projection pursuit Monge map (PPMM), adaptively selects the most
BibTeX
@inproceedings{NEURIPS2019_4bbbe6cb,
author = {Meng, Cheng and Ke, Yuan and Zhang, Jingyi and Zhang, Mengrui and Zhong, Wenxuan and Ma, Ping},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Large-scale optimal transport map estimation using projection pursuit},
url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/4bbbe6cb5982b9110413c40f3cce680b-Paper.pdf},
volume = {32},
year = {2019}
}