2018/06/19 by Aden Forrow, Jan-Christian Hütter, Forrow, Aden +9 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1806.07348
openalex publication_date 2018/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new structural assumption that is similar to the nonnegative rank of a matrix. Regularizing based on this assumption leads to drastic improvements on high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data. These findings are supported by a theoretical analysis that indicates that the transport rank is key in overcoming the curse of dimensionality inherent to data-driven optimal transport.