Low-Rank Optimal Transport: Approximation, Statistics and Debiasing
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to improve more complex methods (e.g. balanced attention in transformers or self-supervised learning). To scale to more challenging problems, there is a growing consensus that OT requires solvers that can operate on millions, not thousands, of points. The low-rank optimal transport (LOT) approach advocated in (Scetbon et al., 2021) holds several promises in that…
Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds of sizes nnn and mmm in Rdmathbb{R}^dRd, entropic OT (EOT) solvers have emerged as the most reliable tool to either solve the Kantorovich problem and…
Optimal transport (OT) theory focuses, among all maps that can morph a probability measure onto another, on those that are the "thriftiest", i.e. such that the averaged cost between and its image be as small as possible. Many computational approaches have been proposed to estimate such Monge maps when is…
Learning meaningful representations of complex objects that can be seen through multiple (k≥3kgeq 3k≥3) views or modalities is a core task in machine learning. Existing methods use losses originally intended for paired views, and extend them to kkk views, either by instantiating 12k(k−1)tfrac12k(k-1)21k(k−1) loss-pairs, or by using reduced embeddings, following…