Sinkhorn Distances: Lightspeed Computation of Optimal Transport
Optimal transportation distances are a fundamental family of parameterized distances for histograms in the probability simplex. Despite their appealing theoretical properties, excellent performance and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the histograms' dimension exceeds a few hundreds. We propose in this work a new family of optimal transportation distances that look at transportation problems from a maximum-entropy perspective. We smooth the classical optimal transportation problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transportation solvers. We also report improved performance on the MNIST benchmark problem over competing distances.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, the…
RetrievalNear-linear time approximation algorithms for optimal transport via Sinkhorn iteration
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empi…
BIG-bench Machine LearningOnline Sinkhorn: Optimal Transport distances from sample streams
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This…
Sinkhorn Divergences for Unbalanced Optimal Transport
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal …
Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficiently
We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solut…