Computational optimal transport: With applications to data science
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
Wasserstein distributionally robust optimization: Theory and applications in machine learning
Many decision problems in science, engineering, and economics are affected by uncertain
parameters whose distribution is only indirectly observable through samples. The goal of …
parameters whose distribution is only indirectly observable through samples. The goal of …
Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm
P Dvurechensky, A Gasnikov… - … conference on machine …, 2018 - proceedings.mlr.press
We analyze two algorithms for approximating the general optimal transport (OT) distance
between two discrete distributions of size $ n $, up to accuracy $\varepsilon $. For the first …
between two discrete distributions of size $ n $, up to accuracy $\varepsilon $. For the first …
Partial optimal tranport with applications on positive-unlabeled learning
Classical optimal transport problem seeks a transportation map that preserves the total mass
between two probability distributions, requiring their masses to be equal. This may be too …
between two probability distributions, requiring their masses to be equal. This may be too …
Sliced wasserstein distance for learning gaussian mixture models
Gaussian mixture models (GMM) are powerful parametric tools with many applications in
machine learning and computer vision. Expectation maximization (EM) is the most popular …
machine learning and computer vision. Expectation maximization (EM) is the most popular …
Point-set distances for learning representations of 3d point clouds
Learning an effective representation of 3D point clouds requires a good metric to measure
the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most …
the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most …
Keypoint-guided optimal transport with applications in heterogeneous domain adaptation
Abstract Existing Optimal Transport (OT) methods mainly derive the optimal transport
plan/matching under the criterion of transport cost/distance minimization, which may cause …
plan/matching under the criterion of transport cost/distance minimization, which may cause …
Most: Multi-source domain adaptation via optimal transport for student-teacher learning
Multi-source domain adaptation (DA) is more challenging than conventional DA because the
knowledge is transferred from several source domains to a target domain. To this end, we …
knowledge is transferred from several source domains to a target domain. To this end, we …
On the complexity of approximating Wasserstein barycenters
We study the complexity of approximating the Wasserstein barycenter of $ m $ discrete
measures, or histograms of size $ n $, by contrasting two alternative approaches that use …
measures, or histograms of size $ n $, by contrasting two alternative approaches that use …
Automatic text evaluation through the lens of Wasserstein barycenters
A new metric\texttt {BaryScore} to evaluate text generation based on deep contextualized
embeddings eg, BERT, Roberta, ELMo) is introduced. This metric is motivated by a new …
embeddings eg, BERT, Roberta, ELMo) is introduced. This metric is motivated by a new …