New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
pyLOT library simplifies machine learning on 3D point clouds via linearized optimal transport.
problem Performing machine learning tasks on 3D point clouds.
method Linearized optimal transport (LOT) to embed distributions into Hilbert space, enabling linear machine learning.
result Downstream tasks on embedded representations are simplified to linear operations.
The paper studies optimal transport in linear quadratic systems and derives interpolation inequalities.
problem Optimal transport problem in Linear Quadratic optimal control systems.
method Well-posedness of the Monge problem, regularity of optimal transport map, displacement interpolation of measures.
result Derivation of general interpolation inequalities for entropy functionals.
Optimal transport aligns source and target distributions for linear regression in 2D.
problem Domain adaptation for linear regression in 2D with limited target data.
method Combining K-means and optimal transport for estimating geometric transformations.
result Optimal transport recovers geometric transformations like rotations, translations, and homotheties.
Extends Optimal Transport to multiple agents, aiming for equitable and optimal distribution.
problem Sharing costs or goods equitably among multiple agents with different preferences.
method Minimizes the maximum transportation cost or maximizes the minimum utility.
result Provides a new algorithm faster than standard linear programming.
Paper relaxes optimal transport using convex functions for data science.
problem Optimal transport problem on finite spaces.
method Relaxation via strictly convex functions (Kullback-Leibler divergence, Bregman divergences). Gradient descent iterative process.
result Mathematical foundations and iterative process for the relaxed optimal transport problem.
New metrics compare rational spectra using optimal transport.
problem Comparing rational spectra efficiently and accurately.
method Optimal transport and linear-systems theory.
result Established connection to Wasserstein distance.
Paper connects surface shape analysis and unbalanced optimal transport.
problem Computing the SRNF shape distance on piecewise linear surfaces.
method Characterizes SRNF shape distance as WFR distance pullback, proposes new algorithm for WFR distance computation.
result Direct computation of SRNF shape distance on piecewise linear surfaces.
The Sinkhorn-Knopp derivatives converge with linear rate.
problem Optimal transport problem with entropic regularization.
method Iterative proportional fitting procedure.
result Derivatives converge with linear rate.
GOAT improves graph matching speed and accuracy using optimal transport.
problem Efficiently matching large graphs in various applications.
method Replaces linear assignment with optimal transport methods.
result GOAT provides improvements in speed and accuracy.
New algorithm for linear bandits tackles Optimal Transport problems.
problem Optimal Transport problems not covered by traditional linear bandits.
method Embed actions into a Hilbertian subspace, penalize optimism, use least-squares estimation.
result Achieves same regret bounds as OFUL but interpolates between i l d e O ( T ) ilde{\mathcal O}(\sqrt{T}) i l d e O ( T ) and O ( T ) {\mathcal O}(T) O ( T ) . Optimal transport aligns rotated linear regression models across domains.
problem Aligning rotated linear regression models across domains with differing statistical properties.
method Combines K-means clustering, OT, and SVD to estimate rotation angle and adapt regression model.
result Optimal transport map recovers underlying rotation in R 2 \mathbb{R}^2 R 2 . LOT framework speeds up event distance computation in collider physics.
problem Computational inefficiency in quantifying event distances.
method Linearized Optimal Transport (LOT) for efficient computation.
result LOT significantly reduces computational cost without sacrificing accuracy.
Algorithm classifies point clouds using deep set linearized optimal transport.
problem Classifying point clouds efficiently and accurately.
method Deep Set Linearized Optimal Transport, ICNNs, and a discriminator network.
result Efficiently distinguishes between various classes of point clouds.
Fast algorithm for online optimization on transport polytopes.
problem Optimizing convex objectives on transport polytopes.
method Mirror Sinkhorn algorithm combining Sinkhorn scaling and mirror descent.
result Robust and efficient online optimization for convex objectives.
New scalable algorithm for non-negative linear regression with entropy-regularized OT loss.
problem Generalizing task-specific linear models to broader applications.
method Sinkhorn-like scaling iterations for convex penalty and datafit terms.
result Simple multiplicative updates for various penalty and datafit terms.
The paper extends optimal transport for linear separability of sheared distributions in supervised learning.
problem Learning on the space of probability measures using shifts and scalings.
method Embedding probability measures into L 2 L^2 L 2 spaces using optimal transport, then applying regular machine learning techniques. result Sheared distributions can be linearly separated under certain conditions, with bounds on transformations.
LOT embeds distributions for linear separability and classification.
problem Distribution discrimination in various scientific fields.
method Linear Optimal Transport (LOT) embedding into L 2 L^2 L 2 space. result LOT embeds distributions into linearly separable spaces for certain transformations and perturbations.
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space, and enables the direct use of generic supervised and unsupervised learning algorit…
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, their computation involves the resolution of a linear program whose cost is prohibitive whenever the hi…
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
The paper examines properties of GW optimal transport plans, showing they can be sparse and permutation-supported.
problem Properties of Gromov-Wasserstein optimal transport plans.
method Exploration of sparsity, permutation support, and cyclical monotonicity properties.
result GW optimal plans can be sparse and permutation-supported under certain conditions.
A new framework for generative modeling using value-driven transport.
problem Developing efficient methods for generative modeling.
method A discrete-time stochastic control formulation of measure transport, formulated as a linear program with dual variables corresponding to the optimal value function.
result Well-trained VDT policies lead to straight transport paths that can be simulated quickly and robustly.
A new algorithm reduces the complexity of solving optimal transport problems.
problem Optimal transport problem with linear constraints.
method Primal-dual accelerated stochastic gradient descent with variance reduction (PDASGD).
result Achieves the best-known computational complexity of O ~ ( n 2 / ε ) \widetilde{\mathcal{O}}(n^2/ε) O ( n 2 / ε ) for OT problems. Survey of Sinkhorn algorithm for optimal transport, emphasizing its geometric origins.
problem Solving optimal transport problems efficiently and accurately.
method Discretization of a non-linear integral equation.
result Geometric interpretation and discretization of the Sinkhorn algorithm.
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 empirical performance, it is unknown whether general optimal transport distances can be approximated in …
New framework for efficient optimal transport distances between Markov chains.
problem Efficient computation of optimal transport distances between Markov chains.
method Developed a new perspective on optimal transport distances using discounted occupancy couplings and linear programming.
result Introduced Sinkhorn Value Iteration (SVI) for efficient calculation of optimal transport distances.
A new method for efficient optimal partial transport in 1D.
problem Limitation of equal mass assumption in optimal transport.
method Sliced Optimal Partial Transport (Sliced-OPT) algorithm.
result Sliced-OPT demonstrates computational and accuracy benefits.
A mesh-free method solves continuum-marginal optimal transport problems.
problem Recovering minimum-energy velocity fields from time-continuous probability marginals.
method Embeds weak continuity equation in a reproducing kernel Hilbert space, optimizing with mini-batch stochastic methods.
result Accurately recovers drift and maintains marginal consistency in synthetic experiments.
Two log-linear approximations speed up optimal transport for deep learning applications.
problem Computing optimal transport in high dimensions is computationally expensive.
method Locality-sensitive hashing (LSH) and Nyström approximation with LSH-based sparse corrections.
result Log-linear time algorithms for entropy-regularized OT perform well in high-dimensional spaces.
POTD estimates SDR subspace using optimal transport for binary response.
problem Insufficient performance of existing SDR methods for categorical responses.
method Principal optimal transport direction (POTD) using optimal transport coupling.
result POTD exclusively estimates SDR subspace for error-free class labels.
We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Ampère type arising from optimal mass transport. Our main result is an exponential rate of convergence for solutions of this evolution equation to the stationary solution of the optimal transport problem. We …
OT-ICA uses optimal transport to find independent components, outperforming traditional methods.
problem Finding independent components from linear mixtures of signals.
method OT-ICA uses the squared Wasserstein distance to maximize non-Gaussianity, optimizing projections via gradient descent.
result OT-ICA outperforms traditional proxy-based methods in various applications.
Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.
problem Optimal transport with relaxed marginal conditions.
method Reformulate UOT as non-negative penalized linear regression, propose multiplicative updates.
result Efficient algorithms for UOT with quadratic penalties, continuity of solutions.
Proposes batch version of Greenkhorn for multimarginal OT, proving convergence.
problem Optimal transport problems with multiple marginals.
method Batch Greenkhorn algorithm, iterative Bregman projections, greedy control.
result Global linear rate of convergence and explicit iteration complexity bounds.
The study establishes stability in WMOT, crucial for finance with imprecise data.
problem Stability in weak martingale optimal transport for finance with imprecise data.
method Established stability through rigorous mathematical analysis.
result Stability of WMOT is proven, with applications to VIX futures and Brownian motion.
A new method for generating SPX and VIX risk scenarios using perturbed optimal transport.
problem Generating accurate risk estimates for SPX and VIX without full recalibration.
method A joint optimal transport calibration with perturbation methodology for sensitivities, combined with Skew Stickiness Ratio dynamics.
result The proposed method produces accurate risk estimates relative to full recalibration and is computationally faster.
Study bounds financial path expectations using martingale distributions.
problem Bounding path-dependent financial expectations over martingale distributions.
method Relaxed martingale optimal transport problem, approximated via linear programming.
result Empirical relaxation can be approximated within O(n^(-1/2)) error.
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 transport have been studied in depth: unbalanced transport, which is robust to the presence of outli…
Sliced Optimal Transport simplifies OT for fast computation.
problem Efficient computation of distances and barycenters for probability measures.
method Combines OT, integral geometry, and statistics for fast computation.
result Retains rich geometric structure while speeding up computations.
A new method matches measures across different spaces using cost-regularized optimal transport.
problem Matching measures in different spaces without aligned data.
method Cost-regularized optimal transport formulation to match measures across two Euclidean spaces.
result Demonstrated applicability to single-cell spatial transcriptomics/multiomics matching tasks.
New method for optimal transport with missing data, debiased and efficient.
problem Solving optimal transport between two distributions with missing values.
method Debiasing Wasserstein distance for empirical Gaussian distributions, entropic regularized optimal transport using ISVT.
result Efficient and consistent estimation of entropic regularized optimal transport.
Paper introduces non-linearity signature to measure deep neural network performance.
problem Difficulty in explaining performance differences among similar DNN architectures.
method Affine Optimal Transport mappings to measure non-linearity.
result Signature provides better understanding of DNN inner workings.
Entropy regularized OT test assesses independence between samples.
problem Testing independence between two samples.
method Entropy regularized optimal transport.
result Non-asymptotic bounds for test statistic established.
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
OTF uses optimal transport to measure classifier fairness.
problem Measuring and reducing unfairness in classifier predictions.
method Introduces Optimal Transport to Fairness (OTF) to quantify and reduce unfairness.
result OTF improves the balance between classifier performance and fairness.
It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these method…
s-OTDD compares datasets efficiently without training, robust to class variations.
problem Efficiently compare datasets without training or class variations.
method Moment Transform Projection (MTP) and sliced optimal transport.
result s-OTDD correlates with optimal transport and transfer learning performance.