Proposes m-POT to improve m-OT's misspecified mappings issue.
problem Misspecified mappings in mini-batch optimal transport.
method Partial optimal transport (POT) between mini-batch empirical measures.
result m-POT alleviates incorrect mappings compared to current methods.
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.
New algorithms solve partial optimal transport problems for applications like PU learning.
problem Optimal transport constraints on equal mass distributions limit applicability.
method Developed exact algorithms for partial Wasserstein and Gromov-Wasserstein problems.
result Partial Wasserstein metrics show effectiveness in positive-unlabeled learning.
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).
New bounds for PDA using partial optimal transport improve domain alignment.
problem Scarcity of labeled target data with abundant source data.
method Derive theoretical bounds based on partial optimal transport.
result Theoretical bounds support partial Wasserstein distance for domain alignment.
New forms of multi-marginal POT problem derived for computational efficiency.
problem Optimizing transport between multiple unbalanced measures with limited supports.
method Developed two equivalence forms of the POT problem and an optimization algorithm, ApproxMPOT.
result ApproxMPOT algorithm achieves optimal value with complexity ildeO(m3(n+1)m/ε2). Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
BalLOT uses optimal transport for balanced k-means clustering.
problem Balanced k-means clustering of data. method BalLOT is an optimal transport approach to alternating minimization.
result BalLOT provides theoretical guarantees for exact and partial recoveries of planted clusters.
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.
Optimal Transport enhances machine learning with new methods.
problem Comparing and manipulating probability distributions in machine learning.
method Probabilistic framework rooted in rich history and theory.
result New solutions in generative modeling and transfer learning.
Improved persistence spheres map measures to functions, stable under partial transport.
problem Representing and comparing measures in topological machine learning.
method Persistence spheres map measures to continuous functions on the sphere, stable under 1-Wasserstein partial transport.
result Persistence spheres provide a stable, parameter-free representation of measures, improving upon existing methods.
PROTOCOL tackles imbalanced multi-view clustering by enhancing contrastive learning.
problem Class imbalance in real-world multi-view data.
method PROTOCOL uses partial optimal transport to perceive and mitigate imbalance, enhancing contrastive learning.
result PROTOCOL significantly improves clustering performance on imbalanced multi-view data.
New algorithm solves online resource allocation problems efficiently.
problem Dynamic resource allocation in operations research.
method Minimal Selection Principle and MSoE algorithm.
result Ensures optimal cumulative regret bounds in dynamic resource allocation.
New method for comparing different mass measures on tree structures using entropy partial transport.
problem Comparing nonnegative measures with different masses on tree structures.
method Entropy Partial Transport (EPT) on extended trees, regularized for fast computation and negative definiteness.
result First closed-form solution for unbalanced OT on tree structures.
Unified approach solves Kyle model with dynamic information.
problem Solving a generalized Kyle model with dynamic information.
method Monge-Kantorovich duality and backward stochastic partial differential equations.
result Characterization of optimal strategies and pricing rules.
New algorithm infers trajectories from partial observations using optimal transport.
problem Inferring trajectories from partial observations of coupled systems.
method Extends MFL algorithm to latent SDEs using observable state space models and partial observations.
result Experiments show significant outperformance over latent-free baseline.
Partial soft-matching distance improves neural representation comparison by allowing some neurons to remain unmatched.
problem Neural representations are noisy and contain outliers, making traditional matching methods unreliable.
method Extends soft-matching distance to a partial optimal transport setting, allowing some neurons to remain unmatched.
result Partial soft-matching provides robust correspondences that are more reliable under noise and outliers.
New control methods improve dynamic measure transport paths.
problem Improving paths for dynamic measure transport.
method Connecting mean-field games to optimization problems for learning paths, advocating for smoothness of velocities.
result Our method recovers more efficient and smooth transport models compared to untilted paths.
New method reduces label and data shifts between domains using optimal transport.
problem Label shift between source and target domains in domain adaptation.
method Developed theory and LDROT method to mitigate label and data shifts.
result Theoretical and experimental validation of LDROT's effectiveness.
DDPM encoder matches optimal transport for natural images.
problem Understanding theoretical properties of DDPM latent space.
method Showed DDPM encoder matches optimal transport for common distributions.
result DDPM encoder map coincides with optimal transport map for natural images.
Partial Wasserstein Covering aims to identify missing patterns in datasets.
problem Identifying missing patterns in datasets compared to actual applications.
method Formulated as a discrete optimization problem with partial Wasserstein divergence. Proved submodular, allowing greedy approximation. Proposed quasi-greedy algorithms with acceleration techniques.
result Efficiently fills gaps and finds missing scenes in real driving scenes datasets.
FedAVOT improves federated learning by aligning user distributions.
problem Partial client participation leads to biased and unstable updates in federated learning.
method Formulates aggregation as masked optimal transport to align availability and importance distributions.
result Achieves a standard O(1/√T) rate, independent of the number of participating users per round.
Optimal transport for functional data using Hilbert-Schmidt operators.
problem Optimal transport for distributions on function spaces with partially represented stochastic maps.
method Regularization technique to restrict transport maps to Hilbert-Schmidt operators, developing an efficient algorithm.
result Existence, uniqueness, and consistency of the Hilbert-Schmidt operator estimate for the transport map.
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.
Partial fusion combines neural networks to balance accuracy and efficiency.
problem Balancing accuracy and computational cost in neural networks.
method Extending weight aggregation methods based on neuron-level similarity, using partial optimal transport to match similar neurons.
result Achieves a flexible tradeoff between computational cost and performance.
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come. In this article, by considering the space of persistence diagrams as a space of d…
FairPOT balances fairness and AUC performance by selectively transforming risk scores.
problem Balancing fairness and AUC performance in high-stakes domains.
method FairPOT uses proportional optimal transport to selectively transform risk scores.
result FairPOT consistently improves fairness with minimal AUC degradation or even positive gains.
Paper develops methods to estimate generalization error across domains.
problem Uncertainty in predicting unseen data distributions.
method Partial identification and transportability theory, Neural Causal Models.
result First general estimation technique for transportability problems.
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be approximated using linear programming (LP) problems which result from a discretisa…
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Connections to geometry, inequalities, and partial differential equations will be discussed, focusing in particular on recen…
Study of a risk-averse informed trader in a multi-asset market with non-Gaussian prices.
problem Existence of equilibrium in a multi-asset market with non-Gaussian prices and a risk-averse informed trader.
method Constructed equilibrium using Fokker-Planck equation and coupled partial differential equations with an optimal transport constraint.
result Equilibrium exists in a market with multiple assets and non-Gaussian prices.
Study robust distribution estimation with Wasserstein distance, achieving optimal risk.
problem Robust distribution estimation under adversarial corruption.
method Combining partial OT and minimum distance estimation, proving structural properties and deriving a novel dual form.
result Achieves minimax-optimal robust estimation risk in many settings.
New method for conditional sampling using M-GANs, likely-free inference.
problem Conditional sampling of probability measures.
method Developed a novel computational approach called M-GANs based on block triangular transport.
result Accurate sampling of conditional measures in various applications.
In this note we will adapt Topping's L-optimal transportation theory for Ricci flow to a more general situation, i.e. to a closed manifold (M,gij(t)) evolving by ∂tgij=−2Sij, where Sij is a symmetric tensor field of (2,0)-type on M. We extend some recent results of Topping, Lott …
The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "conn…
A study on optimizing self-attention in tabular data using Optimal Transport.
problem Improving efficiency and accuracy of self-attention in tabular classification tasks.
method Developed an OT-based algorithm to generate class-specific dummy Gaussian distributions and train an MLP.
result Achieved comparable accuracy to Transformers with reduced computational cost and efficiency.
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…
Defines tangent spaces on causal sets using partial derivatives and metrics.
problem Defining geometric structures on causal sets.
method Using partial derivatives and metrics to define tangent spaces, connection, curvature, parallel transport, and geodesics.
result Approaches expected values for a flat spacetime as density increases.
Novel stability bounds for OT maps improve density estimation.
problem Estimating optimal transport maps between probability distributions.
method Developed novel stability bounds for OT maps, reducing the problem to density estimation.
result Stability bounds allow for sharper guarantees without smoothness assumptions.
A new method for transporting unbalanced measures on graphs efficiently.
problem Optimal transport for measures with unequal total masses on graph metric spaces.
method Developed a novel variant of entropy partial transport (Orlicz-EPT) with Orlicz geometric structure, leading to Orlicz-Sobolev transport (OST).
result OST can be efficiently computed by solving a univariate optimization problem, significantly faster than Orlicz-EPT.
FSBM improves matching efficiency with minimal supervision.
problem Scalability vs. minimal supervision in matching frameworks.
method FSBM uses a small portion of pre-aligned pairs as state feedback to guide non-coupled samples.
result FSBM accelerates training and enhances generalization.
The paper constructs denoisers that recover the Brenier map from higher-order score functions.
problem Estimating the Brenier map from noisy data.
method Constructs a hierarchy of denoisers using higher-order score functions.
result The T∞ denoiser recovers the Brenier map from the additive Gaussian model. Measures time-delay embedding for noisy, sparse data.
problem Applying Takens' embedding theorem to real-world, noisy data.
method Formulated a measure-theoretic generalization of the embedding theorem, using optimal transport.
result Reconstructed full state of dynamical systems from time-lagged partial observations robust to noise and sparsity.
A new training method for normalizing flows without samples.
problem Training normalizing flows without samples but with energy functions.
method Interpolates energy functions to find a transport vector field.
result Optimizes transport vector field and energy function to satisfy continuity equation.
This paper introduces a new formulation of the Conic Gromov-Wasserstein distance for comparing complex network structures.
problem Comparing measures of unequal mass and complex network structures.
method Novel semi-coupling formulation and extension to hypernetworks.
result Establishes fundamental properties and robustness of CGW metric.
Under a complete Ricci flow, we construct a coupling of two Brownian motion such that their L0-distance is a supermartingale. This recovers a result of Lott [J. Lott, Optimal transport and Perelman's reduced volume, Calc. Var. Partial Differential Equations 36 (2009), no. 1, 49--84.] on the monotonicity of…
A new method steers Gaussian distributions with minimal effort.
problem Steering high-dimensional Gaussian distributions efficiently.
method Sliced feedback controller using one-dimensional projections and averaging.
result The method steers Gaussian distributions to targets efficiently.
The paper studies stability of mean-field variational inference for log-concave distributions.
problem Stability of mean-field variational inference for log-concave distributions.
method Novel approach via linearized optimal transport, lifting non-convex problem to convex optimization over transport maps.
result Dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in 2-Wasserstein distance.