Propagates soft labels on hypergraphs using optimal transportation.
problem Semi-supervised learning on hypergraphs.
method Wasserstein barycenters and message-passing algorithm.
result Generalization error bounds for 2-Wasserstein distance.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “Wasserstein propagation”
Study shows uniform-time chaos propagation in mean field Langevin dynamics.
problem Understanding the convergence of marginal distributions in mean field dynamics.
method Assumed functional convexity of energy, used -convergence and Wasserstein metrics.
result Uniform-in-time propagation of chaos proved in both -Wasserstein and relative entropy.
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
QP improves Gaussian process inference by minimizing Wasserstein distance.
problem Approximate inference in Gaussian processes using KL divergence is inadequate.
method Quantile Propagation (QP) minimizes Wasserstein distance instead of KL divergence.
result QP outperforms EP and variational Bayes in classification and Poisson regression.
Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.
problem Understanding long-term behavior of finite-particle systems in relation to their mean-field limits.
method Developed uniform-in-time propagation-of-chaos results for continuous-time SVGD using cutoff strategies and finite-dimensional theories.
result Uniform-in-time propagation-of-chaos bounds in various metrics, including Langevin kernel Stein discrepancy, Wasserstein-1, and Wasserstein-2 distances.
WAEs offer a statistical understanding of density estimation and error bounds.
problem Concurrent density estimation with neural network-induced transformations.
method Statistical analysis of WAEs focusing on upper bounds and error propagation.
result Established deterministic upper bounds on WAE errors and explored their resilience.
Framework for quantifying uncertainty in dynamic processes.
problem Quantifying uncertainty in dynamic stochastic processes.
method Define dynamic uncertainty sets and dynamic robust risk measures.
result Dynamic robust risk measures are time-consistent under specific uncertainty sets.
Study shows how SGD in large neural networks behaves as neurons increase.
problem Understanding SGD behavior in overparameterized neural networks.
method Probabilistic approach to continuous-time dynamics of SGD, focusing on particle interactions.
result Particles' interactions asymptotically vanish, leading to a mean-field limit.
Wasserstein-Splitting Gaussian Process Regression for Heterogeneous Online Bayesian Inferencestat.ML
This work improves Gaussian process regression for large, non-stationary data.
problem Scalability issues and performance degradation for non-stationary data.
method Combines variational free energy approximations with online expectation propagation and local splitting steps.
result Incremental adaptation to locality, heterogeneity, and non-stationarity in training data.
ResNets learn the geodesic curve in Wasserstein space.
problem Characterize the dynamics of deep residual networks during training.
method Modeling ResNet dynamics using continuity equations and optimal transport.
result ResNets learn the geodesic curve in the Wasserstein space.
Optimal transport semi-supervised learning improves GNSS multi-path detection.
problem GNSS multi-path interference detection.
method Wasserstein distance based semi-supervised manifold learning.
result Significant improvement in classification accuracy over fully supervised training.
New method reduces bias in neural networks using Wasserstein-2 regularization.
problem Reduces bias in neural network classifiers, especially in image analysis.
method Introduces a Wasserstein-2 regularization term to neural network loss function.
result Improves accuracy and fairness in predictions across different subgroups.
Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility modelsmath.PR
Existence of calibrated local stochastic volatility models proven for non-regular coefficients.
problem Existence of calibrated local stochastic volatility models in finance.
method Investigation of McKean--Vlasov equations with minimal continuity assumptions on coefficients, providing existence and propagation of chaos results.
result Existence of calibrated local stochastic volatility models for appropriate stochastic volatility parameters.
SGMs are robust to practical errors via uncertainty quantification.
problem Robustness of SGMs to practical implementation errors.
method Wasserstein uncertainty propagation (WUP) theorem and Bernstein estimates.
result SGMs are provably robust to multiple sources of error.
Paper justifies ST estimator using pWGF and proposes an improved variant.
problem Theoretical justification for ST estimator for discrete variables.
method Interpreted ST as pWGF simulation and proposed an improved estimator.
result Established theoretical foundation for ST estimator and improved variant.
New Wasserstein divergence improves generative model robustness and structure preservation.
problem Improving generative model robustness and structure preservation.
method Introduces a novel Wasserstein-1 path-space divergence and a WUP theorem.
result Derives robustness and generalization bounds for flow-based models.
Study controlled contagion with state-dependent killing, proving a comparison principle.
problem Analyzing controlled McKean--Vlasov contagion with state-dependent killing.
method Proof of a comparison principle using Wasserstein smooth-gauge comparison and killing-jump absorption estimates.
result Established a comparison principle for the two-population killed-particle HJB.
A GAN method for stochastic boundary conditions in fast dynamics.
problem Uncertainty quantification in fast dynamics and wave propagation.
method Physics-informed GANs for stochastic boundary conditions.
result Improved convergence and better stochastic boundary conditions.
Bayesian Gaussian Processes layer detects out-of-distribution data in medical imaging.
problem Detecting out-of-distribution data in medical imaging tasks.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates enable superior out-of-distribution detection compared to previous methods.
Generative model creates detailed 3D shapes from text descriptions.
problem Creating high-resolution 3D models from natural language descriptions.
method Two-step process: first generating low-resolution shapes, then high-resolution shapes using Conditional Wasserstein GAN framework.
result Improved method generates 3D shapes more faithful to natural language.
Bayesian layer improves image segmentation and out-of-distribution detection.
problem Outlier detection in image segmentation.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates improve out-of-distribution detection.
Improved convergence rates for Stein Variational Gradient Descent in finite-particle settings.
problem Improving convergence rates for Stein Variational Gradient Descent in finite-particle settings.
method Analyzing the time derivative of relative entropy and splitting it into dominant and smaller parts.
result Finite-particle convergence rates of order 1/\sqrt{N} for Kernelized Stein Discrepancy and Wasserstein-2 metrics.
Uniform bounds for neural network convergence without strong convexity assumptions.
problem Understanding the convergence of neural networks in the feature-learning regime.
method Establishing uniform-in-time weak propagation-of-chaos via mean-field deterministic Wasserstein-gradient-flow dynamics.
result Uniform bounds on the difference between infinite-width and finite-width neural network outputs, showing that fewer neurons can achieve a desired loss.
Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-equilibrium statistical mechanics model in Euclidean space consisting of the stochastic gradient flow of a given (possibly singular) quasi-convex N-particle interaction energy. We show that a deterministic "macroscopic" evolution…
DCMA uses generative models to analyze complex treatment effects on outcome distributions.
problem Analyzing complex and nonlinear causal mechanisms through outcome-level summary contrasts.
method Generative learning framework for identifying and estimating treatment effects on entire outcome distributions.
result Reconstructs interventional outcome distributions via Monte Carlo forward simulation, capturing both summary and distributional contrasts.
Proposes variational Gaussian approximations for solving the Kushner equation.
problem Solving the Kushner equation for state estimation with observations.
method Tractable variational Gaussian approximations of proximal losses based on Wasserstein and Fisher metrics.
result The proposed method leads to a Gaussian flow consistent with Kalman-Bucy and Riccati flows.
The paper tackles gradual domain adaptation with manifold-constrained DRO, showing error bounds across distributions.
problem Gradual domain adaptation challenge with manifold-constrained data distributions.
method Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius.
result Theoretical bounds on classification error across distributions, demonstrating error propagation dynamics.
Improved sampling from complex distributions with reduced bias.
problem Reducing bias in high-dimensional sampling algorithms.
method Hierarchical entropy analysis to weaken assumptions and expand scope.
result Bias reduction in low-dimensional marginals scales with lower dimension, not full dimension.
Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transportcs.LG
Differentiable EM for Gaussian Mixture Models improves model integration.
problem Non-differentiability of EM algorithm limits its use in modern learning pipelines.
method Presented and compared several differentiation strategies for EM.
result Differentiable EM enables the use of Mixture Wasserstein distance in machine learning tasks.
SINF models transform arbitrary PDFs to target PDFs using 1D slices.
problem Transforming arbitrary probability distributions to target distributions efficiently.
method Iterative Optimal Transport of 1D slices, maximizing Wasserstein distance.
result SINF models generate high-quality samples and competitive density estimates.
Improved particle approximation for mean-field neural networks.
problem Particle approximation error for mean-field neural networks.
method Improved particle approximation error by leveraging the problem structure in risk minimization.
result Established an LSI-constant-free particle approximation error concerning the objective gap.
Paper proposes a probabilistic alignment method for domain adaptation.
problem Latent distribution mismatch and miscalibrated uncertainty in adapting large-scale models.
method Bayesian latent transport framework with PAC-Bayesian regularization.
result Reduction in latent manifold discrepancy and improved uncertainty calibration.
Unified neural network framework for context-aware Gaussian overbounds in uncertainty propagation.
problem Uncertainty quantification in safety-critical settings requires conservative bounds, but existing methods often fail to compose and are overly conservative.
method Proposes a learning framework that trains neural networks to produce context-aware Gaussian overbounds with provable conservatism.
result The method yields tighter bounds while maintaining conservatism on the enforced grid and in experiments.
Wasserstein GANs fail to approximate Wasserstein distance, leading to their success.
problem Approximating Wasserstein distance in deep generative models.
method Analysis of differences between theoretical setup and training reality.
result Wasserstein GANs' success is due to their failure to approximate Wasserstein distance.
Study on conditions for achieving optimal robustness in statistical estimators.
problem Achieving the optimal robustness of estimators in statistical models.
method Developed a Wasserstein analogue of the Cramer-Rao inequality and investigated conditions for achieving the Wasserstein-Cramer-Rao lower bound.
result Conditions for the existence of asymptotically efficient estimators in one-parameter models and location-scale families.
One of the main challenges in the parametrization of geological models is the ability to capture complex geological structures often observed in the subsurface. In recent years, generative adversarial networks (GAN) were proposed as an efficient method for the generation and parametrization of complex data, showing sta…
Extends Langevin dynamics for constrained domains.
problem Optimization of constrained probability measures.
method Mirror mean-field Langevin dynamics (MMFLD).
result Linear convergence guarantees and propagation of chaos results.
A method for fast estimation of Wasserstein distances using sliced Wasserstein distances.
problem Efficiently computing Wasserstein distances for multiple pairs of distributions.
method Regression on sliced Wasserstein distances to predict true Wasserstein distances.
result The proposed method provides a better approximation of Wasserstein distance than state-of-the-art models, especially in low-data regimes.
We review and implement an efficient method for calculating entropy-regularized Wasserstein loss.
problem Efficiently calculating entropy-regularized Wasserstein loss.
method Batched Sinkhorn iterations for PyTorch implementation.
result Improved computational efficiency in calculating Wasserstein loss.
New method estimates Wasserstein distances more efficiently.
problem Efficient estimation of Wasserstein distances.
method Orthogonal coupling in Monte Carlo estimation.
result Proposes a new variant of sliced Wasserstein distance.
The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.
problem Approximating posterior measures in inverse problems using conditional Wasserstein distances.
method Introduces a conditional Wasserstein distance with restricted couplings and derives its dual.
result Shows that conditional Wasserstein GANs can yield favorable properties for posterior sampling.
New methods improve stability of Sinkhorn algorithm in machine learning.
problem Stability of Sinkhorn semigroups in high-dimensional settings.
method Semigroup analysis based on contraction coefficients and Lyapunov-type operator-theoretic techniques.
result Unified and simplified arguments in Sinkhorn algorithm stability.
Stability of Wasserstein spaces under various convergence types.
problem Stability and finiteness of Wasserstein spaces over singular and non-singular spaces.
method Gromov--Hausdorff convergence and equivariant Gromov--Hausdorff convergence.
result Analogue of Perelman's stability theorem on Wasserstein spaces.
Spherical Sliced-Wassersteinstat.ML
A new spherical Sliced-Wasserstein distance for data on spheres.
problem Defining Wasserstein distance on manifolds, especially spheres.
method Closed-form solutions of the Wasserstein distance on the circle and a new spherical Radon transform.
result A novel spherical Sliced-Wasserstein (SW) discrepancy for data on spheres.
Algorithm samples from Wasserstein barycenter of measures.
problem Sampling from Wasserstein barycenter of measures.
method Gradient flow of multimarginal formulation with penalization.
result Algorithm samples close to Wasserstein barycenter.
New stability bounds for Sinkhorn's algorithm in entropic optimal transport.
problem Stability and convergence of Sinkhorn's algorithm for entropic optimal transport.
method Semiconcavity approach to analyze stability and convergence.
result Exponential convergence of Sinkhorn's algorithm under semiconcavity conditions.
A new robust metric compares distributions more accurately than existing methods.
problem Sensitivity to outliers and sampling discrepancy in Wasserstein distances.
method Introducing k-RPW, a partial p-Wasserstein distance.
result k-RPW converges faster to true distance and is more robust to outliers.
The paper studies scaling limits of Wasserstein metrics on Gaussian mixture models.
problem Understanding the scaling limits of Wasserstein metrics on Gaussian mixture models.
method Scaling limit approach on Gaussian mixture models, including inhomogeneous and extended models.
result Existence of the limit of the Wasserstein metric after renormalization for GMMs with zero variance.