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arXiv research

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.

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10 results for “max-sliced”

Max-sliced 2-Wasserstein distancemath.PR

Upper bound for max-sliced 2-Wasserstein distance between measures.

problem Estimating distance between probability measures and their empirical counterparts.

method Same technique as previous work, upper bound approach.

result Upper bound for expected max-sliced 2-Wasserstein distance.

max-sliced 2-Wasserstein distance probability measures empirical distribution upper bound

2024-03-04abs ↗pdf ↗

Sharp bounds for max-sliced Wasserstein distancesmath.PR

Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.

problem Estimating the expected max-sliced Wasserstein distance between a probability measure and its empirical distribution.

method Banach space version and operator norm approach for upper bounds.

result Upper bounds for max-sliced Wasserstein distances are essentially matching and sharp up to a log factor.

Wasserstein distance empirical distribution Banach space operator norm symmetric probability measure

2024-03-01abs ↗pdf ↗

Max-Sliced Wasserstein Distance and its use for GANscs.LG

Max-sliced Wasserstein distance improves GAN training on high-dimensional images.

problem Improving GAN training on high-dimensional distributions with reduced hyper-parameters and training time.

method Developed max-sliced Wasserstein distance to reduce projection complexity and sample complexity.

result Trains GANs on high-dimensional images up to 256x256 resolution.

GANs Wasserstein distance max-sliced projection complexity sample complexity

2019-04-11abs ↗pdf ↗

Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHSmath.ST

Max-sliced Wasserstein metric reduces high-dimensional data to 1D for better estimation.

problem Curse of dimensionality in optimal transport.

method Introduces max-sliced Wasserstein metric to reduce high-dimensional problems to 1D.

result Uniform ratio bounds of empirical measures on RKHS concentrate uniformly fast at parametric rates.

max-sliced Wasserstein optimal transport curse of dimensionality reproducing kernel Hilbert space concentration

2024-05-21abs ↗pdf ↗

Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDSstat.ML

This paper improves MDS visualization by adjusting Wasserstein distances for heavy-tailed data.

problem Enhancing Multidimensional Scaling (MDS) for better pattern recognition with heavy-tailed distributions.

method Introduces Max-D-SW, a metric adjustment of Max-Sliced Wasserstein distance that aggregates over orthonormal bases.

result Max-D-SW provides a clear numerical advantage in MDS outcomes, especially for heavy-tailed distributions.

Multidimensional Scaling Wasserstein distance Max-D-SW Heavy-tailed distributions Pattern recognition

2026-06-29abs ↗pdf ↗

Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distancesstat.ML

Paper develops KMS Wasserstein for high-dimensional data reduction.

problem Optimal transport's curse of dimensionality in high-dimensional data.

method Kernel max-sliced (KMS) Wasserstein distance for dimensionality reduction.

result Sharp finite-sample guarantees for KMS

p

-Wasserstein distance.

Optimal transport Wasserstein distance Dimensionality reduction Kernel methods High-dimensional data

2024-05-24abs ↗pdf ↗

Distributional Sliced-Wasserstein and Applications to Generative Modelingstat.ML

A new distance measure balances projection exploration and informativeness.

problem Inefficient and incomplete projection sampling in existing sliced-Wasserstein distances.

method Proposes Distributional Sliced-Wasserstein (DSW) that optimally balances projection exploration and informativeness.

result DSW generalizes Max-SW and can be computed efficiently.

Sliced-Wasserstein Max-Sliced-Wasserstein Generative Modeling Optimal Projection Efficient Computation

2020-02-18abs ↗pdf ↗

Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancesstat.ML

This work improves scalability of Wasserstein distances in high dimensions.

problem Scalability issues in computing Wasserstein distances in high dimensions.

method Empirical convergence rates, robustness to data contamination, and computational methods.

result Established fast rates and robust estimation risks for sliced Wasserstein distances.

Wasserstein distances high dimensions empirical convergence robustness computational methods

2022-10-17abs ↗pdf ↗

Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstructionstat.ML

Improves point-cloud reconstruction by optimizing projections with self-attention.

problem Inefficient and non-metric projection methods for sliced Wasserstein distances.

method Proposes distributional sliced Wasserstein distance with self-attention for permutation-invariant and metric optimization.

result Self-attention amortized distributional projection optimization achieves better performance in point-cloud reconstruction.

point-cloud reconstruction sliced Wasserstein self-attention distributional sliced Wasserstein metricity

2023-01-12abs ↗pdf ↗

On Projection Robust Optimal Transport: Sample Complexity and Model Misspecificationmath.ST

This work improves understanding of projection robust optimal transport distances.

problem Understanding the behavior of minimum Wasserstein estimators in high-dimensional and misspecified models.

method Adopting projection robust (PR) optimal transport, establishing statistical properties, proposing IPRW distance, and providing asymptotic guarantees.

result Established fundamental statistical properties and proposed new distances that outperform Wasserstein distances empirically.

Optimal Transport Wasserstein Distance Projection Robust Statistical Inference Model Misspecification

2020-06-22abs ↗pdf ↗