Proposes a new distance metric for multi-marginal optimal transport.
problem Computational scalability in multi-marginal optimal transport.
method Random one-dimensional projections to construct sliced multi-marginal Wasserstein distance.
result Sliced multi-marginal Wasserstein distance is a metric with dimension-free sample complexity.
Proposes MFSWB for marginal fairness in SWB, improving efficiency and performance.
problem Achieving marginal fairness in SWB averaging.
method Defining MFSWB as a constrained SWB problem, proposing two surrogate problems and a new slicing distribution.
result Surrogate MFSWB problems effectively minimize distances to marginals and encourage marginal fairness.
Advances robustness of metric learning by adversarial margin in input space.
problem Improving robustness of metric learning algorithms.
method Imposing adversarial margin in input space, minimizing perturbation loss.
result Enlarged adversarial margin improves generalization and robustness.
Novel distances between distributions using conditional ground distances.
problem Quantifying distances between statistical multivariate distributions.
method Optimal transport with entropic regularization and ground distance on conditionals.
result Upper bounds for jointly convex distances and improved GMM learning.
Paper proposes a new Wasserstein distance for mixtures of radially contoured distributions.
problem Generalization of Wasserstein distance to non-elliptically contoured distributions.
method Relaxed formulation for mixtures of radially contoured distributions without marginal consistency.
result The new distance yields more stable error and better color distribution in image transfer tasks.
MWGAN tackles multi-marginal matching problem with Wasserstein GAN.
problem Learning mappings to match a source domain to multiple target domains with cross-domain correlations.
method Develops a novel Multi-marginal Wasserstein GAN (MWGAN) with inner- and inter-domain constraints to minimize Wasserstein distance.
result Theoretical and empirical evaluations show MWGAN's effectiveness on balanced and imbalanced translation tasks.
Paper introduces CWDAE for better synthetic data generation.
problem Measuring discrepancy between generative and ground-truth distributions.
method Introduces mixture Cramer-Wold distance for joint and marginal distributional learning.
result CWDAE shows remarkable performance in generating synthetic data.
Gradient penalty improves GAN performance by inducing a large-margin classifier.
problem Improving GAN performance and addressing vanishing gradients.
method A unifying framework of expected margin maximization, showing gradient penalties induce large-margin classifiers.
result Gradient penalties reduce vanishing gradients and produce better generated outputs.
Paper studies statistical properties of DP data synthesis algorithms based on Bayesian networks.
problem Ensuring differential privacy in synthetic data generation for high-dimensional data.
method Introduces random noise to low-dimensional marginals of a probabilistic graphical model (BN) to achieve differential privacy.
result Establishes a rigorous accuracy guarantee for BN-based DP synthetic data generators using total variation (TV) distance.
Proposes a method to learn distance metrics from uncertain data.
problem Challenges of learning distance metrics from large-scale data with uncertainty.
method Margin preserving metric learning framework to learn distance metric and latent examples simultaneously.
result The learned metric is robust to uncertainty and preserves large margin for original data.
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly matc…
The paper proves a margin inequality for separating hyperplanes, useful for analyzing algorithmic bias.
problem Analyzing the implicit bias of algorithms in machine learning.
method Proves a nonsmooth Kurdyka-Lojasiewicz inequality for margin function.
result The bias of algorithm iterates converges at least as fast as the square-root of the margin convergence rate.
New measure predicts deep networks' generalization gap from margin distributions.
problem Predicting deep networks' generalization gap from training data.
method Proposes a measure based on margin distribution across multiple layers.
result Proposed measure correlates strongly with generalization gap on CIFAR datasets.
Paper proposes a deep learning method for person re-identification using set to set distance.
problem Matching images of the same person across different camera views with large appearance variations.
method Uses deep learning to model set to set (S2S) distance, focusing on intra-class compactness and inter-class separation.
result The method effectively finds matched targets in video galleries, outperforming state-of-the-art approaches.
We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.
problem Understanding the behavior of the semi-hard triplet loss function.
method Developed a higher-order asymptotic analysis using the Edgeworth expansion.
result Derived explicit Edgeworth expansions revealing first-order corrections in terms of the third cumulant.
A new metric for comparing HMMs, especially GMM-HMMs, without Monte Carlo samples.
problem Comparing Hidden Markov Models (HMMs) with Gaussian conditional distributions.
method Aggregated Wasserstein metric based on optimal transport between Gaussian mixtures.
result The Aggregated Wasserstein metric is a semi-metric that can be computed efficiently and is invariant to state relabeling.
Improves few-shot learning by adding a large margin to metric-based methods.
problem Few-shot learning's challenge of generalizing well with limited data.
method Unified framework with large margin distance loss function.
result Significant performance improvement with minimal computational overhead.
MMA training maximizes margins for adversarial robustness.
problem Adversarial robustness of neural networks.
method Directly maximizes margins through adaptive adversarial training.
result MMA training improves adversarial robustness compared to fixed ε adversarial training.
Study on convergence rates for optimal transport with regularization.
problem Convergence analysis of divergence-regularized optimal transport.
method Novel methodology using quantization and martingale couplings.
result Sharp rates for various divergences and transport costs.
The paper improves conformal prediction by analyzing the beta law of conditional coverage.
problem Improving finite-sample marginal coverage guarantees for non-i.i.d. data.
method The method uses Wasserstein distances to quantify deviations from the beta law of conditional coverage.
result The framework provides direct bounds on marginal coverage gaps and bad-calibration probabilities.
Paper corrects Max-Margin loss for multi-label tasks.
problem Max-Margin loss inconsistency in multi-label classification.
method Introduced Restricted-Max-Margin loss.
result Consistent loss for multi-label tasks under milder conditions.
New findings show score matching's accuracy doesn't ensure numerical stability in diffusion sampling.
problem Numerical stability issues in diffusion sampling despite small forward-marginal error.
method Constructing a smooth score field with arbitrarily small forward-marginal L2 error, showing nonexplosive behavior and moments of every order. result Euler--Maruyama discretizations can converge in probability even when moments diverge, demonstrating failure of weak convergence.
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.
Proposes a new active learning strategy for deep networks using adversarial examples.
problem Minimizing the number of data annotations needed for training deep neural networks.
method Focuses on examples close to the decision boundary, using adversarial examples to approximate their distance.
result Adversarial active queries lead to faster convergence of CNNs on various datasets.
Large margin approach for deep neural networks.
problem Deep learning's lack of margin enforcement.
method Proposes a novel loss function to enforce margin across layers of deep networks.
result Improved performance on various datasets and tasks.
Neural networks provide bounds for risk aggregation under ambiguous dependence.
problem Quantifying joint effects of risks with uncertain dependencies.
method Dual representation and neural network solution.
result Robust bounds for risk aggregation are derived.
Study improves speaker verification accuracy using angular based embedding learning.
problem Improving discriminative power of embeddings for open-set speaker verification.
method Optimizes angular distance and adds margin penalty, applying various angular margin embedding strategies and proposing inter-class regularization.
result Achieved impressive results with 16.5% improvement in EER and 18.2% improvement in minimum detection cost function.
Analyzes large-margin classifiers under high-dimensional data.
problem Selecting the best classifier among various margin-based methods.
method Investigates asymptotic performance of large-margin classifiers under two component mixture models.
result Analytical results closely match with Monte Carlo simulations.
The paper introduces tests for high-dimensional independence using maximum and average distance correlations.
problem Testing independence in high-dimensional data.
method Characterizes consistency properties, compares test statistics, examines null distributions, and presents a fast chi-square-based procedure.
result The proposed tests are non-parametric and applicable to various metrics.
Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert inf…
The Sinkhorn flow converges to a Wasserstein mirror gradient flow from the Sinkhorn algorithm.
problem Optimizing joint distributions using the Sinkhorn algorithm.
method Wasserstein mirror gradient flow derived from the Sinkhorn algorithm.
result The Sinkhorn flow converges to a Wasserstein mirror gradient flow.
New results on max-entropy distributions with succinct descriptions and stability.
problem Understanding the complexity and stability of max-entropy distributions.
method Polynomial-time algorithms and bounds on bit complexity.
result Polynomial bit complexity of ε-optimal dual solutions to max-entropy convex programs.
Improved SincNet for better speaker recognition.
problem Speaker recognition challenges and the need for better deep learning models.
method Proposes AM-SincNet, a SincNet-based model with an improved AM-Softmax layer.
result Improved speaker recognition performance, achieving a 40% Frame Error Rate reduction.
Optimal transport is #P-hard when components are independent, even with approximate solutions.
problem Computational complexity of optimal transport with independent marginals.
method Proved #P-hardness and developed a pseudo-polynomial time approximation algorithm.
result Optimal transport is #P-hard even with independent components and approximate solutions.
PrAda-GAN improves synthetic data generation under differential privacy.
problem Generating synthetic data under differential privacy with marginal-based methods.
method Sequential generator architecture integrating GAN and marginal-based approaches, with adaptive regularization of Bayes network structure.
result PrAda-GAN outperforms existing methods in privacy-utility trade-off on synthetic and real-world datasets.
Paper studies how to cluster data with a weak oracle, reducing the number of queries needed.
problem Cluster data with limited oracle answers.
method Proposes algorithms for semi-supervised active clustering with weak oracles.
result Shows that a small number of queries is sufficient for effective clustering.
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
Paper defines a new distance metric for comparing learning tasks.
problem Comparing difficulty of learning tasks between source and target.
method Information geometry, optimal transport, coupled transfer distance.
result Coupled transfer distance correlates with fine-tuning difficulty.
New method improves consistency in preference learning for neural networks.
problem Inconsistent surrogate losses in preference learning for neural networks.
method Formulated a margin-shifted ranking framework and introduced Structure-Aware H-consistency. result Proved superior consistency guarantees for capacity-bounded models using heavy-tailed surrogates.
New method for multivariate distribution regression using NPT metric.
problem Regression with multivariate distributional responses and Euclidean predictors.
method Fréchet regression with nonparanormal transport (NPT) metric.
result Efficient estimation and granular interpretation of predictor effects.
POTNet uses penalized optimal transport to generate data without mode collapse.
problem Mode collapse in WGANs leading to poor synthetic data generation.
method POTNet employs marginally-penalized Wasserstein distance for deep generative modeling.
result POTNet effectively captures underlying data structures, including tail behaviors and minor modalities.
Bayesian hierarchical clustering (BHC) is an agglomerative clustering method, where a probabilistic model is defined and its marginal likelihoods are evaluated to decide which clusters to merge. While BHC provides a few advantages over traditional distance-based agglomerative clustering algorithms, successive evaluatio…
Paper calculates robust FVA for OTC derivatives under distributional uncertainty.
problem Distributional uncertainty in over the counter derivatives valuation.
method Wasserstein distance as ambiguity measure, dual formulation of robust FVA optimization.
result Additional FVA charge due to distributional uncertainty measured under various configurations.
SqueezeFit reduces high-dimensional data to lower dimensions while preserving label distances.
problem Label-aware dimensionality reduction in high-dimensional spaces.
method Semidefinite programming relaxation of nearest neighbor classification.
result Provable recovery of a planted projection operator from labeled data.
Bayesian neural flows improve Gaia distance estimates and dust modeling.
problem Improving precision of distance estimates from Gaia DR2 data.
method Normalizing flow for learning flexible color-magnitude diagrams.
result Distance posteriors improved by more than 48% over raw Gaia data.
New metric learning approach for tree data reduces computation cost.
problem Efficiently computing distances between ordered labeled trees.
method Introduced pq-grams and a differentiable weighted pq-gram distance, combined with LMNN for optimization.
result Significantly reduces computation time for tree classification problems.
Novel upper bound for unsupervised domain adaptation considers joint error.
problem Addressing the issue of mixing samples from different classes when matching marginal distributions.
method Proposes a general upper bound that penalizes undesirable joint error, uses constrained hypothesis space, and introduces cross margin discrepancy.
result Our proposal outperforms related approaches in image classification error rates on domain adaptation benchmarks.
A new relaxed framework for pricing illiquid derivatives using bid-ask spreads.
problem Pricing illiquid derivatives with realistic bounds and hedging prices.
method Introducing Bid--Ask Martingale Optimal Transport (BAMOT) that relaxes the exact calibration of model marginals to mid-prices of vanilla options.
result BAMOT yields realistic price bounds and superhedging prices for illiquid derivatives.