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.
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48 results for “Wasserstein Penalization”
Improved convergence rates for MLE in mixture models using penalized log-likelihood.
problem Convergence rates for MLE in finite mixture models.
method Penalizing log-likelihood to discourage vanishing mixing weights, using Wasserstein distance and new loss functions.
result Improved convergence rates for some mixture components, faster than traditional methods.
Generative adversarial networks (GANs) are one of the most popular approaches when it comes to training generative models, among which variants of Wasserstein GANs are considered superior to the standard GAN formulation in terms of learning stability and sample quality. However, Wasserstein GANs require the critic to b…
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.
New method approximates sampling from smooth potential distributions using a vanishing penalty.
problem Sampling from smooth potential distributions on high-dimensional spaces.
method Penalized Langevin dynamics (PLD) with vanishing penalty.
result Established upper bound on Wasserstein-2 distance for PLD approximation.
Introduces new metric for Riemannian metrics, extending unbalanced optimal transport.
problem Extending unbalanced optimal transport to Riemannian metrics.
method Dynamic and static formulations of unbalanced optimal transport on Riemannian metrics.
result Wasserstein--Ebin metric provides a new Riemannian structure on the space of Riemannian metrics.
Optimal payoff choice constrained by Bregman-Wasserstein divergence.
problem Maximizing utility under a deviation constraint from a benchmark.
method Solving the problem using Bregman-Wasserstein divergence with a convex function φ.
result Provided the optimal payoff choice in this setting.
Modified Wasserstein metric for Gaussian distributions, invariant to isometries.
problem Distance measurement for latent Gaussian distributions invariant to isometries.
method Modified Benamou-Brenier approach leading to a Procrustes Wasserstein metric.
result For Gaussian distributions, the metric reduces to Euclidean distance between eigenvalues.
Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterationsmath.OC
New algorithm for computing Wasserstein barycenters with guarantees.
problem Computing Wasserstein barycenters with varying regularization strengths.
method Damped Sinkhorn iterations followed by exact maximization/minimization steps.
result First non-asymptotic convergence guarantees for approximating Wasserstein barycenters.
Unsupervised learning of disentangled representations involves uncovering of different factors of variations that contribute to the data generation process. Total correlation penalization has been a key component in recent methods towards disentanglement. However, Kullback-Leibler (KL) divergence-based total correlatio…
Study improves model estimation and variable selection using GANs with Lasso penalty.
problem Variable selection in high-dimensional data with deep networks.
method Conditional Wasserstein Generative Adversarial Networks with Group Lasso penalization.
result Established convergence rate for variable selection in censored survival data.
Wasserstein Auto-Encodersstat.ML
We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution, which leads to a different regularizer than the one used by the Variational Aut…
To address the challenges in learning deep generative models (e.g.,the blurriness of variational auto-encoder and the instability of training generative adversarial networks, we propose a novel deep generative model, named Wasserstein-Wasserstein auto-encoders (WWAE). We formulate WWAE as minimization of the penalized …
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.
Proposes TCWAE to learn disentangled representations using the Wasserstein Autoencoder.
problem Balancing reconstruction fidelity and disentanglement in learning representations.
method TCWAE (Total Correlation Wasserstein Autoencoder) using different KL estimators.
result Competitive results on data sets with known generative factors, and improved reconstructions on unknown factors.
Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradien…
The paper analyzes insurance contracts under distributional uncertainty using Bregman-Wasserstein divergence.
problem Optimal insurance contracts under distributional ambiguity.
method Utilizes Bregman-Wasserstein ball to characterize ambiguity sets, employs robust optimization.
result Derives optimal indemnity functions in closed form and studies their properties.
Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.
problem Entropy Martingale Optimal Transport problem and its associated optimization problem.
method Combines Entropy Optimal Transport and Martingale Optimal Transport theories, with novel penalization terms and constraints.
result Establishes a nonlinear robust pricing-hedging duality, covering various known robust results.
Generative flows learn distributions on low-dimensional manifolds robustly via Wasserstein proximals.
problem Learning distributions supported on low-dimensional manifolds robustly.
method Combining Wasserstein-1 and Wasserstein-2 proximal operators to formulate well-posed continuous-time generative flows.
result The combination of Wasserstein-1 and Wasserstein-2 proximals ensures the well-posedness of generative flows, leading to unique and robust learning.
Proposes HOT method for robust multi-view learning.
problem Inability of traditional methods to handle unaligned and non-distributionally aligned views.
method Hierarchical optimal transport (HOT) method that penalizes sliced Wasserstein distances between different views.
result HOT method achieves robust performance on both synthetic and real-world tasks.
Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only low-quality samples or fail to converge. We find that these problems are often du…
Revisiting Counterfactual Regression through the Lens of Gromov-Wasserstein Information Bottleneckcs.LG
GWIB improves counterfactual regression by balancing latent distributions and reducing selection bias.
problem Selection bias between control and treatment groups negatively impacts counterfactual regression performance.
method GWIB uses Gromov-Wasserstein information bottleneck to maximize mutual information between covariates and outcomes while penalizing kernelized mutual information between latent representations and covariates.
result GWIB consistently outperforms state-of-the-art CFR methods in ITE estimation tasks.
We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution and the latent variable model distribution . We show that the OT problem can be equivalently written in terms of probabilistic encoders, which are constrained to match the pos…
New method aligns brain surfaces based on functional signatures.
problem Inter-individual variability in neuroimaging data.
method Fused Unbalanced Gromov-Wasserstein (FUGW) based on Optimal Transport.
result FUGW significantly increases between-subject correlation of activity.
Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a dif…
Paper proposes MWDE for estimating finite location-scale mixtures.
problem Estimating finite location-scale mixtures using MLE is problematic.
method Investigates minimum Wasserstein distance estimators (MWDE).
result MWDE is consistent and provides a numerical solution.
Study dynamic risk measures with distributional uncertainty using optimal transport.
problem Risk robustification under distributional uncertainty in Markovian models.
method Characterize risk measures via convex monotone semigroups and optimal transport costs.
result Identify generator and correction terms for dynamic risk measures under different scaling regimes.
Develops a new divergence framework that combines -divergences and IPMs.
problem Comparing distributions that are not absolutely continuous.
method Introduces -divergences as a two-stage mass-redistribution/mass-transport process.
result Improves estimation, learning, and uncertainty quantification in GANs for heavy-tailed distributions.
Wasserstein GANs with Gradient Penalty compute a different optimal transport problem called congested transport.
problem Training generative models to produce high-quality synthetic data.
method Wasserstein GANs with Gradient Penalty (WGAN-GP) approach to calculate the Wasserstein 1 distance.
result WGAN-GP computes the minimum of the congested transport problem, not the Wasserstein 1 distance.
A popular heuristic for improved performance in Generative adversarial networks (GANs) is to use some form of gradient penalty on the discriminator. This gradient penalty was originally motivated by a Wasserstein distance formulation. However, the use of gradient penalty in other GAN formulations is not well motivated.…
The variational autoencoder (VAE) imposes a probabilistic distribution (typically Gaussian) on the latent space and penalizes the Kullback--Leibler (KL) divergence between the posterior and prior. In NLP, VAEs are extremely difficult to train due to the problem of KL collapsing to zero. One has to implement various heu…
New autoencoder framework learns structured latent priors.
problem Learning autoencoders with flexible priors.
method Relational regularization on latent prior, scalable algorithms.
result RAE outperforms existing autoencoders in image generation.
To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1 distance. However, it was not clear how cycleGAN-type generative models can be deriv…
Building on a recent framework for distributionally robust optimization, we consider estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of a Wasserstein ambiguity set specifically tailored to this estimation problem, leading to a tractable class of regularized estimators. Speci…
Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative …
CD converges linearly for MCP/SCAD penalized least squares.
problem Recovering sparse signals from data.
method Coordinate descent for MCP/SCAD penalized least squares.
result CD converges linearly to solutions of MCP/SCAD penalized least squares.
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.
AgFlow: Fast Model Selection of Penalized PCA via Implicit Regularization Effects of Gradient Flowcs.LG
AgFlow speeds up model selection in penalized PCA.
problem Efficient model selection in penalized PCA for HDLSS settings.
method Implicit regularization effect of gradient flow to reduce computation complexity.
result AgFlow achieves the complete solution path of L2-penalized PCA.
We consider the Willmore functional on graphs, with an additional penalization of the area where the curvature is non-zero. Interpreting the penalization parameter as a Lagrange multiplier, this corresponds to the Willmore functional with a constraint on the area where the graph is flat. Sending the penalization parame…
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
Develops a method to predict stock returns with time-varying risk premia.
problem Predicting stock returns with time-varying risk premia while maintaining no-arbitrage restrictions.
method Penalized two-pass regression with time-varying factor loadings, incorporating penalization in the first pass and grouping in the second pass.
result The proposed method reduces prediction errors compared to other approaches.
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.
Paper develops a new method for optimal stopping in American options.
problem Optimal stopping in American options with singular generators.
method Entropy-regularized penalization scheme for reflected BSDEs with singular generators.
result Limit of the penalization scheme solves a reflected BSDE with a logarithmically singular generator.
Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome for the so-called optimized certainty equivalent risk measure (OCE) -- including t…
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.
In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for Penalized Likelihood Estimators. Both the convex penalty (such as LASSO) and the nonc…
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.