A new algorithm improves Wasserstein discriminant analysis for better data classification.
problem Improving data classification in machine learning.
method Bi-level nonlinear eigenvector algorithm (WDA-nepv) for optimal transport and trace ratio optimizations.
result WDA-nepv enhances classification accuracy and scalability.
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA selects the projection matrix that maximizes the …
The paper explores multidimensional critic output in GANs, improving convergence and diversity.
problem Underexplored in GANs literature, multidimensional critic output.
method Generalized Wasserstein GAN framework, SRVT block, maximal p-centrality discrepancy.
result High-dimensional critic output improves GAN performance in convergence and diversity.
WGANs improve probability distribution approximation with depth and width trade-offs.
problem Approximating complex probability distributions accurately.
method Wasserstein GANs with GroupSort discriminators, quantified generalization bound.
result High-capacity discriminators are crucial for WGANs' performance.
Wasserstein GANs are shown to have hidden convexity, enabling exact solutions with convex optimization.
problem Non-convex and non-concave optimization in GANs.
method Convex duality analysis of Wasserstein GANs with two-layer neural network discriminators.
result Wasserstein GANs can be solved exactly with convex optimization under certain conditions.
In this paper, we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the discriminative function space commonly suffer from the problem that the gradient produced by …
The insurance industry uses predictions based on customer characteristics, but this can lead to discrimination. We propose using Wasserstein barycenters to mitigate biases.
problem Discrimination in insurance predictions based on sensitive features like gender or race.
method Propose using Wasserstein barycenters instead of simple scaling to mitigate biases in insurance predictions.
result Demonstrates the effectiveness of Wasserstein barycenters in mitigating biases in insurance predictions.
Wasserstein-GANs have been introduced to address the deficiencies of generative adversarial networks (GANs) regarding the problems of vanishing gradients and mode collapse during the training, leading to improved convergence behaviour and improved image quality. However, Wasserstein-GANs require the discriminator to be…
While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent works have shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al. suggests a dilemma about GANs' statistical properties: powerful d…
Paper introduces a new method to improve GANs by leveraging the discriminator's energy.
problem Improving the quality of generated samples in GANs.
method Discriminator Contrastive Divergence (DCD) method.
result Significant improvement in generation quality on synthetic and real-world data.
Simplified GAN model shows how discriminator improves generalization.
problem Understanding GAN's generalization ability and avoiding memorization.
method Analyzing a simplified GAN model with early stopping and Wasserstein metric.
result Generalization error escapes from curse of dimensionality with early stopping.
Optimized GAN discriminator using polyharmonic interpolation.
problem Optimizing the discriminator in GANs with higher-order gradient regularization.
method Polyharmonic interpolation and variational calculus.
result The optimal discriminator is a polyharmonic radial basis function.
New findings show fixed-kernel discriminators are weaker than feature-learning ones.
problem Comparing performance of fixed-kernel and feature-learning discriminators.
method Using function classes F2 and F1, constructing pairs of distributions, and linking IPMs with sliced Wasserstein distances. result Fixed-kernel IPM and SD cannot discriminate certain distributions that feature-learning IPM and SD can.
Study on deep matrix factorization with Bures-Wasserstein loss, focusing on critical points and convergence.
problem Analyzing critical points and convergence of generative deep linear networks trained with Bures-Wasserstein loss.
method Characterization of critical points and minimizers of Bures-Wasserstein distance, analysis of Hessian at low-rank matrices, convergence results for gradient flow and descent.
result Established convergence results for gradient flow and finite step size gradient descent under certain assumptions.
MonoFlow rethinks GANs using Wasserstein gradient flows.
problem Inconsistencies between GAN theory and practice.
method Unified generative modeling framework based on Wasserstein gradient flows.
result Adversarial training can be seen as particle flow optimization.
In this paper, we investigate the underlying factor that leads to failure and success in the training of GANs. We study the property of the optimal discriminative function and show that in many GANs, the gradient from the optimal discriminative function is not reliable, which turns out to be the fundamental cause of fa…
Generative modelling is often cast as minimizing a similarity measure between a data distribution and a model distribution. Recently, a popular choice for the similarity measure has been the Wasserstein metric, which can be expressed in the Kantorovich duality formulation as the optimum difference of the expected value…
Generative adversarial networks (GANs) have enjoyed much success in learning high-dimensional distributions. Learning objectives approximately minimize an f-divergence (f-GANs) or an integral probability metric (Wasserstein GANs) between the model and the data distribution using a discriminator. Wasserstein GANs en…
Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a different but related data distribution. One solution to domain adaptation is to learn domain invariant feature representations while the learned representations sh…
New tools for estimating and inferring Wasserstein distance in topic models.
problem Estimating and inferring the Wasserstein distance between mixing measures in topic models.
method New canonical interpretation and tools for inference on Wasserstein distance in topic models.
result First minimax lower bounds and fully data-driven inferential tools for the Wasserstein distance in topic models.
We investigate under and overfitting in Generative Adversarial Networks (GANs), using discriminators unseen by the generator to measure generalization. We find that the model capacity of the discriminator has a significant effect on the generator's model quality, and that the generator's poor performance coincides with…
Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in various learning contexts. They do not, however, live in a space naturally endo…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine with typical machine learning workflows. In this paper we introduce persistence c…
The paper explores theoretical insights into WGANs for better understanding and stability.
problem Stabilizing the training process of GANs.
method Theoretical analysis and statistical convergence study of WGANs.
result Theoretical properties and convergence of WGANs are clarified.
We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form of the optimal transportation problem, the Brenier theorem states that the optim…
New metrics improve quantum ensemble learning efficiency and power.
problem Quantum ensembles' distances poorly understood due to measurement constraints.
method Introduce MMD-k hierarchy of integral probability metrics for quantum ensembles. result MMD-k requires fewer samples for full discriminative power at higher k. This study analyzes how well GANs approximate distributions from small samples.
problem Understanding how well GANs approximate distributions from limited data.
method Analysis of GANs using integral probability metrics and Hölder classes.
result GANs can adaptively learn low-dimensional structures or Hölder densities.
Within a broad class of generative adversarial networks, we show that discriminator optimization process increases a lower bound of the dual cost function for the Wasserstein distance between the target distribution p and the generator distribution pG. It implies that the trained discriminator can approximate opti…
New PAC-Bayesian bounds improve Sliced-Wasserstein distances.
problem Improving statistical properties of Sliced-Wasserstein distances.
method Leveraging PAC-Bayesian theory to provide bounds and learning procedures.
result PAC-Bayesian generalization bounds for adaptive SW distances.
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 …
Algorithm classifies point clouds using deep set linearized optimal transport.
problem Classifying point clouds efficiently and accurately.
method Deep Set Linearized Optimal Transport, ICNNs, and a discriminator network.
result Efficiently distinguishes between various classes of point clouds.
Proposes Sig-Wasserstein GANs for generating time series with temporal dependence.
problem Challenges in generating time series with temporal dependence and high-dimensional data.
method Integrates Wasserstein-GANs with signature feature extraction for conditional time series generation.
result Consistently outperforms state-of-the-art benchmarks in similarity and predictive ability.
We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and define a corresponding input-dependent additive noise data augmentation model. …
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.…
This work introduces novel methods to identify and compare cycles across topological objects.
problem Identifying and comparing topological features, particularly cycles, across different topological objects.
method Two complementary approaches: dendrogram-based merge-tree algorithms and Stratified Gradient Sampling.
result Transformed cycle matching into hierarchical clustering and topological optimization framework.
Paper provides statistical guarantees for GANs estimating Hölder space densities.
problem Statistical properties and theoretical guarantees for GANs.
method Approximation and statistical guarantees for GANs using Hölder space densities.
result GANs are consistent estimators of data distributions under strong discrepancy metrics.
Proposes a fair classification model using robust optimization.
problem Preventing discrimination in classification models.
method Distributionally robust logistic regression with Wasserstein ball and convex unfairness measure.
result Improves fairness with minimal loss in predictive accuracy.
Improves GANs' generalization by promoting local robustness.
problem Stability and generalization issues in GANs.
method Designs a robust optimization framework where generator and discriminator compete in worst-case setting within a small Wasserstein ball.
result Proves tighter generalization upper bound for RGAN than traditional GANs under mild assumptions.
Proposes fair mapping to prevent bias in model predictions without distorting data.
problem Reduces bias in model predictions without altering the data distribution.
method Uses Wasserstein GAN and AttGAN frameworks to transform data distributions while preserving privacy and interpretability.
result Preserves data interpretability and fairness in subsequent analysis tasks.
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.
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
problem Limited effectiveness of linear discriminant analysis in capturing nonlinear features.
method Study of nonlinear embeddings in kernel discriminant analysis using polynomial and Gaussian kernels, solving generalized eigenvalue problems.
result Polynomial and Gaussian discriminants capture class differences through population moments and randomized projections.
New analysis improves convergence guarantees for diffusion-based samplers in Wasserstein distance.
problem Improving convergence guarantees for diffusion-based generative models.
method Simple framework to analyze discretization, initialization, and score estimation errors.
result First Wasserstein convergence bound for the Heun sampler and improved results for Euler sampler.
Paper proposes distributed sparse multicategory discriminant analysis for classification.
problem Sparse multicategory classification with distributed data.
method Convex formulation, distributed setting, invariant discriminant subspace recovery.
result Distributed sparse multicategory linear discriminant analysis performs as good as centralized version after a few rounds of communications.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
Paper optimizes classification of distributions using Wasserstein metric.
problem Classifying instances represented by distributions on a vector space.
method Maximizing Fisher's ratio in the Wasserstein metric space through iterative algorithm.
result The method enhances classification performance and is robust to variations in distribution summaries.
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.
Proposes an energy-based sliced Wasserstein distance for improved probability measure comparison.
problem Inefficiencies and limitations in existing sliced Wasserstein distance approaches.
method Introduces an energy-based slicing distribution for better performance and stability.
result Demonstrates superior performance of the EBSW distance in various applications.
Introduces MSW distances to improve SW metrics.
problem Redundant projections in SW distance.
method Imposes Markov structure on projecting directions.
result MSW distances improve SW metrics.