The paper explores statistical and topological properties of sliced probability divergences.
problem Understanding the topological, statistical, and computational consequences of slicing divergences.
method Deriving theoretical properties of sliced probability divergences, including metric axioms preservation and weak continuity.
result Sliced divergences share similar topological properties and have stable sample complexity.
This work investigates the properties of Gaussian-smoothed sliced divergences for comparing distributions.
problem Comparing probability distributions while preserving privacy.
method Investigates the theoretical properties of Gaussian-smoothed sliced Wasserstein distance and generalized versions.
result Gaussian smoothed sliced Wasserstein distance converges with a rate of \(O(n^{-1/2})\).
A new Wasserstein distance method for comparing incomparable distributions.
problem Comparing distributions that are not supported on the same metric space.
method Distributional slicing, embeddings, and closed-form computation of Wasserstein distance.
result HWD preserves properties like rotation-invariance and can be efficiently learned.
Sliced-regularized OT improves transport plan accuracy.
problem Optimal transport (OT) approximation accuracy.
method Sliced-regularized optimal transport (SROT) formulation.
result SROT yields more accurate approximations of exact OT than entropic OT.
A new method for comparing image probability measures using convolution operators.
problem Efficiently comparing images using conventional sliced Wasserstein methods.
method Proposed convolution sliced Wasserstein (CSW) methods with stride, dilation, and non-linear activation.
result CSW demonstrates favorable performance over conventional sliced Wasserstein in image comparison and deep generative modeling.
A new variational inference method using sliced Wasserstein distance is proposed.
problem The inefficiency and unreasonable properties of Kullback-Leibler divergence.
method Minimizing sliced Wasserstein distance, a valid metric from optimal transport.
result The proposed method approximates the unnormalized distribution efficiently and without requiring a tractable density function.
A new method optimizes slicing directions for SW distances to improve high-dimensional probability measure comparison.
problem Challenging identification of informative slicing directions for SW distances.
method Constrained learning approach to optimize slicing directions, using continuous relaxations and gradient-based primal-dual approach.
result Demonstrated efficacy in learning more informative slicing directions on various high-dimensional data.
In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional forecasts into a single forecast. We adapt basic mixable (and exponentially conc…
Rank-statistic method approximates f-divergences without density-ratio estimation.
problem Approximating f-divergences without explicit density-ratio estimation. method Mapping distribution rank histograms to discrete f-divergence and averaging over random projections. result The rank-statistic estimator is a lower bound of the true f-divergence and converges under mild conditions. 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.
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM guarantees only convergence to a stationary point of the log-likelihood function, which c…
Researchers developed a differentially private method for computing Wasserstein distances.
problem Computing divergences between distributions while preserving privacy.
method They focused on the Sliced Wasserstein Distance and added Gaussian perturbations to make it differentially private.
result They introduced a new differentially private distance, the Smoothed Sliced Wasserstein Distance, which performs well in generative models and domain adaptation.
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.
Analyzed a generative model framework through Wasserstein Gradient Flow.
problem Generative modeling challenges.
method Wasserstein Gradient Flow (WGF) interpretation of Drifting Models (GMD).
result Different algorithms correspond to specific limiting points of WGFs on various divergences.
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.
A new method optimizes projection directions for sliced Wasserstein distances.
problem Finding informative projecting directions for sliced Wasserstein distances is computationally expensive.
method Amortized projection optimization to predict directions efficiently.
result Proposed amortized models improve generative modeling performance.
Develops a new divergence framework that combines f-divergences and IPMs.
problem Comparing distributions that are not absolutely continuous.
method Introduces (f,Γ)-divergences as a two-stage mass-redistribution/mass-transport process. result Improves estimation, learning, and uncertainty quantification in GANs for heavy-tailed distributions.
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.
This paper aims to define and study currents and slices of currents in the Heisenberg group Hn. Currents, depending on their integration properties and on those of their boundaries, can be classified into subspaces and, assuming their support to be compact, we can work with currents of finite mass, define t…
New hyperbolic sliced-Wasserstein distances derived for efficient comparison.
problem Efficient comparison of distributions in hyperbolic spaces.
method Projections on geodesics or horospheres to derive novel sliced-Wasserstein distances.
result Novel hyperbolic sliced-Wasserstein distances are more computationally efficient.
This paper proposes a new method to solve functional minimization problems in probability distributions using sliced-Wasserstein gradient flows.
problem Solving functional minimization problems in high-dimensional probability distributions is computationally challenging.
method The paper introduces a new approach using sliced-Wasserstein gradient flows to approximate the Jordan-Kinderlehrer-Otto (JKO) scheme, parameterizing densities with generative models.
result The proposed method is more flexible and computationally tractable compared to existing methods like JKO-ICNN.
f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance e…
Sliced Optimal Transport simplifies OT for fast computation.
problem Efficient computation of distances and barycenters for probability measures.
method Combines OT, integral geometry, and statistics for fast computation.
result Retains rich geometric structure while speeding up computations.
We propose fast approximations for the generalized sliced-Wasserstein distance.
problem Efficient approximation of the generalized sliced-Wasserstein distance in high dimensions.
method Deterministic approximations using random projections and concentration of measure results.
result One-dimensional projections of high-dimensional random vectors are approximately Gaussian.
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.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.
problem Unified understanding of KL-divergence and IPMs.
method Unified representation via maximum likelihood density-ratio estimation (DRE).
result Unified form of IPMs and novel DRM metrics.
Sharp bounds for high-probability estimation of discrete distributions.
problem Estimating discrete distributions with high probability under χ2-divergence. method Sharp upper and lower bounds for the classical Laplace estimator, and characterization of minimax high-probability risk for any estimator.
result Sharp bounds for high-probability estimation of discrete distributions can be achieved through a simple smoothing strategy.
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
We analyze critical points of the Sliced Wasserstein Distance for optimization stability.
problem Understanding the behavior of optimization algorithms for models trained with the Sliced Wasserstein Distance.
method Explicit perturbations and critical point analysis of the SW objective.
result Stable critical points of SW cannot concentrate on segments, providing optimization stability.
Proposes QMC-based QSW for 3D SW distance.
problem Intractable SW distance in 3D.
method Quasi-Monte Carlo (QMC) for QSW approximations.
result QMC-based QSW improves SW estimation.
A new method for distribution regression using sliced Wasserstein distance.
problem Learning functions over spaces of probabilities.
method Proposes an OT-based estimator using the Sliced Wasserstein distance.
result Proves universal consistency and excess risk bounds for the proposed estimator.
New KQEs improve probability metrics without mean function constraints.
problem Improving probability metrics without relying on mean function representations.
method Kernel quantile embeddings (KQEs) to construct new distances.
result KQEs offer a competitive alternative to MMD with near-linear cost.
Proposes a new divergence measure for probability distributions.
problem Challenges in estimating divergences from empirical samples.
method Embeds data into RKHS, computes Jensen-Shannon divergence between covariance operators.
result Establishes RJSD as a lower bound on Jensen-Shannon divergence, enabling variational estimation.
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.
Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance requires solving a complex non convex quadratic program which is most of the time very…
Paper introduces GSPMs for robust probability metrics.
problem Lack of well-established convergence behavior for probability metrics.
method Introduces Generalized Sliced Probability Metrics (GSPMs) based on generalized Radon transform.
result GSPMs converge to global optimum under mild assumptions for generative modeling.
The paper explores geometry of probability measures and barycenter maps.
problem Understanding the space of probability measures and their barycenter.
method Information geometry, Fisher metric, dualistic structures, divergences, geodesics.
result Recent developments in the geometry of probability measures and barycenter.
Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for approximating the true distribution. To improve the performance of machine learning …
Theoretical proof shows COMs are a type of contrastive divergence model with improved sampling.
problem Improving sampling quality in offline model-based optimization.
method Showed COMs are contrastive divergence models, proposed Langevin MCMC sampler, and decoupled model.
result Improved sampling quality achieved by decoupling model and using Langevin MCMC.
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutio…
The paper studies properties of Sliced Wasserstein energy for discrete measures.
problem Optimizing discrete probability measures using Sliced Wasserstein loss.
method Investigates the regularity and optimisation properties of the Sliced Wasserstein energy and its Monte-Carlo approximation.
result Convergence results on the critical points of Monte-Carlo approximations to the Sliced Wasserstein energy.
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common divergences on distributions such as Kullback-Leibler or Jensen-Shannon, it is (weakly) co…
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.
CNFs learn on manifolds using PPD, improving likelihood and sample quality.
problem Training CNFs on manifolds efficiently and accurately.
method Minimizing PPD, a novel divergence, to train CNFs on manifolds.
result CNFs trained with PPD achieve state-of-the-art results on manifold benchmarks.
In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical er…
A new method using spherical harmonics approximates the Sliced-Wasserstein distance.
problem Approximating the Sliced-Wasserstein distance between probability measures.
method Spherical Harmonics Control Variates (SHCV) method for Monte Carlo approximation of the SW distance.
result SHCV method provides an improved rate of convergence compared to Monte Carlo for general measures.
Paper introduces S3W distance for spherical probability distributions.
problem Comparing spherical probability distributions efficiently and accurately.
method S3W distance using stereographic projection and generalized Radon transform.
result Extensive theoretical analysis and evaluation of S3W performance.