Centered plug-in estimation of Wasserstein distances

• URL: http://arxiv.org/abs/2203.11627v2
• Date: Tue, 29 Apr 2025 17:31:42 GMT
• Title: Centered plug-in estimation of Wasserstein distances
• Authors: Tamás P. Papp, Chris Sherlock,
• Abstract summary: The plug-in estimator of the squared Euclidean 2-Wasserstein distance is conservative, however due to its large positive bias it is often uninformative.<n>We construct a pair of centered plug-in estimators that decrease with the true Wasserstein distance, and are therefore guaranteed to be informative, for any finite sample size.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The plug-in estimator of the squared Euclidean 2-Wasserstein distance is conservative, however due to its large positive bias it is often uninformative. We eliminate most of this bias using a simple centering procedure based on linear combinations. We construct a pair of centered plug-in estimators that decrease with the true Wasserstein distance, and are therefore guaranteed to be informative, for any finite sample size. Crucially, we demonstrate that these estimators can often be viewed as complementary upper and lower bounds on the squared Wasserstein distance. Finally, we apply the estimators to Bayesian computation, developing methods for estimating (i) the bias of approximate inference methods and (ii) the convergence of MCMC algorithms.

Related papers

• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers. We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions. This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances [0.4419843514606336]
  In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. We will introduce a conditional Wasserstein distance with a set of restricted couplings that equals the expected Wasserstein distance of the posteriors.
  arXiv  Detail & Related papers  (2023-10-20T11:46:05Z)
• Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributions [7.070726553564701]
  We introduce a class of distances based on diffeomorphic embeddings of the normal manifold into a submanifold. We show that the projective Hilbert distance on the cone yields a metric on the embedded normal submanifold. We show how to use those distances in clustering tasks.
  arXiv  Detail & Related papers  (2023-07-20T07:14:58Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Energy-Based Sliced Wasserstein Distance [47.18652387199418]
  A key component of the sliced Wasserstein (SW) distance is the slicing distribution. We propose to design the slicing distribution as an energy-based distribution that is parameter-free. We then derive a novel sliced Wasserstein metric, energy-based sliced Waserstein (EBSW) distance.
  arXiv  Detail & Related papers  (2023-04-26T14:28:45Z)
• Estimation and inference for the Wasserstein distance between mixing measures in topic models [18.66039789963639]
  The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models. This work proposes a new canonical interpretation of this distance and provides tools to perform inference on the Wasserstein distance in topic models.
  arXiv  Detail & Related papers  (2022-06-26T02:33:40Z)
• Hilbert Curve Projection Distance for Distribution Comparison [34.8765820950517]
  We propose a novel metric, called Hilbert curve projection (HCP) distance, to measure the distance between two probability distributions. We show that HCP distance is a proper metric and is well-defined for probability measures with bounded supports. Experiments on both synthetic and real-world data show that our HCP distance works as an effective surrogate of the Wasserstein distance with low complexity.
  arXiv  Detail & Related papers  (2022-05-30T12:40:32Z)
• Wasserstein Iterative Networks for Barycenter Estimation [80.23810439485078]
  We present an algorithm to approximate the Wasserstein-2 barycenters of continuous measures via a generative model. Based on the celebrity faces dataset, we construct Ave, celeba! dataset which can be used for quantitative evaluation of barycenter algorithms.
  arXiv  Detail & Related papers  (2022-01-28T16:59:47Z)
• Near-optimal estimation of smooth transport maps with kernel sums-of-squares [81.02564078640275]
  Under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. The object of interest for applications such as generative modeling is the underlying optimal transport map. We propose the first tractable algorithm for which the statistical $L2$ error on the maps nearly matches the existing minimax lower-bounds for smooth map estimation.
  arXiv  Detail & Related papers  (2021-12-03T13:45:36Z)
• Density Ratio Estimation via Infinitesimal Classification [85.08255198145304]
  We propose DRE-infty, a divide-and-conquer approach to reduce Density ratio estimation (DRE) to a series of easier subproblems. Inspired by Monte Carlo methods, we smoothly interpolate between the two distributions via an infinite continuum of intermediate bridge distributions. We show that our approach performs well on downstream tasks such as mutual information estimation and energy-based modeling on complex, high-dimensional datasets.
  arXiv  Detail & Related papers  (2021-11-22T06:26:29Z)
• Understanding Entropic Regularization in GANs [5.448283690603358]
  We study the influence of regularization on the learned solution of Wasserstein distance. We show that entropy regularization promotes the solution sparsification, while replacing the Wasserstein distance with the Sinkhorn divergence recovers the unregularized solution. We conclude that these regularization techniques can improve the quality of the generator learned from empirical data for a large class of distributions.
  arXiv  Detail & Related papers  (2021-11-02T06:08:16Z)
• Plugin Estimation of Smooth Optimal Transport Maps [25.23336043463205]
  We show that a number of natural estimators for the optimal transport map between two distributions are minimax optimal. Our work provides new bounds on the risk of corresponding plugin estimators for the quadratic Wasserstein distance.
  arXiv  Detail & Related papers  (2021-07-26T17:58:48Z)
• Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization [94.18714844247766]
  Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. We present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the input measures.
  arXiv  Detail & Related papers  (2021-02-02T21:01:13Z)
• Two-sample Test using Projected Wasserstein Distance [18.46110328123008]
  We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions.
  arXiv  Detail & Related papers  (2020-10-22T18:08:58Z)
• Continuous Regularized Wasserstein Barycenters [51.620781112674024]
  We introduce a new dual formulation for the regularized Wasserstein barycenter problem. We establish strong duality and use the corresponding primal-dual relationship to parametrize the barycenter implicitly using the dual potentials of regularized transport problems.
  arXiv  Detail & Related papers  (2020-08-28T08:28:06Z)
• Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations [79.23797234241471]
  Discriminating between distributions is an important problem in a number of scientific fields. The Linear Optimal Transportation (LOT) embeds the space of distributions into an $L2$-space. We demonstrate the benefits of LOT on a number of distribution classification problems.
  arXiv  Detail & Related papers  (2020-08-20T19:09:33Z)
• On Projection Robust Optimal Transport: Sample Complexity and Model Misspecification [101.0377583883137]
  Projection robust (PR) OT seeks to maximize the OT cost between two measures by choosing a $k$-dimensional subspace onto which they can be projected. Our first contribution is to establish several fundamental statistical properties of PR Wasserstein distances. Next, we propose the integral PR Wasserstein (IPRW) distance as an alternative to the PRW distance, by averaging rather than optimizing on subspaces.
  arXiv  Detail & Related papers  (2020-06-22T14:35:33Z)
• $\gamma$-ABC: Outlier-Robust Approximate Bayesian Computation Based on a Robust Divergence Estimator [95.71091446753414]
  We propose to use a nearest-neighbor-based $gamma$-divergence estimator as a data discrepancy measure. Our method achieves significantly higher robustness than existing discrepancy measures.
  arXiv  Detail & Related papers  (2020-06-13T06:09:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.