An improved central limit theorem and fast convergence rates for entropic transportation costs

• URL: http://arxiv.org/abs/2204.09105v1
• Date: Tue, 19 Apr 2022 19:26:59 GMT
• Title: An improved central limit theorem and fast convergence rates for entropic transportation costs
• Authors: Eustasio del Barrio and Alberto Gonzalez-Sanz and Jean-Michel Loubes and Jonathan Niles-Weed
• Abstract summary: We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures. We complement these results with new, faster, convergence rates for the expected entropic transportation cost between empirical measures.
• Score: 13.9170193921377
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal transport between measures which are not necessarily discrete. In the compactly supported case, we complement these results with new, faster, convergence rates for the expected entropic transportation cost between empirical measures. Our proof is based on strengthening convergence results for dual solutions to the entropic optimal transport problem.

Related papers

• Conditional Optimal Transport on Function Spaces [53.9025059364831]
  We develop a theory of constrained optimal transport problems that describe block-triangular Monge maps. This generalizes the theory of optimal triangular transport to separable infinite-dimensional function spaces with general cost functions. We present numerical experiments that demonstrate the computational applicability of our theoretical results for amortized and likelihood-free inference of functional parameters.
  arXiv  Detail & Related papers  (2023-11-09T18:44:42Z)
• New Perspectives on Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization [8.564319625930892]
  We study optimal transport-based distributionally robust optimization problems where a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by a prescribed reference distribution at a finite transportation cost.
  arXiv  Detail & Related papers  (2023-03-07T13:52:32Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Convergence Rates for Regularized Optimal Transport via Quantization [3.04585143845864]
  We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. A novel methodology using quantization and martingale couplings is suitable for non-compact marginals.
  arXiv  Detail & Related papers  (2022-08-30T16:58:40Z)
• 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)
• Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport [0.483420384410068]
  We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. Our results also entail a non-asymptotic and tight expansion of the difference between the entropic and the unregularized costs.
  arXiv  Detail & Related papers  (2021-10-25T06:52:45Z)
• Estimation of Stationary Optimal Transport Plans [4.662321040754878]
  We study optimal transport problems in which finite-valued quantities evolve dynamically over time in a stationary fashion. We introduce estimators of both optimal joinings and the optimal joining cost. We extend the consistency and rate analysis to an entropy-penalized version of the optimal joining problem.
  arXiv  Detail & Related papers  (2021-07-25T17:46:21Z)
• Interplay between transport and quantum coherences in free fermionic systems [58.720142291102135]
  We study the quench dynamics in free fermionic systems. In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
  arXiv  Detail & Related papers  (2021-03-24T17:47:53Z)
• Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution [8.465228064780748]
  We prove that computing the Wasserstein distance between a discrete probability measure supported on two points is already #P-hard. We introduce a distributionally robust dual optimal transport problem whose objective function is smoothed with the most adverse disturbance distributions. We show that smoothing the dual objective function is equivalent to regularizing the primal objective function.
  arXiv  Detail & Related papers  (2021-03-10T18:53:59Z)
• Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency [83.02999769628593]
  We offer a theoretical characterization of off-policy evaluation (OPE) in reinforcement learning. We show that the minimax approach enables us to achieve a fast rate of convergence for weights and quality functions. We present the first finite-sample result with first-order efficiency in non-tabular environments.
  arXiv  Detail & Related papers  (2021-02-05T03:20:39Z)
• Comparing Probability Distributions with Conditional Transport [63.11403041984197]
  We propose conditional transport (CT) as a new divergence and approximate it with the amortized CT (ACT) cost. ACT amortizes the computation of its conditional transport plans and comes with unbiased sample gradients that are straightforward to compute. On a wide variety of benchmark datasets generative modeling, substituting the default statistical distance of an existing generative adversarial network with ACT is shown to consistently improve the performance.
  arXiv  Detail & Related papers  (2020-12-28T05:14:22Z)

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.