optimal transport diagnostics

Multivariate geostatistical simulation struggles to accurately represent complex nonlinear dependence structures such as bimodal distributions, stepwise relationships, and heteroscedasticity. This work proposes a novel approach grounded in optimal transport theory, leveraging the Sinkhorn algorithm to directly match high-dimensional joint distributions. By treating all variables holistically and processing them simultaneously, the method achieves end-to-end faithful reconstruction of the full joint distribution while preserving spatial correlations. It overcomes the limitations of conventional assumptions based on linear correlation or Gaussian copulas, marking the first successful reproduction of intricate nonlinear dependencies in multivariate geostatistical simulation. Experimental results demonstrate its significant superiority over existing techniques, including LU decomposition and Gaussian copula-based methods.

This work addresses the limitation of traditional causal inference methods—such as average treatment effects—which capture only local differences in outcome distributions and thus fail to fully characterize the treatment’s impact on the entire distribution. The authors propose the Sinkhorn Treatment Effect, which for the first time integrates entropy-regularized optimal transport into causal inference. By constructing a smooth transformation of counterfactual mean embeddings, they derive a differentiable functional representation of distributional treatment effects. Building on this framework, they develop a debiased estimator with asymptotic efficiency and a multi-regularization-parameter aggregation test. Both theoretical analysis and empirical experiments demonstrate that the proposed approach substantially enhances the identification and detection of distributional causal effects on synthetic and image data.

This work addresses the limitations of traditional Bayesian inference, which relies on exact likelihoods and suffers when the likelihood is misspecified, intractable, or misaligned with the target discrepancy. The authors propose the first integration of Sinkhorn divergence as a generalized Bayesian loss within Hamiltonian Monte Carlo (HMC) and its adaptive variant NUTS, accommodating both balanced and unbalanced optimal transport settings. They further incorporate common random numbers to handle stochastic simulators and introduce a heuristic for hyperparameter selection that preserves gradient consistency with Hamiltonian dynamics. Empirical evaluations on Gaussian models, noisy spiral manifolds, pulse misalignment, and CIFAR-10 image patch alignment demonstrate the method’s effectiveness, robustness, and the nuanced differences between transport mechanisms.

In entropy-regularized optimal transport under Gaussian distributions, the Sinkhorn algorithm struggles to solve nonlinear transformations exactly. Method: This paper proposes a finite-dimensional recursive Sinkhorn algorithm. It establishes, for the first time, an explicit recursive analytical form of Sinkhorn iterations in the Gaussian setting, deeply coupling iterative scaling with the Kalman filter and Riccati matrix difference equation frameworks. Contributions/Results: We derive closed-form solutions for both the entropic transport map and the Schrödinger bridge. Moreover, we provide the first complete convergence analysis, rigorously proving linear convergence. The method enables exact, efficient, and analytically tractable numerical computation for multivariate Gaussian settings—without approximation. By unifying optimal transport, Schrödinger bridges, and filtering theory, it offers a novel tool for probabilistic modeling and dynamic inference.

To address the high computational cost and curse-of-dimensionality challenges in sampling optimal transport (OT) couplings for large-scale, high-dimensional data, this paper proposes an efficient learning framework based on score-based generative models. Specifically, conditioned on source samples, it iteratively generates target samples following the Sinkhorn-regularized OT coupling via Langevin dynamics. Crucially, it jointly parameterizes the score function and Sinkhorn potential functions—enabling, for the first time, end-to-end co-learning of score-based generation and OT coupling. We theoretically establish the convergence of gradient descent on the network parameters under mild assumptions. Experiments demonstrate that our method significantly improves both accuracy and speed of coupling estimation across diverse large-scale OT tasks, while maintaining scalability and practical applicability.

本文提出SinkSLOT方法，通过稀疏提升的运输计划解决大规模数据集上熵最优传输计算效率低和独立耦合问题。

This study addresses the two-sample homogeneity testing problem by proposing a novel approach based on entropy-regularized optimal transport (EOT) maps. The test statistic is constructed as the squared L² distance between two empirical EOT maps evaluated over the unit sphere, and its non-pivotal null distribution is calibrated via a weighted multiplier bootstrap. This work is the first to incorporate EOT maps into two-sample testing, enabling not only detection of global distributional discrepancies but also diagnosis of their specific patterns. Theoretical analysis establishes a Gaussian quadratic form as the limiting null distribution and derives asymptotic power under local alternatives. Numerical experiments demonstrate that the method achieves accurate size control and high power in finite samples, exhibiting particular sensitivity to location shifts, while both simulations and real-data analyses corroborate its effectiveness and diagnostic capability.

This study addresses the limitations of existing outlier generation methods, which often rely on heuristics, exhibit instability, and struggle to cover extreme out-of-distribution scenarios. To overcome these challenges, this work proposes the SBOG framework, which pioneers the use of Sinkhorn optimal transport-induced support costs to guide sampling toward weakly supported boundary regions. By integrating distributionally robust optimization with latent-space semantic constraints, SBOG generates controlled, structured outliers in the latent space, thereby transcending the limitations of conventional arbitrary sparse sampling. Experimental results demonstrate that SBOG produces informative and semantically controllable samples in both time-series anomaly and image outlier synthesis tasks, significantly enhancing the capability for robustness evaluation across downstream cross-modal applications.

研究使用经验Sinkhorn估计器解决熵最优传输势函数的统计收敛问题，通过结合Birkhoff-Hopf收缩定理和熵界来实现，并提出几何条件以改进依赖于正则化参数的方法。

本文针对Sinkhorn分布鲁棒假设检验问题，提出一种生成框架，通过学习最不利分布并利用Hyper Input Convex神经网络有效训练和端到端采样来解决大规模锥规划的可扩展性问题。