AI 中文总结
本研究提出Sinkhorn哈密顿蒙特卡洛方法，将Sinkhorn散度作为泛化贝叶斯损失，结合公共随机数策略处理随机模拟器场景，经四类实验验证其对误设的鲁棒性及平衡与非平衡设置的差异。
AI 中文摘要
贝叶斯后验采样是参数点估计不足问题的通用范式，适用于风险分析、不确定性量化等场景，但似然函数可能存在误设、难以处理、计算成本高或无法反映关注差异等问题。泛化贝叶斯通过使用其他损失函数扩展基于似然的后验更新，而Sinkhorn散度具有吸引人的几何特性：可直接比较经验测度，且因熵正则化产生平滑梯度。本研究将Sinkhorn散度作为泛化贝叶斯损失函数应用于哈密顿蒙特卡洛（HMC）和无回跳采样器（NUTS），还提出了用于设置超参数的启发式方法，这些超参数影响稳定性和校准质量，包括Sinkhorn迭代次数、熵正则化强度和边际松弛惩罚。在前向模型依赖随机模拟器的场景中，将HMC/NUTS与公共随机数策略结合，得到保留梯度和哈密顿动力学的确定性替代目标。研究同时涵盖保质量的平衡设置和松弛的非平衡设置，通过四类实验进行实证评估：一是简单高斯模型的合理性检验；二是基于含噪螺旋流形的分布，其中基于似然的方法拟合效果差；三是因变量误差导致错位的高斯脉冲模型，突出对误设的鲁棒性；四是扰动下的CIFAR-10图像块对齐，强调平衡与非平衡设置的差异。
英文摘要
Bayesian posterior sampling is a ubiquitous paradigm for problems where a point estimate of parameters is not sufficient, such as risk analysis and uncertainty quantification. However, likelihoods may be misspecified, intractable, computationally expensive, or not representative of the discrepancy of interest. Generalized Bayes extends likelihood-based posterior updates by using other losses. Sinkhorn divergences have appealing geometric properties: they compare empirical measures directly and yield smooth gradients thanks to entropic regularization. In this work, we introduce Sinkhorn divergences as Generalized Bayes losses for Hamiltonian Monte Carlo (HMC) and No-U-Turn Sampler (NUTS). We also propose heuristics to set hyperparameters that affect the stability and calibration quality, such as the number of Sinkhorn iterations, the entropic regularization strength, and the marginal relaxation penalty. In regimes where the forward model relies on a stochastic simulator, we combine HMC/NUTS with a common-random-numbers strategy to obtain a deterministic surrogate objective that preserves gradients and Hamiltonian dynamics. We study both mass-preserving balanced and relaxed unbalanced settings. We evaluate our method empirically on (1) a simple Gaussian model as a sanity check; (2) a distribution supported on a noisy spiral manifold where a likelihood-based approach is a poor fit; (3) a Gaussian pulse model with misalignment due to errors-in-variables, emphasizing robustness to misspecification; and (4) CIFAR-10 image patch alignment under perturbations, highlighting differences between balanced and unbalanced regimes.
