We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score-based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a stochastic differential equation evolution. The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling. We demonstrate fast convergence on various problems and show improved dimensional dependence of mixing time bounds for the case of Gaussian distributions compared to the unadjusted Langevin algorithm (ULA) and the Metropolis-adjusted Langevin algorithm (MALA). We additionally derive closed form expressions for the distributions at each iterate for quadratic potential functions, characterizing the variance reduction. Empirical results demonstrate that the particles behave in an organized manner, lying on level set contours of the potential. Moreover, the posterior mean estimator of the proposed method is shown to be closer to the maximum a-posteriori estimator compared to ULA and MALA, in the context of Bayesian logistic regression.

基于潜在函数模型抽样的显式基于评分的MCMC方法，以确定性的方式演化粒子，使用核卷积逼近的方法得到评分项，表现出快速收敛性和改进的维度依赖性相对于未调整的Langevin算法（ULA）和Metropolis调整的Langevin算法（MALA）的混合时间界限，在二次势函数下导出了每次迭代的分布的闭式表达，表征了方差降低，实证结果表明粒子以有序的方式行动，位于潜在函数的等值线上，此外，基于提出方法的后验均值估计器相对于ULA和MALA更接近最大后验估计器，在贝叶斯逻辑回归中表现出来。

通过正则化的Wasserstein近似实现无噪声采样算法