论文标题
黑盒抽样，用于使用P将高斯平滑的弱光滑的Langevin Monte Carlo
Black-box sampling for weakly smooth Langevin Monte Carlo using p-generalized Gaussian smoothing
论文作者
论文摘要
连续时间扩散过程的离散化是采样的广泛认识的方法。但是，Langevin扩散过程的规范Euler-Maruyama离散化，也称为Langevin Monte Carlo（LMC），主要是在平滑（渐变 - lipschitz）的背景下进行的，并且在包括计算统计学在内的许多科学方面对其进行了重大限制，这是对其在包括计算统计学在内的许多科学的重大限制。在本文中，我们对此类抽样方法的文献建立了一些理论贡献。特别是，我们概括了高斯平滑，使用p将高斯平滑的梯度近似梯度，并在黑盒抽样的背景下利用它。我们首先提出了一种非巧妙的凹面和弱光滑的黑盒LMC算法，非常适合在一般环境中采样挑战的实际适用性。
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler-Maruyama discretization of the Langevin diffusion process, also named as Langevin Monte Carlo (LMC), studied mostly in the context of smooth (gradient-Lipschitz) and strongly log-concave densities, a significant constraint for its deployment in many sciences, including computational statistics and statistical learning. In this paper, we establish several theoretical contributions to the literature on such sampling methods. Particularly, we generalize the Gaussian smoothing, approximate the gradient using p-generalized Gaussian smoothing and take advantage of it in the context of black-box sampling. We first present a non-strongly concave and weakly smooth black-box LMC algorithm, ideal for practical applicability of sampling challenges in a general setting.
