论文标题
无调整的汉密尔顿蒙特卡洛的融合用于平均场模型
Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models
论文作者
论文摘要
我们提出了无调整的哈密顿蒙特卡洛算法的无维度收敛和离散误差界限，该算法应用于平均场类型的高维概率分布。这些界限要求离散的步骤足够小，但不需要平均场模型中存在的一式或成对潜在项的强凸度。为了处理高维度，我们的证明使用粒子耦合，该耦合在互补的粒子方向上是合同的。
We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization step to be sufficiently small, but do not require strong convexity of either the unary or pairwise potential terms present in the mean-field model. To handle high dimensionality, our proof uses a particlewise coupling that is contractive in a complementary particlewise metric.
