论文标题
随机坐标不足的Langevin Monte Carlo
Random Coordinate Underdamped Langevin Monte Carlo
论文作者
论文摘要
阻尼不足的Langevin Monte Carlo（ULMC）是一种流行的马尔可夫链蒙特卡洛采样方法。它需要计算每次迭代时对数密度的完整梯度，如果问题的尺寸很高，则需要昂贵的操作。我们提出了一种称为随机坐标ULMC（RC-ULMC）的采样方法，该方法在每次迭代处选择一个坐标以进行更新，并使其他坐标未触及。我们研究了RC-ULMC的计算复杂性，并将其与经典的ULMC进行比较，以实现强烈的对数符合概率分布。我们表明，RC-ULMC总是比经典ULMC便宜，当问题高度偏斜并且高维时，其成本大幅降低。我们对RC-ULMC的复杂性在维度依赖方面也很紧。
The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem is high. We propose a sampling method called Random Coordinate ULMC (RC-ULMC), which selects a single coordinate at each iteration to be updated and leaves the other coordinates untouched. We investigate the computational complexity of RC-ULMC and compare it with the classical ULMC for strongly log-concave probability distributions. We show that RC-ULMC is always cheaper than the classical ULMC, with a significant cost reduction when the problem is highly skewed and high dimensional. Our complexity bound for RC-ULMC is also tight in terms of dimension dependence.
