论文标题
大都会调整后的兰格文轨迹：哈密顿蒙特卡洛的强大替代品
Metropolis Adjusted Langevin Trajectories: a robust alternative to Hamiltonian Monte Carlo
论文作者
论文摘要
我们介绍麦芽：基于（动力学）兰格文扩散的新大都市调整后的采样器。与广义的汉密尔顿蒙特卡洛（GHMC）相比，大都市的校正应用于整个兰格文轨迹，该轨迹可防止动量翻转并允许更大的步进尺寸。我们认为麦芽产生了HMC的整洁扩展，并保留了许多理想的特性。我们将HMC的最佳缩放结果扩展到各向同性靶标的麦芽，并在没有其他假设的情况下获得相同的比例。我们表明，麦芽既可以提高调整的鲁棒性，也可以提高HMC对各向异性靶标的采样性能。我们将方法与随机HMC进行比较，该方法最近以其稳健性而受到称赞。我们表明，在连续的时间内，Langevin扩散达到了强烈的对数凸目标目标的最快混合速率。然后，我们评估麦芽，GHMC，HMC和RHMC的准确性在对贝叶斯逻辑回归上的玩具模型和实际数据实验上进行数值集成。我们表明，麦芽表现优于GHMC，标准HMC，并且与RHMC具有竞争力。
We introduce MALT: a new Metropolis adjusted sampler built upon the (kinetic) Langevin diffusion. Compared to Generalized Hamiltonian Monte Carlo (GHMC), the Metropolis correction is applied to whole Langevin trajectories, which prevents momentum flips, and allows for larger step-sizes. We argue that MALT yields a neater extension of HMC, preserving many desirable properties. We extend optimal scaling results of HMC to MALT for isotropic targets, and obtain the same scaling with respect to the dimension without additional assumptions. We show that MALT improves both the robustness to tuning and the sampling performance of HMC on anisotropic targets. We compare our approach with Randomized HMC, recently praised for its robustness. We show that, in continuous time, the Langevin diffusion achieves the fastest mixing rate for strongly log-concave targets. We then assess the accuracies of MALT, GHMC, HMC and RHMC when performing numerical integration on anisotropic targets, both on toy models and real data experiments on a Bayesian logistic regression. We show that MALT outperforms GHMC, standard HMC, and is competitive with RHMC.
