The Scalable Langevin Exact Algorithm : Bayesian Inference for Big Data
The Scalable Langevin Exact Algorithm : Bayesian Inference for Big Data
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发表时间：
2016-09
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通讯作者：
M. Pollock;P. Fearnhead;A. M. Johansen;G. Roberts
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作者：
M. Pollock;P. Fearnhead;A. M. Johansen;G. Roberts
本文介绍了一类基于模拟马尔可夫过程的蒙特卡罗算法，该过程的准平稳分布与兴趣分布一致。这与当前的马尔可夫链蒙特卡罗（Markov chain Monte Carlo）有着根本的不同，在蒙特卡罗中，我们模拟的马尔可夫链的目标是平稳分布。我们展示了如何通过仔细结合顺序蒙特卡罗方法与扩散的精确模拟方法来近似感兴趣的分布。我们的方法是特别有前途的，因为它是适用于同一类问题的梯度为基础的马尔可夫链蒙特卡罗算法，但完全规避需要进行大都会黑斯廷斯型接受/拒绝步骤，同时保持准确性：我们有理论保证，我们恢复正确的限制目标分布。此外，这种方法非常适合大数据问题。通过对现有的朴素子采样技术进行修改，我们可以获得一个仍然精确但具有作为数据大小的函数的次线性迭代成本的算法。
This paper introduces a class of Monte Carlo algorithms which are based upon simulating a Markov process whose quasi-stationary distribution coincides with the distribution of interest. This differs fundamentally from, say, current Markov chain Monte Carlo in which we simulate a Markov chain whose stationary distribution is the target. We show how to approximate distributions of interest by carefully combining sequential Monte Carlo methods with methodology for the exact simulation of diffusions. Our methodology is particularly promising in that it is applicable to the same class of problems as gradient based Markov chain Monte Carlo algorithms but entirely circumvents the need to conduct Metropolis-Hastings type accept/reject steps whilst retaining exactness: we have theoretical guarantees that we recover the correct limiting target distribution. Furthermore, this methodology is highly amenable to big data problems. By employing a modification to existing naive subsampling techniques we can obtain an algorithm which is still exact but has sub-linear iterative cost as a function of data size.