Towards scaling up Markov chain Monte Carlo: an adaptive subsampling approach
Towards scaling up Markov chain Monte Carlo: an adaptive subsampling approach
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发表时间：
2014-06
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通讯作者：
R. Bardenet;A. Doucet;C. Holmes
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作者：
R. Bardenet;A. Doucet;C. Holmes
马尔可夫链蒙特卡罗（MCMC）方法通常被认为计算量太大，对于大型数据集没有任何实际用途。本文介绍了一种方法，其目的是扩大大都市黑斯廷斯（MH）算法在这种情况下。我们提出了一个近似实现的接受/拒绝步骤的MH，只需要评估的数据的随机子集的可能性，但保证符合接受/拒绝步骤的基础上，以一个概率上级用户指定的公差水平的完整数据集。这种自适应子采样技术是在（Korattikara等人，2014），并且它允许我们严格地建立所得到的近似MH算法从感兴趣的目标分布的扰动版本采样，其到该目标的总变化距离被明确地控制。我们探讨的好处和限制，这一计划的几个例子。
Markov chain Monte Carlo (MCMC) methods are often deemed far too computationally intensive to be of any practical use for large datasets. This paper describes a methodology that aims to scale up the Metropolis-Hastings (MH) algorithm in this context. We propose an approximate implementation of the accept/reject step of MH that only requires evaluating the likelihood of a random subset of the data, yet is guaranteed to coincide with the accept/reject step based on the full dataset with a probability superior to a user-specified tolerance level. This adaptive subsampling technique is an alternative to the recent approach developed in (Korattikara et al., 2014), and it allows us to establish rigorously that the resulting approximate MH algorithm samples from a perturbed version of the target distribution of interest, whose total variation distance to this very target is controlled explicitly. We explore the benefits and limitations of this scheme on several examples.