Efficient and generalizable tuning strategies for stochastic gradient MCMC
Efficient and generalizable tuning strategies for stochastic gradient MCMC
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DOI：
10.1007/s11222-023-10233-3
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发表时间：
2021-05
影响因子：
2.2
通讯作者：
Jeremie Coullon;Leah F. South;C. Nemeth
中科院分区：
文献类型：
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作者：
Jeremie Coullon;Leah F. South;C. Nemeth
随机梯度马尔可夫链蒙特卡罗（SGMCMC）是一类流行的算法，可扩展的贝叶斯推理。然而，这些算法包括超参数，如步长或批量大小，影响基于所获得的后验样本的估计的准确性。因此，这些超参数必须由从业者调整，并且目前不存在调整它们的原则性和自动化方式。基于接受率的标准马尔可夫链蒙特卡罗调整方法不能用于SGMCMC，因此需要替代工具和诊断。我们提出了一种新的基于带宽的算法，通过最小化真实后验和其蒙特卡罗近似之间的Stein差异来调整SGMCMC超参数。我们提供了支持这种方法的理论结果，并评估各种斯坦为基础的差异。我们支持我们的结果与模拟和真实的数据集上的实验，并发现这种方法是实用的广泛的应用。
Stochastic gradient Markov chain Monte Carlo (SGMCMC) is a popular class of algorithms for scalable Bayesian inference. However, these algorithms include hyperparameters such as step size or batch size that influence the accuracy of estimators based on the obtained posterior samples. As a result, these hyperparameters must be tuned by the practitioner and currently no principled and automated way to tune them exists. Standard Markov chain Monte Carlo tuning methods based on acceptance rates cannot be used for SGMCMC, thus requiring alternative tools and diagnostics. We propose a novel bandit-based algorithm that tunes the SGMCMC hyperparameters by minimizing the Stein discrepancy between the true posterior and its Monte Carlo approximation. We provide theoretical results supporting this approach and assess various Stein-based discrepancies. We support our results with experiments on both simulated and real datasets, and find that this method is practical for a wide range of applications.