arXiv 1402.41022014-02stat.MEcs.LGstat.ML

随机梯度哈密顿蒙特卡罗

Stochastic Gradient Hamiltonian Monte Carlo

University of Washington（华盛顿大学）

Tianqi Chen, Emily B. Fox, Carlos Guestrin

备注：: ICML 2014 version

摘要：

哈密顿蒙特卡罗（HMC）采样方法提供了一种在Metropolis-Hastings框架中定义具有高接受概率的远程提案的机制，从而比标准随机游走提案更有效地探索状态空间。近年来，这种方法的普及程度显著提高。然而，HMC方法的局限性是用于哈密顿动力系统的模拟所需的梯度计算-这种计算在涉及大样本量或流数据的问题中是不可行的。相反，我们必须依赖于从数据的子集计算的噪声梯度估计。在本文中，我们探讨这样一个随机梯度HMC方法的属性。令人惊讶的是，随机逼近的自然实现可以是任意坏的。为了解决这个问题，我们引入了一个变体，该变体使用具有摩擦项的二阶朗之万动力学，该摩擦项抵消了噪声梯度的影响，保持所需的目标分布为不变分布。模拟数据的结果验证了我们的理论。我们还提供了一个应用程序的分类任务，使用神经网络和在线贝叶斯矩阵分解的方法。

英文摘要：

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard random-walk proposals. The popularity of such methods has grown significantly in recent years. However, a limitation of HMC methods is the required gradient computation for simulation of the Hamiltonian dynamical system-such computation is infeasible in problems involving a large sample size or streaming data. Instead, we must rely on a noisy gradient estimate computed from a subset of the data. In this paper, we explore the properties of such a stochastic gradient HMC approach. Surprisingly, the natural implementation of the stochastic approximation can be arbitrarily bad. To address this problem we introduce a variant that uses second-order Langevin dynamics with a friction term that counteracts the effects of the noisy gradient, maintaining the desired target distribution as the invariant distribution. Results on simulated data validate our theory. We also provide an application of our methods to a classification task using neural networks and to online Bayesian matrix factorization.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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