For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov chain Monte Carlo methods, namely, Hamiltonian Monte Carlo. The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the-art methods.

中文翻译：

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使用具有随机基的替代函数的哈密顿蒙特卡罗加速度。

对于大数据分析，贝叶斯方法的高计算成本通常会限制其在实践中的应用。近年来，已经进行了许多尝试来提高贝叶斯推断的计算效率。在这里，我们为最先进的马尔可夫链蒙特卡罗方法（即汉密尔顿蒙特卡洛）提出了一种高效且可扩展的计算技术。关键思想是为潜在的概率模型探索和利用参数空间的结构和规则性，以构造其几何特性的有效近似值。为此，我们建立了一个替代函数近似使用适当选取随机基地和高效的优化处理对象分布。由此产生的方法提供了一种灵活，可扩展且高效的采样算法，收敛到正确的目标分布。我们表明，通过不同地选择基本函数和优化过程，我们的方法可以与其他替代函数的构建方法相关，例如广义加性模型或高斯过程模型。基于模拟数据和真实数据的实验表明，与现有的最新方法相比，我们的方法可导致更高效的采样算法。