How Deep Are Deep Gaussian Processes?
How Deep Are Deep Gaussian Processes?
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发表时间：
2017-11
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通讯作者：
Matthew M. Dunlop;M. Girolami;A. Stuart;A. Teckentrup
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作者：
Matthew M. Dunlop;M. Girolami;A. Stuart;A. Teckentrup
最近的研究表明了深度高斯过程的潜在效用。这些深层结构是通过分层构造设计的概率分布，并且是条件高斯分布。在本文中，当前发表的工作主体被放置在一个通用框架中，并通过递归定义了几类深度高斯过程。从深度高斯过程生成的结果样本具有关于深度参数的马尔可夫结构，并且结果过程的有效深度根据结果马尔可夫链的遍历性或非遍历性来解释。对于引入的深度高斯过程的类别，我们提供了有关其遍历性以及有效深度的结果。我们还演示了如何将这些过程用于推理；特别是，我们展示了如何使用跨越层次结构级别的吉布斯内的大都市构造来派生采样工具，这些工具对于用于表示计算机上的函数的分辨率水平来说是鲁棒的。为了便于说明，我们在一些简单的数值例子中考虑遍历性的影响。
Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current published body of work is placed in a common framework and, through recursion, several classes of deep Gaussian processes are defined. The resulting samples generated from a deep Gaussian process have a Markovian structure with respect to the depth parameter, and the effective depth of the resulting process is interpreted in terms of the ergodicity, or non-ergodicity, of the resulting Markov chain. For the classes of deep Gaussian processes introduced, we provide results concerning their ergodicity and hence their effective depth. We also demonstrate how these processes may be used for inference; in particular we show how a Metropolis-within-Gibbs construction across the levels of the hierarchy can be used to derive sampling tools which are robust to the level of resolution used to represent the functions on a computer. For illustration, we consider the effect of ergodicity in some simple numerical examples.