Transformed Gaussian Processes (TGPs) are stochastic processes specified by transforming samples from the joint distribution from a prior process (typically a GP) using an invertible transformation; increasing the flexibility of the base process. Furthermore, they achieve competitive results compared with Deep Gaussian Processes (DGPs), which are another generalization constructed by a hierarchical concatenation of GPs. In this work, we propose a generalization of TGPs named Deep Transformed Gaussian Processes (DTGPs), which follows the trend of concatenating layers of stochastic processes. More precisely, we obtain a multi-layer model in which each layer is a TGP. This generalization implies an increment of flexibility with respect to both TGPs and DGPs. Exact inference in such a model is intractable. However, we show that one can use variational inference to approximate the required computations yielding a straightforward extension of the popular DSVI inference algorithm Salimbeni et al (2017). The experiments conducted evaluate the proposed novel DTGPs in multiple regression datasets, achieving good scalability and performance.

翻译：变换高斯过程（TGPs）是通过可逆变换对先验过程（通常为高斯过程）联合分布中的样本进行变换而定义的一类随机过程，从而提高了基础过程的灵活性。此外，与另一种通过高斯过程层次级联构建的广义模型——深度高斯过程（DGPs）相比，TGPs取得了具有竞争力的结果。本文提出一种名为深度变换高斯过程（DTGPs）的TGPs推广形式，遵循随机过程层级串联的发展趋势。具体而言，我们构建了一个每层均为TGP的多层模型。这一推广意味着相对于TGPs和DGPs均提升了灵活性。此类模型的精确推断难以实现，但研究表明可借助变分推断近似计算所需步骤，从而直接扩展Salimbeni等人（2017）提出的DSVI推断算法。实验在多个回归数据集上对所提出的新型DTGPs进行评估，验证了其良好的可扩展性与性能。