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）是通过使用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，其目的是增强基过程的灵活性。此外，与深度高斯过程（DGPs）——另一种通过高斯过程层次级联构建的推广——相比，TGPs也能取得具有竞争力的结果。本文提出TGPs的推广形式，命名为深度变换高斯过程（DTGPs），该模型遵循随机过程层级级联的趋势。具体而言，我们构建了一个多层模型，其中每一层均为TGP。这一推广在灵活性上相对于TGPs和DGPs均有提升。该模型中的精确推理是不可解的，但我们证明可利用变分推断来近似所需计算，从而得到Salimbeni等人（2017）提出的DSVI推断算法的直接扩展。实验在多个回归数据集上评估了所提出的新型DTGPs，结果表明其具有良好的可扩展性与性能。