  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.
