# Deep Transformed Gaussian Processes

arXiv: https://arxiv.org/abs/2310.18230 · HTML: https://mlsanity.com/paper/2310.18230/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 11 of 11)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Sparse Gaussian Processes with Spherical Harmonic Features](https://mlsanity.com/paper/2006.16649/) (2020)
- [Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1806.05490/) (2018)
- [Transforming Gaussian Processes With Normalizing Flows](https://mlsanity.com/paper/2011.01596/) (2020)
- [Compositionally-Warped Gaussian Processes](https://mlsanity.com/paper/1906.09665/) (2019)
- [Inter-domain Deep Gaussian Processes](https://mlsanity.com/paper/2011.00415/) (2020)
- [Deep Variational Implicit Processes](https://mlsanity.com/paper/2206.06720/) (2022)
- [Probabilistic Attention based on Gaussian Processes for Deep Multiple Instance Learning](https://mlsanity.com/paper/2302.04061/) (2023)
- [Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification](https://mlsanity.com/paper/2205.15008/) (2022)

## Built on by (most cited first, 1 of 1)

- [An Analysis of Posterior Collapse, Parameterization and Initialization in Variational Deep Gaussian Processes](https://mlsanity.com/paper/2606.25882/) (2026)

## Abstract (arXiv)

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.