# Transformed Latent Variable Multi-Output Gaussian Processes

arXiv: https://arxiv.org/abs/2605.05133 · HTML: https://mlsanity.com/paper/2605.05133/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 81 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [A Framework for Interdomain and Multioutput Gaussian Processes](https://mlsanity.com/paper/2003.01115/) (2020)
- [SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradient](https://mlsanity.com/paper/1811.04504/) (2018)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (2018)
- [Scalable Exact Inference in Multi-Output Gaussian Processes](https://mlsanity.com/paper/1911.06287/) (2019)
- [Multi-task Learning for Aggregated Data using Gaussian Processes](https://mlsanity.com/paper/1906.09412/) (2019)
- [Sparse within Sparse Gaussian Processes using Neighbor Information](https://mlsanity.com/paper/2011.05041/) (2020)
- [Meta-Learning Mean Functions for Gaussian Processes](https://mlsanity.com/paper/1901.08098/) (2019)
- [Representing smooth functions as compositions of near-identity functions with implications for deep network optimization](https://mlsanity.com/paper/1804.05012/) (2018)
- [Efficient Modeling of Latent Information in Supervised Learning using Gaussian Processes](https://mlsanity.com/paper/1705.09862/) (2017)
- [The Gaussian Process Autoregressive Regression Model (GPAR)](https://mlsanity.com/paper/1802.07182/) (2018)
- [Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures](https://mlsanity.com/paper/2202.09233/) (2022)
- [Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessment](https://mlsanity.com/paper/2007.14052/) (2020)
- [Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization](https://mlsanity.com/paper/2109.09261/) (2021)
- [A Fully Natural Gradient Scheme for Improving Inference of the Heterogeneous Multi-Output Gaussian Process Model](https://mlsanity.com/paper/1911.10225/) (2019)
- [Bayesian Alignments of Warped Multi-Output Gaussian Processes](https://mlsanity.com/paper/1710.02766/) (2017)
- [A conditional one-output likelihood formulation for multitask Gaussian processes](https://mlsanity.com/paper/2006.03495/) (2020)
- [Cluster-Specific Predictions with Multi-Task Gaussian Processes](https://mlsanity.com/paper/2011.07866/) (2020)

## Abstract (arXiv)

Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To maintain tractability, existing methods typically resort to restrictive assumptions, such as employing low-rank or sum-of-separable kernels, which can limit expressiveness. We propose the Transformed Latent Variable MOGP (T-LVMOGP), a novel framework that scales MOGPs to a massive number of outputs while preserving the capacity to capture meaningful inter-output dependencies. T-LVMOGP constructs a flexible multi-output deep kernel by mapping inputs and output-specific latent variables into an embedding space using a Lipschitz-regularised neural network. Combined with stochastic variational inference, our model effectively scales to high-dimensional output settings. Across diverse benchmarks, including climate modelling with over 10,000 outputs and zero-inflated spatial transcriptomics data, T-LVMOGP outperforms baselines in both predictive accuracy and computational efficiency.